Modelling the Impact of Data Anomalies on Tourism Demand Forecasts

Master’s Final Work

1 Exploratory Data Analysis

1.1 Overnight Stays per Region from 2000 to 2022

# Import excel file and create tibble "tourism" with all data
tourism <- read_excel("C:\\Users\\Rosan\\OneDrive - ISEG\\# Masterthesis\\My MFW\\Summary_MonthlyOvernightStays_perRegion.xlsx",sheet = "2000") %>%
  pivot_longer(-Region, values_to = "Overnight_Stays") %>%
  mutate(Month = paste(name, "2000")) %>%
  select(-name)

for (i in 2001:2022){
  tourism_next_year <- read_excel("C:\\Users\\Rosan\\OneDrive - ISEG\\# Masterthesis\\My MFW\\Summary_MonthlyOvernightStays_perRegion.xlsx",sheet = as.character(i)) %>%
    pivot_longer(-Region, values_to = "Overnight_Stays") %>%
    mutate(Month = paste(name, as.character(i))) %>%
    select(-name)
  tourism <- rbind(tourism, tourism_next_year)}

rm(tourism_next_year) # remove variable "tourism_next_year" from R environment

# Transform tibble "tourism" to tsibble
tourism <- tourism %>%
  mutate (Month = yearmonth(Month)) %>%
  as_tsibble(index = Month, key = Region) %>%
  filter(!is.na(Overnight_Stays)) %>%
  select(Month, Region, Overnight_Stays)

# Change Region Names to English
tourism["Region"][tourism["Region"] == "Açores"] <- "Azores"
tourism["Region"][tourism["Region"] == "A.M. Lisboa"] <- "Lisbon M.A."
tourism["Region"][tourism["Region"] == "Centro"] <- "Central"
tourism["Region"][tourism["Region"] == "Norte"] <- "North"

# Show tsibble
tourism %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Monthly Number of Overnight Stays per Region: 2000-2022</span>", format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2:3, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Monthly Number of Overnight Stays per Region: 2000-2022

Month	Region	Overnight_Stays
2000 Jan	Lisbon M.A.	384,891
2000 Feb	Lisbon M.A.	457,135
2000 Mar	Lisbon M.A.	638,385
2000 Apr	Lisbon M.A.	742,277
2000 May	Lisbon M.A.	759,297
2000 Jun	Lisbon M.A.	675,220
2000 Jul	Lisbon M.A.	773,085
2000 Aug	Lisbon M.A.	895,083
2000 Sep	Lisbon M.A.	795,462
2000 Oct	Lisbon M.A.	724,107
2000 Nov	Lisbon M.A.	536,210
2000 Dec	Lisbon M.A.	442,543
2001 Jan	Lisbon M.A.	419,156
2001 Feb	Lisbon M.A.	454,963
2001 Mar	Lisbon M.A.	657,731
2001 Apr	Lisbon M.A.	753,864
2001 May	Lisbon M.A.	738,898
2001 Jun	Lisbon M.A.	688,409
2001 Jul	Lisbon M.A.	710,209
2001 Aug	Lisbon M.A.	868,552
2001 Sep	Lisbon M.A.	746,060
2001 Oct	Lisbon M.A.	703,350
2001 Nov	Lisbon M.A.	489,092
2001 Dec	Lisbon M.A.	377,295
2002 Jan	Lisbon M.A.	373,756
2002 Feb	Lisbon M.A.	421,368
2002 Mar	Lisbon M.A.	633,290
2002 Apr	Lisbon M.A.	651,973
2002 May	Lisbon M.A.	747,055
2002 Jun	Lisbon M.A.	654,052
2002 Jul	Lisbon M.A.	715,038
2002 Aug	Lisbon M.A.	980,033
2002 Sep	Lisbon M.A.	805,345
2002 Oct	Lisbon M.A.	693,341
2002 Nov	Lisbon M.A.	483,156
2002 Dec	Lisbon M.A.	389,760
2003 Jan	Lisbon M.A.	329,772
2003 Feb	Lisbon M.A.	356,674
2003 Mar	Lisbon M.A.	487,299
2003 Apr	Lisbon M.A.	594,631
2003 May	Lisbon M.A.	623,255
2003 Jun	Lisbon M.A.	561,125
2003 Jul	Lisbon M.A.	643,765
2003 Aug	Lisbon M.A.	778,908
2003 Sep	Lisbon M.A.	659,019
2003 Oct	Lisbon M.A.	609,750
2003 Nov	Lisbon M.A.	407,759
2003 Dec	Lisbon M.A.	372,749
2004 Jan	Lisbon M.A.	333,053
2004 Feb	Lisbon M.A.	377,134
2004 Mar	Lisbon M.A.	502,854
2004 Apr	Lisbon M.A.	629,711
2004 May	Lisbon M.A.	684,854
2004 Jun	Lisbon M.A.	716,698
2004 Jul	Lisbon M.A.	671,102
2004 Aug	Lisbon M.A.	823,916
2004 Sep	Lisbon M.A.	722,876
2004 Oct	Lisbon M.A.	657,981
2004 Nov	Lisbon M.A.	444,449
2004 Dec	Lisbon M.A.	430,155
2005 Jan	Lisbon M.A.	361,900
2005 Feb	Lisbon M.A.	379,500
2005 Mar	Lisbon M.A.	612,800
2005 Apr	Lisbon M.A.	602,300
2005 May	Lisbon M.A.	704,700
2005 Jun	Lisbon M.A.	637,700
2005 Jul	Lisbon M.A.	696,700
2005 Aug	Lisbon M.A.	889,200
2005 Sep	Lisbon M.A.	741,700
2005 Oct	Lisbon M.A.	676,300
2005 Nov	Lisbon M.A.	487,500
2005 Dec	Lisbon M.A.	466,700
2006 Jan	Lisbon M.A.	405,700
2006 Feb	Lisbon M.A.	443,600
2006 Mar	Lisbon M.A.	594,500
2006 Apr	Lisbon M.A.	775,300
2006 May	Lisbon M.A.	783,500
2006 Jun	Lisbon M.A.	692,100
2006 Jul	Lisbon M.A.	756,100
2006 Aug	Lisbon M.A.	998,600
2006 Sep	Lisbon M.A.	825,300
2006 Oct	Lisbon M.A.	782,900
2006 Nov	Lisbon M.A.	564,600
2006 Dec	Lisbon M.A.	540,500
2007 Jan	Lisbon M.A.	455,460
2007 Feb	Lisbon M.A.	459,408
2007 Mar	Lisbon M.A.	654,552
2007 Apr	Lisbon M.A.	799,543
2007 May	Lisbon M.A.	805,746
2007 Jun	Lisbon M.A.	729,833
2007 Jul	Lisbon M.A.	846,060
2007 Aug	Lisbon M.A.	1,060,820
2007 Sep	Lisbon M.A.	883,812
2007 Oct	Lisbon M.A.	807,158
2007 Nov	Lisbon M.A.	637,232
2007 Dec	Lisbon M.A.	539,416
2008 Jan	Lisbon M.A.	464,119
2008 Feb	Lisbon M.A.	521,684
2008 Mar	Lisbon M.A.	724,447
2008 Apr	Lisbon M.A.	743,063
2008 May	Lisbon M.A.	862,483
2008 Jun	Lisbon M.A.	713,066
2008 Jul	Lisbon M.A.	831,560
2008 Aug	Lisbon M.A.	972,507
2008 Sep	Lisbon M.A.	851,965
2008 Oct	Lisbon M.A.	773,337
2008 Nov	Lisbon M.A.	509,611
2008 Dec	Lisbon M.A.	442,563
2009 Jan	Lisbon M.A.	407,589
2009 Feb	Lisbon M.A.	428,634
2009 Mar	Lisbon M.A.	574,330
2009 Apr	Lisbon M.A.	739,842
2009 May	Lisbon M.A.	748,305
2009 Jun	Lisbon M.A.	667,653
2009 Jul	Lisbon M.A.	788,034
2009 Aug	Lisbon M.A.	961,944
2009 Sep	Lisbon M.A.	829,387
2009 Oct	Lisbon M.A.	752,140
2009 Nov	Lisbon M.A.	524,380
2009 Dec	Lisbon M.A.	483,699
2010 Jan	Lisbon M.A.	432,339
2010 Feb	Lisbon M.A.	466,948
2010 Mar	Lisbon M.A.	625,511
2010 Apr	Lisbon M.A.	725,879
2010 May	Lisbon M.A.	803,988
2010 Jun	Lisbon M.A.	723,308
2010 Jul	Lisbon M.A.	898,946
2010 Aug	Lisbon M.A.	1,087,091
2010 Sep	Lisbon M.A.	909,176
2010 Oct	Lisbon M.A.	866,756
2010 Nov	Lisbon M.A.	548,480
2010 Dec	Lisbon M.A.	532,001
2011 Jan	Lisbon M.A.	444,265
2011 Feb	Lisbon M.A.	469,297
2011 Mar	Lisbon M.A.	638,588
2011 Apr	Lisbon M.A.	828,257
2011 May	Lisbon M.A.	831,034
2011 Jun	Lisbon M.A.	867,081
2011 Jul	Lisbon M.A.	973,814
2011 Aug	Lisbon M.A.	1,152,487
2011 Sep	Lisbon M.A.	930,987
2011 Oct	Lisbon M.A.	868,872
2011 Nov	Lisbon M.A.	529,295
2011 Dec	Lisbon M.A.	493,455
2012 Jan	Lisbon M.A.	458,819
2012 Feb	Lisbon M.A.	471,861
2012 Mar	Lisbon M.A.	661,018
2012 Apr	Lisbon M.A.	849,417
2012 May	Lisbon M.A.	900,442
2012 Jun	Lisbon M.A.	874,725
2012 Jul	Lisbon M.A.	1,020,011
2012 Aug	Lisbon M.A.	1,187,629
2012 Sep	Lisbon M.A.	1,004,037
2012 Oct	Lisbon M.A.	902,410
2012 Nov	Lisbon M.A.	605,833
2012 Dec	Lisbon M.A.	503,651
2013 Jan	Lisbon M.A.	463,293
2013 Feb	Lisbon M.A.	507,082
2013 Mar	Lisbon M.A.	753,725
2013 Apr	Lisbon M.A.	830,420
2013 May	Lisbon M.A.	1,031,226
2013 Jun	Lisbon M.A.	983,419
2013 Jul	Lisbon M.A.	1,114,934
2013 Aug	Lisbon M.A.	1,313,606
2013 Sep	Lisbon M.A.	1,105,515
2013 Oct	Lisbon M.A.	1,023,526
2013 Nov	Lisbon M.A.	675,552
2013 Dec	Lisbon M.A.	584,407
2014 Jan	Lisbon M.A.	542,320
2014 Feb	Lisbon M.A.	567,855
2014 Mar	Lisbon M.A.	832,494
2014 Apr	Lisbon M.A.	1,089,636
2014 May	Lisbon M.A.	1,214,956
2014 Jun	Lisbon M.A.	1,120,513
2014 Jul	Lisbon M.A.	1,329,630
2014 Aug	Lisbon M.A.	1,537,060
2014 Sep	Lisbon M.A.	1,312,659
2014 Oct	Lisbon M.A.	1,216,156
2014 Nov	Lisbon M.A.	811,841
2014 Dec	Lisbon M.A.	704,302
2015 Jan	Lisbon M.A.	700,410
2015 Feb	Lisbon M.A.	710,730
2015 Mar	Lisbon M.A.	962,993
2015 Apr	Lisbon M.A.	1,177,605
2015 May	Lisbon M.A.	1,321,588
2015 Jun	Lisbon M.A.	1,253,701
2015 Jul	Lisbon M.A.	1,415,970
2015 Aug	Lisbon M.A.	1,610,307
2015 Sep	Lisbon M.A.	1,405,167
2015 Oct	Lisbon M.A.	1,295,271
2015 Nov	Lisbon M.A.	850,486
2015 Dec	Lisbon M.A.	764,431
2016 Jan	Lisbon M.A.	699,920
2016 Feb	Lisbon M.A.	786,306
2016 Mar	Lisbon M.A.	1,109,978
2016 Apr	Lisbon M.A.	1,175,212
2016 May	Lisbon M.A.	1,406,835
2016 Jun	Lisbon M.A.	1,379,594
2016 Jul	Lisbon M.A.	1,587,366
2016 Aug	Lisbon M.A.	1,772,090
2016 Sep	Lisbon M.A.	1,517,421
2016 Oct	Lisbon M.A.	1,461,023
2016 Nov	Lisbon M.A.	1,026,784
2016 Dec	Lisbon M.A.	877,817
2017 Jan	Lisbon M.A.	878,774
2017 Feb	Lisbon M.A.	920,076
2017 Mar	Lisbon M.A.	1,221,321
2017 Apr	Lisbon M.A.	1,506,142
2017 May	Lisbon M.A.	1,533,018
2017 Jun	Lisbon M.A.	1,572,130
2017 Jul	Lisbon M.A.	1,724,545
2017 Aug	Lisbon M.A.	1,898,121
2017 Sep	Lisbon M.A.	1,656,960
2017 Oct	Lisbon M.A.	1,603,352
2017 Nov	Lisbon M.A.	1,170,082
2017 Dec	Lisbon M.A.	1,010,685
2018 Jan	Lisbon M.A.	945,235
2018 Feb	Lisbon M.A.	1,026,053
2018 Mar	Lisbon M.A.	1,382,399
2018 Apr	Lisbon M.A.	1,491,302
2018 May	Lisbon M.A.	1,640,458
2018 Jun	Lisbon M.A.	1,610,548
2018 Jul	Lisbon M.A.	1,799,402
2018 Aug	Lisbon M.A.	1,966,456
2018 Sep	Lisbon M.A.	1,721,805
2018 Oct	Lisbon M.A.	1,656,830
2018 Nov	Lisbon M.A.	1,220,549
2018 Dec	Lisbon M.A.	1,055,938
2019 Jan	Lisbon M.A.	999,656
2019 Feb	Lisbon M.A.	1,057,221
2019 Mar	Lisbon M.A.	1,443,330
2019 Apr	Lisbon M.A.	1,636,193
2019 May	Lisbon M.A.	1,773,863
2019 Jun	Lisbon M.A.	1,750,628
2019 Jul	Lisbon M.A.	1,874,219
2019 Aug	Lisbon M.A.	2,057,193
2019 Sep	Lisbon M.A.	1,821,478
2019 Oct	Lisbon M.A.	1,728,503
2019 Nov	Lisbon M.A.	1,329,017
2019 Dec	Lisbon M.A.	1,167,761
2020 Jan	Lisbon M.A.	1,082,826
2020 Feb	Lisbon M.A.	1,113,308
2020 Mar	Lisbon M.A.	510,510
2020 Apr	Lisbon M.A.	40,771
2020 May	Lisbon M.A.	66,383
2020 Jun	Lisbon M.A.	138,646
2020 Jul	Lisbon M.A.	319,160
2020 Aug	Lisbon M.A.	628,027
2020 Sep	Lisbon M.A.	503,158
2020 Oct	Lisbon M.A.	396,225
2020 Nov	Lisbon M.A.	215,790
2020 Dec	Lisbon M.A.	239,550
2021 Jan	Lisbon M.A.	186,812
2021 Feb	Lisbon M.A.	123,161
2021 Mar	Lisbon M.A.	153,987
2021 Apr	Lisbon M.A.	222,261
2021 May	Lisbon M.A.	397,428
2021 Jun	Lisbon M.A.	551,385
2021 Jul	Lisbon M.A.	651,841
2021 Aug	Lisbon M.A.	1,166,724
2021 Sep	Lisbon M.A.	1,056,749
2021 Oct	Lisbon M.A.	1,330,915
2021 Nov	Lisbon M.A.	1,111,639
2021 Dec	Lisbon M.A.	778,611
2022 Jan	Lisbon M.A.	547,654
2022 Feb	Lisbon M.A.	854,792
2022 Mar	Lisbon M.A.	1,208,967
2022 Apr	Lisbon M.A.	1,600,523
2022 May	Lisbon M.A.	1,712,746
2022 Jun	Lisbon M.A.	1,753,231
2000 Jan	Azores	21,327
2000 Feb	Azores	24,099
2000 Mar	Azores	34,106
2000 Apr	Azores	50,675
2000 May	Azores	49,880
2000 Jun	Azores	56,708
2000 Jul	Azores	74,256
2000 Aug	Azores	90,849
2000 Sep	Azores	64,818
2000 Oct	Azores	50,612
2000 Nov	Azores	38,772
2000 Dec	Azores	24,116
2001 Jan	Azores	29,285
2001 Feb	Azores	32,045
2001 Mar	Azores	47,743
2001 Apr	Azores	59,041
2001 May	Azores	60,851
2001 Jun	Azores	74,542
2001 Jul	Azores	96,552
2001 Aug	Azores	103,607
2001 Sep	Azores	78,670
2001 Oct	Azores	60,817
2001 Nov	Azores	43,279
2001 Dec	Azores	29,861
2002 Jan	Azores	35,113
2002 Feb	Azores	38,989
2002 Mar	Azores	55,274
2002 Apr	Azores	64,401
2002 May	Azores	64,421
2002 Jun	Azores	77,598
2002 Jul	Azores	106,098
2002 Aug	Azores	121,990
2002 Sep	Azores	82,126
2002 Oct	Azores	58,228
2002 Nov	Azores	43,212
2002 Dec	Azores	30,485
2003 Jan	Azores	33,437
2003 Feb	Azores	36,732
2003 Mar	Azores	46,228
2003 Apr	Azores	59,990
2003 May	Azores	71,206
2003 Jun	Azores	83,418
2003 Jul	Azores	98,617
2003 Aug	Azores	126,684
2003 Sep	Azores	82,629
2003 Oct	Azores	74,000
2003 Nov	Azores	53,857
2003 Dec	Azores	37,230
2004 Jan	Azores	38,838
2004 Feb	Azores	47,317
2004 Mar	Azores	65,079
2004 Apr	Azores	78,603
2004 May	Azores	81,398
2004 Jun	Azores	85,119
2004 Jul	Azores	120,984
2004 Aug	Azores	157,841
2004 Sep	Azores	106,109
2004 Oct	Azores	79,977
2004 Nov	Azores	61,201
2004 Dec	Azores	42,618
2005 Jan	Azores	45,800
2005 Feb	Azores	51,200
2005 Mar	Azores	80,100
2005 Apr	Azores	90,900
2005 May	Azores	101,000
2005 Jun	Azores	115,900
2005 Jul	Azores	144,100
2005 Aug	Azores	177,400
2005 Sep	Azores	128,800
2005 Oct	Azores	105,100
2005 Nov	Azores	59,000
2005 Dec	Azores	36,100
2006 Jan	Azores	35,900
2006 Feb	Azores	39,900
2006 Mar	Azores	71,000
2006 Apr	Azores	105,200
2006 May	Azores	116,500
2006 Jun	Azores	123,800
2006 Jul	Azores	155,200
2006 Aug	Azores	187,900
2006 Sep	Azores	134,100
2006 Oct	Azores	110,700
2006 Nov	Azores	62,200
2006 Dec	Azores	37,700
2007 Jan	Azores	45,548
2007 Feb	Azores	46,315
2007 Mar	Azores	75,386
2007 Apr	Azores	99,231
2007 May	Azores	114,985
2007 Jun	Azores	128,941
2007 Jul	Azores	158,894
2007 Aug	Azores	189,532
2007 Sep	Azores	131,773
2007 Oct	Azores	105,907
2007 Nov	Azores	56,342
2007 Dec	Azores	31,521
2008 Jan	Azores	33,849
2008 Feb	Azores	40,219
2008 Mar	Azores	72,746
2008 Apr	Azores	93,051
2008 May	Azores	117,191
2008 Jun	Azores	123,353
2008 Jul	Azores	158,488
2008 Aug	Azores	184,039
2008 Sep	Azores	124,291
2008 Oct	Azores	88,123
2008 Nov	Azores	59,011
2008 Dec	Azores	33,152
2009 Jan	Azores	38,302
2009 Feb	Azores	40,333
2009 Mar	Azores	59,114
2009 Apr	Azores	91,406
2009 May	Azores	107,465
2009 Jun	Azores	116,552
2009 Jul	Azores	136,349
2009 Aug	Azores	162,239
2009 Sep	Azores	106,187
2009 Oct	Azores	72,410
2009 Nov	Azores	45,536
2009 Dec	Azores	28,911
2010 Jan	Azores	28,697
2010 Feb	Azores	38,804
2010 Mar	Azores	58,925
2010 Apr	Azores	77,461
2010 May	Azores	109,482
2010 Jun	Azores	117,156
2010 Jul	Azores	148,637
2010 Aug	Azores	175,813
2010 Sep	Azores	125,674
2010 Oct	Azores	82,915
2010 Nov	Azores	44,803
2010 Dec	Azores	26,664
2011 Jan	Azores	28,216
2011 Feb	Azores	35,800
2011 Mar	Azores	57,953
2011 Apr	Azores	76,975
2011 May	Azores	101,368
2011 Jun	Azores	122,674
2011 Jul	Azores	157,725
2011 Aug	Azores	178,385
2011 Sep	Azores	120,251
2011 Oct	Azores	83,264
2011 Nov	Azores	42,878
2011 Dec	Azores	28,016
2012 Jan	Azores	28,213
2012 Feb	Azores	37,194
2012 Mar	Azores	50,978
2012 Apr	Azores	75,473
2012 May	Azores	90,736
2012 Jun	Azores	106,078
2012 Jul	Azores	145,844
2012 Aug	Azores	175,723
2012 Sep	Azores	113,907
2012 Oct	Azores	67,904
2012 Nov	Azores	34,871
2012 Dec	Azores	27,819
2013 Jan	Azores	26,465
2013 Feb	Azores	34,481
2013 Mar	Azores	53,958
2013 Apr	Azores	77,672
2013 May	Azores	104,433
2013 Jun	Azores	124,777
2013 Jul	Azores	180,119
2013 Aug	Azores	198,510
2013 Sep	Azores	139,957
2013 Oct	Azores	92,969
2013 Nov	Azores	41,392
2013 Dec	Azores	28,793
2014 Jan	Azores	26,769
2014 Feb	Azores	33,527
2014 Mar	Azores	52,477
2014 Apr	Azores	85,274
2014 May	Azores	101,828
2014 Jun	Azores	130,463
2014 Jul	Azores	173,734
2014 Aug	Azores	199,640
2014 Sep	Azores	137,414
2014 Oct	Azores	91,682
2014 Nov	Azores	51,758
2014 Dec	Azores	35,977
2015 Jan	Azores	35,006
2015 Feb	Azores	41,000
2015 Mar	Azores	62,207
2015 Apr	Azores	102,882
2015 May	Azores	129,472
2015 Jun	Azores	157,794
2015 Jul	Azores	196,209
2015 Aug	Azores	216,360
2015 Sep	Azores	162,468
2015 Oct	Azores	112,232
2015 Nov	Azores	64,059
2015 Dec	Azores	54,753
2016 Jan	Azores	57,951
2016 Feb	Azores	65,527
2016 Mar	Azores	101,992
2016 Apr	Azores	123,731
2016 May	Azores	155,191
2016 Jun	Azores	181,089
2016 Jul	Azores	220,245
2016 Aug	Azores	238,078
2016 Sep	Azores	192,539
2016 Oct	Azores	144,051
2016 Nov	Azores	81,004
2016 Dec	Azores	56,123
2017 Jan	Azores	61,471
2017 Feb	Azores	74,415
2017 Mar	Azores	112,264
2017 Apr	Azores	161,877
2017 May	Azores	185,146
2017 Jun	Azores	212,386
2017 Jul	Azores	256,235
2017 Aug	Azores	274,097
2017 Sep	Azores	216,866
2017 Oct	Azores	155,452
2017 Nov	Azores	82,903
2017 Dec	Azores	69,239
2018 Jan	Azores	76,002
2018 Feb	Azores	89,714
2018 Mar	Azores	135,791
2018 Apr	Azores	172,027
2018 May	Azores	207,739
2018 Jun	Azores	228,625
2018 Jul	Azores	295,788
2018 Aug	Azores	319,871
2018 Sep	Azores	250,951
2018 Oct	Azores	179,615
2018 Nov	Azores	100,406
2018 Dec	Azores	69,297
2019 Jan	Azores	80,699
2019 Feb	Azores	91,680
2019 Mar	Azores	136,645
2019 Apr	Azores	192,939
2019 May	Azores	221,573
2019 Jun	Azores	255,410
2019 Jul	Azores	311,246
2019 Aug	Azores	338,222
2019 Sep	Azores	258,710
2019 Oct	Azores	190,742
2019 Nov	Azores	111,772
2019 Dec	Azores	88,167
2020 Jan	Azores	87,648
2020 Feb	Azores	108,770
2020 Mar	Azores	59,488
2020 Apr	Azores	453
2020 May	Azores	773
2020 Jun	Azores	9,231
2020 Jul	Azores	48,595
2020 Aug	Azores	111,265
2020 Sep	Azores	86,913
2020 Oct	Azores	72,191
2020 Nov	Azores	39,878
2020 Dec	Azores	29,171
2021 Jan	Azores	22,881
2021 Feb	Azores	24,040
2021 Mar	Azores	41,317
2021 Apr	Azores	54,953
2021 May	Azores	76,205
2021 Jun	Azores	136,234
2021 Jul	Azores	211,826
2021 Aug	Azores	291,580
2021 Sep	Azores	232,687
2021 Oct	Azores	187,197
2021 Nov	Azores	108,102
2021 Dec	Azores	69,468
2022 Jan	Azores	58,170
2022 Feb	Azores	82,080
2022 Mar	Azores	130,699
2022 Apr	Azores	184,334
2022 May	Azores	227,436
2022 Jun	Azores	270,905
2000 Jan	Alentejo	34,281
2000 Feb	Alentejo	42,287
2000 Mar	Alentejo	67,520
2000 Apr	Alentejo	85,884
2000 May	Alentejo	65,339
2000 Jun	Alentejo	71,263
2000 Jul	Alentejo	93,501
2000 Aug	Alentejo	132,360
2000 Sep	Alentejo	87,037
2000 Oct	Alentejo	64,620
2000 Nov	Alentejo	51,168
2000 Dec	Alentejo	49,890
2001 Jan	Alentejo	41,628
2001 Feb	Alentejo	52,517
2001 Mar	Alentejo	67,176
2001 Apr	Alentejo	91,294
2001 May	Alentejo	73,966
2001 Jun	Alentejo	83,290
2001 Jul	Alentejo	105,089
2001 Aug	Alentejo	136,296
2001 Sep	Alentejo	86,028
2001 Oct	Alentejo	66,974
2001 Nov	Alentejo	51,649
2001 Dec	Alentejo	41,657
2002 Jan	Alentejo	39,474
2002 Feb	Alentejo	55,105
2002 Mar	Alentejo	83,450
2002 Apr	Alentejo	72,810
2002 May	Alentejo	76,625
2002 Jun	Alentejo	83,525
2002 Jul	Alentejo	102,151
2002 Aug	Alentejo	139,476
2002 Sep	Alentejo	89,516
2002 Oct	Alentejo	63,692
2002 Nov	Alentejo	55,950
2002 Dec	Alentejo	42,334
2003 Jan	Alentejo	42,969
2003 Feb	Alentejo	47,839
2003 Mar	Alentejo	66,493
2003 Apr	Alentejo	88,707
2003 May	Alentejo	91,450
2003 Jun	Alentejo	89,474
2003 Jul	Alentejo	103,914
2003 Aug	Alentejo	138,159
2003 Sep	Alentejo	93,305
2003 Oct	Alentejo	72,716
2003 Nov	Alentejo	61,119
2003 Dec	Alentejo	51,236
2004 Jan	Alentejo	45,473
2004 Feb	Alentejo	63,350
2004 Mar	Alentejo	67,470
2004 Apr	Alentejo	89,156
2004 May	Alentejo	89,156
2004 Jun	Alentejo	90,271
2004 Jul	Alentejo	102,341
2004 Aug	Alentejo	155,529
2004 Sep	Alentejo	99,960
2004 Oct	Alentejo	83,283
2004 Nov	Alentejo	55,812
2004 Dec	Alentejo	51,215
2005 Jan	Alentejo	45,800
2005 Feb	Alentejo	51,200
2005 Mar	Alentejo	71,500
2005 Apr	Alentejo	75,700
2005 May	Alentejo	88,100
2005 Jun	Alentejo	80,200
2005 Jul	Alentejo	90,700
2005 Aug	Alentejo	147,300
2005 Sep	Alentejo	92,900
2005 Oct	Alentejo	73,000
2005 Nov	Alentejo	64,700
2005 Dec	Alentejo	58,100
2006 Jan	Alentejo	46,800
2006 Feb	Alentejo	56,500
2006 Mar	Alentejo	61,600
2006 Apr	Alentejo	93,100
2006 May	Alentejo	82,700
2006 Jun	Alentejo	79,100
2006 Jul	Alentejo	99,000
2006 Aug	Alentejo	136,600
2006 Sep	Alentejo	98,800
2006 Oct	Alentejo	83,500
2006 Nov	Alentejo	68,300
2006 Dec	Alentejo	72,600
2007 Jan	Alentejo	51,510
2007 Feb	Alentejo	60,557
2007 Mar	Alentejo	78,912
2007 Apr	Alentejo	99,059
2007 May	Alentejo	89,326
2007 Jun	Alentejo	96,349
2007 Jul	Alentejo	113,127
2007 Aug	Alentejo	164,837
2007 Sep	Alentejo	109,348
2007 Oct	Alentejo	89,006
2007 Nov	Alentejo	77,312
2007 Dec	Alentejo	69,226
2008 Jan	Alentejo	51,548
2008 Feb	Alentejo	63,947
2008 Mar	Alentejo	88,989
2008 Apr	Alentejo	84,580
2008 May	Alentejo	101,576
2008 Jun	Alentejo	91,173
2008 Jul	Alentejo	107,299
2008 Aug	Alentejo	153,743
2008 Sep	Alentejo	117,477
2008 Oct	Alentejo	94,237
2008 Nov	Alentejo	70,628
2008 Dec	Alentejo	60,476
2009 Jan	Alentejo	50,256
2009 Feb	Alentejo	63,694
2009 Mar	Alentejo	67,975
2009 Apr	Alentejo	96,647
2009 May	Alentejo	97,936
2009 Jun	Alentejo	107,295
2009 Jul	Alentejo	114,085
2009 Aug	Alentejo	176,426
2009 Sep	Alentejo	109,573
2009 Oct	Alentejo	92,353
2009 Nov	Alentejo	68,602
2009 Dec	Alentejo	59,473
2010 Jan	Alentejo	53,653
2010 Feb	Alentejo	62,257
2010 Mar	Alentejo	77,588
2010 Apr	Alentejo	99,982
2010 May	Alentejo	101,387
2010 Jun	Alentejo	108,611
2010 Jul	Alentejo	126,498
2010 Aug	Alentejo	178,380
2010 Sep	Alentejo	127,822
2010 Oct	Alentejo	104,174
2010 Nov	Alentejo	69,271
2010 Dec	Alentejo	62,935
2011 Jan	Alentejo	60,457
2011 Feb	Alentejo	67,260
2011 Mar	Alentejo	83,464
2011 Apr	Alentejo	102,958
2011 May	Alentejo	101,223
2011 Jun	Alentejo	120,148
2011 Jul	Alentejo	136,999
2011 Aug	Alentejo	212,668
2011 Sep	Alentejo	129,606
2011 Oct	Alentejo	101,185
2011 Nov	Alentejo	62,121
2011 Dec	Alentejo	65,563
2012 Jan	Alentejo	49,716
2012 Feb	Alentejo	58,638
2012 Mar	Alentejo	72,210
2012 Apr	Alentejo	87,406
2012 May	Alentejo	96,946
2012 Jun	Alentejo	115,885
2012 Jul	Alentejo	139,695
2012 Aug	Alentejo	194,368
2012 Sep	Alentejo	127,610
2012 Oct	Alentejo	89,649
2012 Nov	Alentejo	58,900
2012 Dec	Alentejo	51,122
2013 Jan	Alentejo	50,313
2013 Feb	Alentejo	58,615
2013 Mar	Alentejo	92,426
2013 Apr	Alentejo	100,996
2013 May	Alentejo	123,431
2013 Jun	Alentejo	143,946
2013 Jul	Alentejo	171,016
2013 Aug	Alentejo	252,423
2013 Sep	Alentejo	158,839
2013 Oct	Alentejo	109,956
2013 Nov	Alentejo	82,040
2013 Dec	Alentejo	72,692
2014 Jan	Alentejo	56,872
2014 Feb	Alentejo	64,346
2014 Mar	Alentejo	102,852
2014 Apr	Alentejo	151,151
2014 May	Alentejo	148,593
2014 Jun	Alentejo	154,231
2014 Jul	Alentejo	194,227
2014 Aug	Alentejo	303,902
2014 Sep	Alentejo	186,247
2014 Oct	Alentejo	133,884
2014 Nov	Alentejo	86,161
2014 Dec	Alentejo	81,830
2015 Jan	Alentejo	68,436
2015 Feb	Alentejo	84,417
2015 Mar	Alentejo	116,291
2015 Apr	Alentejo	145,183
2015 May	Alentejo	172,016
2015 Jun	Alentejo	182,765
2015 Jul	Alentejo	238,708
2015 Aug	Alentejo	358,044
2015 Sep	Alentejo	216,474
2015 Oct	Alentejo	148,376
2015 Nov	Alentejo	99,794
2015 Dec	Alentejo	93,804
2016 Jan	Alentejo	74,572
2016 Feb	Alentejo	97,522
2016 Mar	Alentejo	144,216
2016 Apr	Alentejo	153,386
2016 May	Alentejo	168,235
2016 Jun	Alentejo	215,800
2016 Jul	Alentejo	271,212
2016 Aug	Alentejo	380,776
2016 Sep	Alentejo	249,098
2016 Oct	Alentejo	175,862
2016 Nov	Alentejo	102,775
2016 Dec	Alentejo	100,859
2017 Jan	Alentejo	83,249
2017 Feb	Alentejo	105,210
2017 Mar	Alentejo	121,167
2017 Apr	Alentejo	217,906
2017 May	Alentejo	196,622
2017 Jun	Alentejo	248,582
2017 Jul	Alentejo	323,496
2017 Aug	Alentejo	431,571
2017 Sep	Alentejo	287,242
2017 Oct	Alentejo	212,357
2017 Nov	Alentejo	127,745
2017 Dec	Alentejo	132,238
2018 Jan	Alentejo	95,453
2018 Feb	Alentejo	120,303
2018 Mar	Alentejo	162,886
2018 Apr	Alentejo	187,186
2018 May	Alentejo	239,851
2018 Jun	Alentejo	264,588
2018 Jul	Alentejo	339,564
2018 Aug	Alentejo	446,375
2018 Sep	Alentejo	304,516
2018 Oct	Alentejo	230,827
2018 Nov	Alentejo	149,080
2018 Dec	Alentejo	135,316
2019 Jan	Alentejo	114,710
2019 Feb	Alentejo	122,635
2019 Mar	Alentejo	172,412
2019 Apr	Alentejo	241,790
2019 May	Alentejo	259,714
2019 Jun	Alentejo	306,048
2019 Jul	Alentejo	360,566
2019 Aug	Alentejo	484,403
2019 Sep	Alentejo	327,937
2019 Oct	Alentejo	238,677
2019 Nov	Alentejo	171,296
2019 Dec	Alentejo	138,642
2020 Jan	Alentejo	126,349
2020 Feb	Alentejo	167,411
2020 Mar	Alentejo	70,530
2020 Apr	Alentejo	13,892
2020 May	Alentejo	38,343
2020 Jun	Alentejo	159,738
2020 Jul	Alentejo	272,786
2020 Aug	Alentejo	407,020
2020 Sep	Alentejo	258,651
2020 Oct	Alentejo	167,448
2020 Nov	Alentejo	73,734
2020 Dec	Alentejo	73,353
2021 Jan	Alentejo	48,435
2021 Feb	Alentejo	40,443
2021 Mar	Alentejo	60,251
2021 Apr	Alentejo	85,179
2021 May	Alentejo	169,690
2021 Jun	Alentejo	254,243
2021 Jul	Alentejo	329,058
2021 Aug	Alentejo	461,844
2021 Sep	Alentejo	308,273
2021 Oct	Alentejo	250,949
2021 Nov	Alentejo	156,624
2021 Dec	Alentejo	115,100
2022 Jan	Alentejo	96,107
2022 Feb	Alentejo	141,508
2022 Mar	Alentejo	167,854
2022 Apr	Alentejo	248,959
2022 May	Alentejo	258,413
2022 Jun	Alentejo	300,520
2000 Jan	Algarve	482,298
2000 Feb	Algarve	668,668
2000 Mar	Algarve	940,769
2000 Apr	Algarve	1,204,711
2000 May	Algarve	1,370,289
2000 Jun	Algarve	1,635,456
2000 Jul	Algarve	1,994,355
2000 Aug	Algarve	2,155,769
2000 Sep	Algarve	1,730,037
2000 Oct	Algarve	1,308,086
2000 Nov	Algarve	632,830
2000 Dec	Algarve	448,204
2001 Jan	Algarve	495,966
2001 Feb	Algarve	731,372
2001 Mar	Algarve	899,198
2001 Apr	Algarve	1,155,935
2001 May	Algarve	1,282,699
2001 Jun	Algarve	1,586,267
2001 Jul	Algarve	1,936,420
2001 Aug	Algarve	2,067,675
2001 Sep	Algarve	1,624,419
2001 Oct	Algarve	1,164,255
2001 Nov	Algarve	560,068
2001 Dec	Algarve	395,918
2002 Jan	Algarve	461,045
2002 Feb	Algarve	699,389
2002 Mar	Algarve	1,047,155
2002 Apr	Algarve	994,476
2002 May	Algarve	1,312,043
2002 Jun	Algarve	1,629,825
2002 Jul	Algarve	2,003,531
2002 Aug	Algarve	2,326,464
2002 Sep	Algarve	1,695,076
2002 Oct	Algarve	1,141,575
2002 Nov	Algarve	581,628
2002 Dec	Algarve	402,096
2003 Jan	Algarve	467,884
2003 Feb	Algarve	686,326
2003 Mar	Algarve	905,474
2003 Apr	Algarve	1,124,760
2003 May	Algarve	1,351,136
2003 Jun	Algarve	1,651,162
2003 Jul	Algarve	1,965,914
2003 Aug	Algarve	2,309,345
2003 Sep	Algarve	1,558,200
2003 Oct	Algarve	1,087,039
2003 Nov	Algarve	532,301
2003 Dec	Algarve	398,038
2004 Jan	Algarve	464,629
2004 Feb	Algarve	675,615
2004 Mar	Algarve	836,069
2004 Apr	Algarve	1,049,221
2004 May	Algarve	1,162,483
2004 Jun	Algarve	1,408,698
2004 Jul	Algarve	1,782,330
2004 Aug	Algarve	2,262,316
2004 Sep	Algarve	1,551,469
2004 Oct	Algarve	1,118,943
2004 Nov	Algarve	506,085
2004 Dec	Algarve	435,015
2005 Jan	Algarve	471,700
2005 Feb	Algarve	667,300
2005 Mar	Algarve	901,300
2005 Apr	Algarve	919,100
2005 May	Algarve	1,307,000
2005 Jun	Algarve	1,535,200
2005 Jul	Algarve	1,921,300
2005 Aug	Algarve	2,345,800
2005 Sep	Algarve	1,630,200
2005 Oct	Algarve	1,150,200
2005 Nov	Algarve	539,700
2005 Dec	Algarve	425,300
2006 Jan	Algarve	471,700
2006 Feb	Algarve	631,400
2006 Mar	Algarve	800,700
2006 Apr	Algarve	1,164,700
2006 May	Algarve	1,238,200
2006 Jun	Algarve	1,563,700
2006 Jul	Algarve	2,037,800
2006 Aug	Algarve	2,419,500
2006 Sep	Algarve	1,672,600
2006 Oct	Algarve	1,136,000
2006 Nov	Algarve	547,200
2006 Dec	Algarve	480,100
2007 Jan	Algarve	492,114
2007 Feb	Algarve	641,596
2007 Mar	Algarve	908,698
2007 Apr	Algarve	1,173,146
2007 May	Algarve	1,340,818
2007 Jun	Algarve	1,627,451
2007 Jul	Algarve	2,115,385
2007 Aug	Algarve	2,439,108
2007 Sep	Algarve	1,741,610
2007 Oct	Algarve	1,185,860
2007 Nov	Algarve	563,182
2007 Dec	Algarve	475,416
2008 Jan	Algarve	470,877
2008 Feb	Algarve	674,063
2008 Mar	Algarve	991,973
2008 Apr	Algarve	946,986
2008 May	Algarve	1,381,549
2008 Jun	Algarve	1,558,966
2008 Jul	Algarve	2,028,623
2008 Aug	Algarve	2,436,162
2008 Sep	Algarve	1,693,992
2008 Oct	Algarve	1,140,194
2008 Nov	Algarve	530,826
2008 Dec	Algarve	410,953
2009 Jan	Algarve	411,615
2009 Feb	Algarve	557,401
2009 Mar	Algarve	710,502
2009 Apr	Algarve	1,017,779
2009 May	Algarve	1,138,068
2009 Jun	Algarve	1,489,130
2009 Jul	Algarve	1,891,157
2009 Aug	Algarve	2,315,586
2009 Sep	Algarve	1,539,886
2009 Oct	Algarve	1,010,273
2009 Nov	Algarve	475,789
2009 Dec	Algarve	370,417
2010 Jan	Algarve	366,296
2010 Feb	Algarve	533,056
2010 Mar	Algarve	742,227
2010 Apr	Algarve	902,745
2010 May	Algarve	1,107,303
2010 Jun	Algarve	1,464,695
2010 Jul	Algarve	2,050,478
2010 Aug	Algarve	2,468,924
2010 Sep	Algarve	1,696,356
2010 Oct	Algarve	1,104,659
2010 Nov	Algarve	445,221
2010 Dec	Algarve	365,490
2011 Jan	Algarve	357,209
2011 Feb	Algarve	503,831
2011 Mar	Algarve	761,343
2011 Apr	Algarve	1,177,115
2011 May	Algarve	1,169,516
2011 Jun	Algarve	1,576,730
2011 Jul	Algarve	2,208,160
2011 Aug	Algarve	2,572,404
2011 Sep	Algarve	1,731,056
2011 Oct	Algarve	1,161,751
2011 Nov	Algarve	427,550
2011 Dec	Algarve	333,201
2012 Jan	Algarve	359,355
2012 Feb	Algarve	531,709
2012 Mar	Algarve	751,024
2012 Apr	Algarve	1,017,976
2012 May	Algarve	1,194,673
2012 Jun	Algarve	1,678,327
2012 Jul	Algarve	2,296,474
2012 Aug	Algarve	2,622,801
2012 Sep	Algarve	1,829,252
2012 Oct	Algarve	1,244,751
2012 Nov	Algarve	453,958
2012 Dec	Algarve	346,474
2013 Jan	Algarve	369,969
2013 Feb	Algarve	520,055
2013 Mar	Algarve	840,024
2013 Apr	Algarve	986,191
2013 May	Algarve	1,382,234
2013 Jun	Algarve	1,814,108
2013 Jul	Algarve	2,387,304
2013 Aug	Algarve	2,764,686
2013 Sep	Algarve	1,943,037
2013 Oct	Algarve	1,291,360
2013 Nov	Algarve	455,695
2013 Dec	Algarve	358,062
2014 Jan	Algarve	377,387
2014 Feb	Algarve	543,470
2014 Mar	Algarve	749,773
2014 Apr	Algarve	1,337,145
2014 May	Algarve	1,538,342
2014 Jun	Algarve	1,994,167
2014 Jul	Algarve	2,529,246
2014 Aug	Algarve	3,069,865
2014 Sep	Algarve	2,089,656
2014 Oct	Algarve	1,477,481
2014 Nov	Algarve	502,473
2014 Dec	Algarve	382,543
2015 Jan	Algarve	381,607
2015 Feb	Algarve	544,777
2015 Mar	Algarve	827,071
2015 Apr	Algarve	1,242,844
2015 May	Algarve	1,654,526
2015 Jun	Algarve	2,079,484
2015 Jul	Algarve	2,688,710
2015 Aug	Algarve	3,108,357
2015 Sep	Algarve	2,196,681
2015 Oct	Algarve	1,553,142
2015 Nov	Algarve	552,778
2015 Dec	Algarve	426,419
2016 Jan	Algarve	443,150
2016 Feb	Algarve	664,278
2016 Mar	Algarve	1,089,392
2016 Apr	Algarve	1,335,308
2016 May	Algarve	1,828,292
2016 Jun	Algarve	2,288,337
2016 Jul	Algarve	2,848,570
2016 Aug	Algarve	3,204,047
2016 Sep	Algarve	2,378,618
2016 Oct	Algarve	1,793,822
2016 Nov	Algarve	653,514
2016 Dec	Algarve	478,510
2017 Jan	Algarve	495,629
2017 Feb	Algarve	704,532
2017 Mar	Algarve	1,015,421
2017 Apr	Algarve	1,765,170
2017 May	Algarve	1,970,072
2017 Jun	Algarve	2,417,100
2017 Jul	Algarve	2,968,641
2017 Aug	Algarve	3,295,406
2017 Sep	Algarve	2,470,298
2017 Oct	Algarve	1,911,961
2017 Nov	Algarve	680,373
2017 Dec	Algarve	512,548
2018 Jan	Algarve	503,908
2018 Feb	Algarve	731,090
2018 Mar	Algarve	1,151,455
2018 Apr	Algarve	1,575,078
2018 May	Algarve	2,003,996
2018 Jun	Algarve	2,381,154
2018 Jul	Algarve	2,981,643
2018 Aug	Algarve	3,371,918
2018 Sep	Algarve	2,499,368
2018 Oct	Algarve	1,956,693
2018 Nov	Algarve	732,141
2018 Dec	Algarve	554,803
2019 Jan	Algarve	548,686
2019 Feb	Algarve	739,981
2019 Mar	Algarve	1,078,918
2019 Apr	Algarve	1,795,494
2019 May	Algarve	1,990,529
2019 Jun	Algarve	2,425,834
2019 Jul	Algarve	2,988,668
2019 Aug	Algarve	3,439,271
2019 Sep	Algarve	2,573,527
2019 Oct	Algarve	1,930,852
2019 Nov	Algarve	785,875
2019 Dec	Algarve	602,860
2020 Jan	Algarve	560,368
2020 Feb	Algarve	844,247
2020 Mar	Algarve	513,360
2020 Apr	Algarve	25,614
2020 May	Algarve	40,932
2020 Jun	Algarve	330,393
2020 Jul	Algarve	1,035,732
2020 Aug	Algarve	2,090,569
2020 Sep	Algarve	1,418,185
2020 Oct	Algarve	696,087
2020 Nov	Algarve	181,873
2020 Dec	Algarve	153,351
2021 Jan	Algarve	105,336
2021 Feb	Algarve	66,194
2021 Mar	Algarve	84,413
2021 Apr	Algarve	138,661
2021 May	Algarve	502,057
2021 Jun	Algarve	1,182,009
2021 Jul	Algarve	1,551,789
2021 Aug	Algarve	2,762,537
2021 Sep	Algarve	1,869,194
2021 Oct	Algarve	1,584,764
2021 Nov	Algarve	651,051
2021 Dec	Algarve	376,031
2022 Jan	Algarve	344,634
2022 Feb	Algarve	590,122
2022 Mar	Algarve	873,841
2022 Apr	Algarve	1,629,377
2022 May	Algarve	1,867,744
2022 Jun	Algarve	2,230,207
2000 Jan	Central	97,748
2000 Feb	Central	112,210
2000 Mar	Central	141,973
2000 Apr	Central	173,166
2000 May	Central	173,781
2000 Jun	Central	167,906
2000 Jul	Central	211,569
2000 Aug	Central	296,264
2000 Sep	Central	213,978
2000 Oct	Central	162,932
2000 Nov	Central	131,786
2000 Dec	Central	116,821
2001 Jan	Central	97,835
2001 Feb	Central	117,057
2001 Mar	Central	138,851
2001 Apr	Central	164,615
2001 May	Central	168,582
2001 Jun	Central	171,690
2001 Jul	Central	200,343
2001 Aug	Central	287,122
2001 Sep	Central	211,241
2001 Oct	Central	163,283
2001 Nov	Central	125,344
2001 Dec	Central	110,652
2002 Jan	Central	99,913
2002 Feb	Central	118,807
2002 Mar	Central	156,803
2002 Apr	Central	154,440
2002 May	Central	172,775
2002 Jun	Central	172,701
2002 Jul	Central	185,184
2002 Aug	Central	288,336
2002 Sep	Central	211,734
2002 Oct	Central	158,020
2002 Nov	Central	125,915
2002 Dec	Central	108,691
2003 Jan	Central	136,669
2003 Feb	Central	146,512
2003 Mar	Central	196,309
2003 Apr	Central	240,487
2003 May	Central	282,940
2003 Jun	Central	256,314
2003 Jul	Central	297,678
2003 Aug	Central	439,293
2003 Sep	Central	319,576
2003 Oct	Central	257,783
2003 Nov	Central	183,431
2003 Dec	Central	161,020
2004 Jan	Central	144,481
2004 Feb	Central	169,494
2004 Mar	Central	206,316
2004 Apr	Central	263,603
2004 May	Central	290,185
2004 Jun	Central	308,510
2004 Jul	Central	308,175
2004 Aug	Central	442,413
2004 Sep	Central	331,474
2004 Oct	Central	300,534
2004 Nov	Central	182,155
2004 Dec	Central	163,759
2005 Jan	Central	146,800
2005 Feb	Central	172,000
2005 Mar	Central	251,100
2005 Apr	Central	264,200
2005 May	Central	299,900
2005 Jun	Central	293,000
2005 Jul	Central	348,200
2005 Aug	Central	496,700
2005 Sep	Central	353,900
2005 Oct	Central	294,200
2005 Nov	Central	198,200
2005 Dec	Central	179,200
2006 Jan	Central	146,300
2006 Feb	Central	184,500
2006 Mar	Central	219,800
2006 Apr	Central	317,200
2006 May	Central	320,500
2006 Jun	Central	294,000
2006 Jul	Central	358,000
2006 Aug	Central	534,200
2006 Sep	Central	388,300
2006 Oct	Central	316,100
2006 Nov	Central	208,200
2006 Dec	Central	221,000
2007 Jan	Central	162,664
2007 Feb	Central	190,582
2007 Mar	Central	238,453
2007 Apr	Central	330,410
2007 May	Central	337,547
2007 Jun	Central	319,452
2007 Jul	Central	407,512
2007 Aug	Central	585,003
2007 Sep	Central	426,485
2007 Oct	Central	381,577
2007 Nov	Central	256,977
2007 Dec	Central	214,573
2008 Jan	Central	173,254
2008 Feb	Central	219,018
2008 Mar	Central	294,598
2008 Apr	Central	290,743
2008 May	Central	351,702
2008 Jun	Central	316,824
2008 Jul	Central	408,282
2008 Aug	Central	580,934
2008 Sep	Central	409,743
2008 Oct	Central	357,244
2008 Nov	Central	264,189
2008 Dec	Central	213,744
2009 Jan	Central	166,779
2009 Feb	Central	197,479
2009 Mar	Central	212,005
2009 Apr	Central	307,991
2009 May	Central	355,799
2009 Jun	Central	353,815
2009 Jul	Central	393,285
2009 Aug	Central	570,434
2009 Sep	Central	393,219
2009 Oct	Central	358,297
2009 Nov	Central	236,307
2009 Dec	Central	202,107
2010 Jan	Central	167,236
2010 Feb	Central	197,763
2010 Mar	Central	247,044
2010 Apr	Central	322,575
2010 May	Central	364,444
2010 Jun	Central	332,855
2010 Jul	Central	415,097
2010 Aug	Central	601,702
2010 Sep	Central	418,552
2010 Oct	Central	382,358
2010 Nov	Central	230,033
2010 Dec	Central	204,889
2011 Jan	Central	166,269
2011 Feb	Central	187,122
2011 Mar	Central	264,990
2011 Apr	Central	349,355
2011 May	Central	375,316
2011 Jun	Central	372,731
2011 Jul	Central	443,371
2011 Aug	Central	640,525
2011 Sep	Central	438,580
2011 Oct	Central	377,120
2011 Nov	Central	214,577
2011 Dec	Central	213,585
2012 Jan	Central	157,861
2012 Feb	Central	197,428
2012 Mar	Central	255,032
2012 Apr	Central	308,630
2012 May	Central	332,088
2012 Jun	Central	350,535
2012 Jul	Central	417,941
2012 Aug	Central	582,826
2012 Sep	Central	427,111
2012 Oct	Central	337,000
2012 Nov	Central	201,363
2012 Dec	Central	200,109
2013 Jan	Central	147,373
2013 Feb	Central	202,632
2013 Mar	Central	293,463
2013 Apr	Central	275,123
2013 May	Central	357,422
2013 Jun	Central	386,860
2013 Jul	Central	444,630
2013 Aug	Central	666,109
2013 Sep	Central	455,064
2013 Oct	Central	345,179
2013 Nov	Central	230,013
2013 Dec	Central	218,548
2014 Jan	Central	164,482
2014 Feb	Central	197,452
2014 Mar	Central	266,164
2014 Apr	Central	356,417
2014 May	Central	412,447
2014 Jun	Central	387,620
2014 Jul	Central	507,752
2014 Aug	Central	760,371
2014 Sep	Central	519,031
2014 Oct	Central	408,778
2014 Nov	Central	241,182
2014 Dec	Central	265,253
2015 Jan	Central	204,025
2015 Feb	Central	251,055
2015 Mar	Central	315,197
2015 Apr	Central	381,085
2015 May	Central	469,603
2015 Jun	Central	456,652
2015 Jul	Central	577,406
2015 Aug	Central	818,386
2015 Sep	Central	574,858
2015 Oct	Central	458,028
2015 Nov	Central	267,849
2015 Dec	Central	284,302
2016 Jan	Central	227,990
2016 Feb	Central	274,288
2016 Mar	Central	386,968
2016 Apr	Central	402,244
2016 May	Central	481,045
2016 Jun	Central	530,672
2016 Jul	Central	638,700
2016 Aug	Central	913,984
2016 Sep	Central	655,512
2016 Oct	Central	513,522
2016 Nov	Central	294,148
2016 Dec	Central	324,719
2017 Jan	Central	249,052
2017 Feb	Central	306,019
2017 Mar	Central	370,214
2017 Apr	Central	581,188
2017 May	Central	595,545
2017 Jun	Central	649,224
2017 Jul	Central	776,426
2017 Aug	Central	1,032,644
2017 Sep	Central	807,610
2017 Oct	Central	654,819
2017 Nov	Central	368,111
2017 Dec	Central	373,430
2018 Jan	Central	276,097
2018 Feb	Central	340,804
2018 Mar	Central	453,235
2018 Apr	Central	524,889
2018 May	Central	593,154
2018 Jun	Central	610,021
2018 Jul	Central	762,431
2018 Aug	Central	1,028,850
2018 Sep	Central	763,328
2018 Oct	Central	629,796
2018 Nov	Central	405,111
2018 Dec	Central	390,111
2019 Jan	Central	297,993
2019 Feb	Central	327,770
2019 Mar	Central	448,196
2019 Apr	Central	590,560
2019 May	Central	642,734
2019 Jun	Central	683,896
2019 Jul	Central	778,019
2019 Aug	Central	1,075,817
2019 Sep	Central	779,106
2019 Oct	Central	646,304
2019 Nov	Central	452,661
2019 Dec	Central	411,807
2020 Jan	Central	333,965
2020 Feb	Central	417,768
2020 Mar	Central	158,354
2020 Apr	Central	20,017
2020 May	Central	41,571
2020 Jun	Central	174,232
2020 Jul	Central	392,962
2020 Aug	Central	769,475
2020 Sep	Central	458,303
2020 Oct	Central	316,766
2020 Nov	Central	131,475
2020 Dec	Central	147,123
2021 Jan	Central	97,104
2021 Feb	Central	66,703
2021 Mar	Central	91,445
2021 Apr	Central	142,793
2021 May	Central	304,098
2021 Jun	Central	430,313
2021 Jul	Central	543,816
2021 Aug	Central	912,711
2021 Sep	Central	585,501
2021 Oct	Central	572,658
2021 Nov	Central	383,198
2021 Dec	Central	322,122
2022 Jan	Central	253,236
2022 Feb	Central	334,306
2022 Mar	Central	392,018
2022 Apr	Central	604,245
2022 May	Central	594,487
2022 Jun	Central	657,104
2000 Jan	Madeira	343,435
2000 Feb	Madeira	377,815
2000 Mar	Madeira	482,568
2000 Apr	Madeira	503,229
2000 May	Madeira	423,632
2000 Jun	Madeira	378,303
2000 Jul	Madeira	425,313
2000 Aug	Madeira	485,276
2000 Sep	Madeira	409,729
2000 Oct	Madeira	401,244
2000 Nov	Madeira	397,636
2000 Dec	Madeira	333,601
2001 Jan	Madeira	368,946
2001 Feb	Madeira	410,103
2001 Mar	Madeira	429,832
2001 Apr	Madeira	529,260
2001 May	Madeira	468,422
2001 Jun	Madeira	453,162
2001 Jul	Madeira	502,384
2001 Aug	Madeira	571,143
2001 Sep	Madeira	478,452
2001 Oct	Madeira	454,265
2001 Nov	Madeira	416,310
2001 Dec	Madeira	356,069
2002 Jan	Madeira	362,185
2002 Feb	Madeira	412,179
2002 Mar	Madeira	527,093
2002 Apr	Madeira	512,065
2002 May	Madeira	433,851
2002 Jun	Madeira	452,241
2002 Jul	Madeira	482,783
2002 Aug	Madeira	598,974
2002 Sep	Madeira	486,537
2002 Oct	Madeira	450,965
2002 Nov	Madeira	398,179
2002 Dec	Madeira	351,654
2003 Jan	Madeira	384,462
2003 Feb	Madeira	417,825
2003 Mar	Madeira	513,219
2003 Apr	Madeira	557,918
2003 May	Madeira	481,655
2003 Jun	Madeira	452,219
2003 Jul	Madeira	492,289
2003 Aug	Madeira	607,407
2003 Sep	Madeira	494,775
2003 Oct	Madeira	460,731
2003 Nov	Madeira	385,485
2003 Dec	Madeira	350,000
2004 Jan	Madeira	360,594
2004 Feb	Madeira	419,520
2004 Mar	Madeira	480,002
2004 Apr	Madeira	528,281
2004 May	Madeira	480,137
2004 Jun	Madeira	418,633
2004 Jul	Madeira	479,276
2004 Aug	Madeira	581,746
2004 Sep	Madeira	500,631
2004 Oct	Madeira	489,199
2004 Nov	Madeira	400,182
2004 Dec	Madeira	354,875
2005 Jan	Madeira	403,100
2005 Feb	Madeira	407,500
2005 Mar	Madeira	483,000
2005 Apr	Madeira	491,000
2005 May	Madeira	467,100
2005 Jun	Madeira	459,500
2005 Jul	Madeira	510,500
2005 Aug	Madeira	636,500
2005 Sep	Madeira	520,700
2005 Oct	Madeira	490,700
2005 Nov	Madeira	407,900
2005 Dec	Madeira	360,900
2006 Jan	Madeira	382,300
2006 Feb	Madeira	390,100
2006 Mar	Madeira	492,100
2006 Apr	Madeira	569,000
2006 May	Madeira	511,400
2006 Jun	Madeira	477,000
2006 Jul	Madeira	517,500
2006 Aug	Madeira	645,700
2006 Sep	Madeira	524,700
2006 Oct	Madeira	481,200
2006 Nov	Madeira	386,400
2006 Dec	Madeira	351,800
2007 Jan	Madeira	363,880
2007 Feb	Madeira	389,302
2007 Mar	Madeira	511,248
2007 Apr	Madeira	578,926
2007 May	Madeira	542,489
2007 Jun	Madeira	514,256
2007 Jul	Madeira	576,100
2007 Aug	Madeira	666,401
2007 Sep	Madeira	552,536
2007 Oct	Madeira	498,484
2007 Nov	Madeira	432,492
2007 Dec	Madeira	363,901
2008 Jan	Madeira	385,313
2008 Feb	Madeira	443,346
2008 Mar	Madeira	560,943
2008 Apr	Madeira	574,615
2008 May	Madeira	578,922
2008 Jun	Madeira	548,283
2008 Jul	Madeira	605,631
2008 Aug	Madeira	688,895
2008 Sep	Madeira	577,442
2008 Oct	Madeira	507,067
2008 Nov	Madeira	395,395
2008 Dec	Madeira	342,292
2009 Jan	Madeira	337,043
2009 Feb	Madeira	371,317
2009 Mar	Madeira	473,879
2009 Apr	Madeira	525,648
2009 May	Madeira	510,850
2009 Jun	Madeira	501,923
2009 Jul	Madeira	523,383
2009 Aug	Madeira	623,297
2009 Sep	Madeira	517,222
2009 Oct	Madeira	454,129
2009 Nov	Madeira	350,155
2009 Dec	Madeira	308,080
2010 Jan	Madeira	319,379
2010 Feb	Madeira	329,697
2010 Mar	Madeira	388,978
2010 Apr	Madeira	427,950
2010 May	Madeira	431,385
2010 Jun	Madeira	432,522
2010 Jul	Madeira	492,382
2010 Aug	Madeira	624,383
2010 Sep	Madeira	496,609
2010 Oct	Madeira	450,841
2010 Nov	Madeira	327,330
2010 Dec	Madeira	272,069
2011 Jan	Madeira	286,010
2011 Feb	Madeira	319,015
2011 Mar	Madeira	448,224
2011 Apr	Madeira	517,979
2011 May	Madeira	575,401
2011 Jun	Madeira	519,950
2011 Jul	Madeira	589,288
2011 Aug	Madeira	678,877
2011 Sep	Madeira	577,108
2011 Oct	Madeira	471,268
2011 Nov	Madeira	319,900
2011 Dec	Madeira	262,266
2012 Jan	Madeira	289,312
2012 Feb	Madeira	329,299
2012 Mar	Madeira	399,988
2012 Apr	Madeira	508,131
2012 May	Madeira	521,638
2012 Jun	Madeira	509,865
2012 Jul	Madeira	602,837
2012 Aug	Madeira	681,135
2012 Sep	Madeira	562,007
2012 Oct	Madeira	468,951
2012 Nov	Madeira	350,902
2012 Dec	Madeira	283,620
2013 Jan	Madeira	322,235
2013 Feb	Madeira	365,343
2013 Mar	Madeira	462,258
2013 Apr	Madeira	516,930
2013 May	Madeira	608,081
2013 Jun	Madeira	578,633
2013 Jul	Madeira	677,083
2013 Aug	Madeira	775,941
2013 Sep	Madeira	639,271
2013 Oct	Madeira	535,649
2013 Nov	Madeira	390,742
2013 Dec	Madeira	342,783
2014 Jan	Madeira	374,568
2014 Feb	Madeira	401,859
2014 Mar	Madeira	503,533
2014 Apr	Madeira	557,275
2014 May	Madeira	610,148
2014 Jun	Madeira	595,332
2014 Jul	Madeira	687,207
2014 Aug	Madeira	787,020
2014 Sep	Madeira	652,671
2014 Oct	Madeira	554,671
2014 Nov	Madeira	415,750
2014 Dec	Madeira	366,832
2015 Jan	Madeira	399,040
2015 Feb	Madeira	442,963
2015 Mar	Madeira	545,523
2015 Apr	Madeira	586,230
2015 May	Madeira	628,998
2015 Jun	Madeira	654,715
2015 Jul	Madeira	766,557
2015 Aug	Madeira	829,230
2015 Sep	Madeira	696,849
2015 Oct	Madeira	597,629
2015 Nov	Madeira	475,257
2015 Dec	Madeira	407,035
2016 Jan	Madeira	448,784
2016 Feb	Madeira	506,179
2016 Mar	Madeira	611,987
2016 Apr	Madeira	663,878
2016 May	Madeira	726,980
2016 Jun	Madeira	759,256
2016 Jul	Madeira	849,148
2016 Aug	Madeira	891,091
2016 Sep	Madeira	768,042
2016 Oct	Madeira	702,530
2016 Nov	Madeira	545,468
2016 Dec	Madeira	457,565
2017 Jan	Madeira	503,654
2017 Feb	Madeira	541,368
2017 Mar	Madeira	647,679
2017 Apr	Madeira	710,409
2017 May	Madeira	745,096
2017 Jun	Madeira	794,118
2017 Jul	Madeira	864,476
2017 Aug	Madeira	939,077
2017 Sep	Madeira	818,705
2017 Oct	Madeira	734,287
2017 Nov	Madeira	582,743
2017 Dec	Madeira	478,377
2018 Jan	Madeira	534,281
2018 Feb	Madeira	555,841
2018 Mar	Madeira	652,082
2018 Apr	Madeira	689,214
2018 May	Madeira	755,491
2018 Jun	Madeira	782,628
2018 Jul	Madeira	837,740
2018 Aug	Madeira	936,644
2018 Sep	Madeira	806,267
2018 Oct	Madeira	721,989
2018 Nov	Madeira	575,096
2018 Dec	Madeira	496,993
2019 Jan	Madeira	486,306
2019 Feb	Madeira	498,081
2019 Mar	Madeira	606,616
2019 Apr	Madeira	608,322
2019 May	Madeira	665,724
2019 Jun	Madeira	714,041
2019 Jul	Madeira	747,112
2019 Aug	Madeira	828,426
2019 Sep	Madeira	719,254
2019 Oct	Madeira	629,555
2019 Nov	Madeira	508,290
2019 Dec	Madeira	445,470
2020 Jan	Madeira	488,461
2020 Feb	Madeira	540,254
2020 Mar	Madeira	297,649
2020 Apr	Madeira	2,191
2020 May	Madeira	2,955
2020 Jun	Madeira	14,932
2020 Jul	Madeira	95,576
2020 Aug	Madeira	240,322
2020 Sep	Madeira	251,221
2020 Oct	Madeira	253,895
2020 Nov	Madeira	116,634
2020 Dec	Madeira	137,446
2021 Jan	Madeira	93,013
2021 Feb	Madeira	40,883
2021 Mar	Madeira	60,163
2021 Apr	Madeira	95,116
2021 May	Madeira	179,599
2021 Jun	Madeira	321,985
2021 Jul	Madeira	552,399
2021 Aug	Madeira	780,123
2021 Sep	Madeira	697,572
2021 Oct	Madeira	655,682
2021 Nov	Madeira	521,638
2021 Dec	Madeira	397,592
2022 Jan	Madeira	341,744
2022 Feb	Madeira	391,699
2022 Mar	Madeira	569,482
2022 Apr	Madeira	727,326
2022 May	Madeira	779,426
2022 Jun	Madeira	833,955
2000 Jan	North	162,389
2000 Feb	North	162,637
2000 Mar	North	226,010
2000 Apr	North	262,865
2000 May	North	264,497
2000 Jun	North	273,881
2000 Jul	North	324,962
2000 Aug	North	397,405
2000 Sep	North	331,155
2000 Oct	North	263,217
2000 Nov	North	186,445
2000 Dec	North	157,210
2001 Jan	North	155,740
2001 Feb	North	166,108
2001 Mar	North	217,441
2001 Apr	North	257,545
2001 May	North	270,718
2001 Jun	North	291,765
2001 Jul	North	315,131
2001 Aug	North	392,386
2001 Sep	North	335,067
2001 Oct	North	274,619
2001 Nov	North	200,603
2001 Dec	North	168,877
2002 Jan	North	165,653
2002 Feb	North	181,005
2002 Mar	North	249,214
2002 Apr	North	253,274
2002 May	North	302,028
2002 Jun	North	301,465
2002 Jul	North	314,560
2002 Aug	North	444,991
2002 Sep	North	361,181
2002 Oct	North	287,383
2002 Nov	North	221,910
2002 Dec	North	179,766
2003 Jan	North	155,527
2003 Feb	North	177,818
2003 Mar	North	214,106
2003 Apr	North	258,519
2003 May	North	293,531
2003 Jun	North	271,454
2003 Jul	North	318,706
2003 Aug	North	433,211
2003 Sep	North	343,534
2003 Oct	North	281,472
2003 Nov	North	219,463
2003 Dec	North	178,439
2004 Jan	North	162,924
2004 Feb	North	181,864
2004 Mar	North	224,550
2004 Apr	North	279,773
2004 May	North	317,318
2004 Jun	North	355,310
2004 Jul	North	324,421
2004 Aug	North	426,911
2004 Sep	North	342,064
2004 Oct	North	311,541
2004 Nov	North	221,222
2004 Dec	North	182,752
2005 Jan	North	168,100
2005 Feb	North	166,800
2005 Mar	North	247,000
2005 Apr	North	268,500
2005 May	North	316,900
2005 Jun	North	307,700
2005 Jul	North	358,500
2005 Aug	North	472,400
2005 Sep	North	362,200
2005 Oct	North	315,900
2005 Nov	North	233,400
2005 Dec	North	221,300
2006 Jan	North	180,700
2006 Feb	North	195,100
2006 Mar	North	237,200
2006 Apr	North	352,600
2006 May	North	361,200
2006 Jun	North	331,500
2006 Jul	North	388,400
2006 Aug	North	524,500
2006 Sep	North	406,500
2006 Oct	North	353,300
2006 Nov	North	258,800
2006 Dec	North	254,700
2007 Jan	North	193,557
2007 Feb	North	211,310
2007 Mar	North	281,402
2007 Apr	North	360,280
2007 May	North	386,910
2007 Jun	North	374,585
2007 Jul	North	430,388
2007 Aug	North	576,398
2007 Sep	North	459,023
2007 Oct	North	387,453
2007 Nov	North	302,985
2007 Dec	North	264,674
2008 Jan	North	213,747
2008 Feb	North	243,433
2008 Mar	North	338,014
2008 Apr	North	316,810
2008 May	North	398,896
2008 Jun	North	348,835
2008 Jul	North	436,672
2008 Aug	North	576,194
2008 Sep	North	462,477
2008 Oct	North	380,182
2008 Nov	North	282,529
2008 Dec	North	252,975
2009 Jan	North	205,713
2009 Feb	North	229,748
2009 Mar	North	262,532
2009 Apr	North	342,056
2009 May	North	380,402
2009 Jun	North	370,520
2009 Jul	North	446,992
2009 Aug	North	594,862
2009 Sep	North	476,222
2009 Oct	North	410,463
2009 Nov	North	287,514
2009 Dec	North	262,943
2010 Jan	North	229,317
2010 Feb	North	243,334
2010 Mar	North	302,045
2010 Apr	North	368,733
2010 May	North	408,430
2010 Jun	North	380,916
2010 Jul	North	466,332
2010 Aug	North	587,802
2010 Sep	North	482,377
2010 Oct	North	414,282
2010 Nov	North	282,979
2010 Dec	North	271,209
2011 Jan	North	227,701
2011 Feb	North	236,136
2011 Mar	North	295,242
2011 Apr	North	387,011
2011 May	North	409,634
2011 Jun	North	426,688
2011 Jul	North	493,085
2011 Aug	North	631,859
2011 Sep	North	496,839
2011 Oct	North	423,081
2011 Nov	North	257,631
2011 Dec	North	262,098
2012 Jan	North	221,078
2012 Feb	North	251,935
2012 Mar	North	296,446
2012 Apr	North	371,244
2012 May	North	412,704
2012 Jun	North	421,011
2012 Jul	North	477,186
2012 Aug	North	620,262
2012 Sep	North	513,418
2012 Oct	North	411,888
2012 Nov	North	284,832
2012 Dec	North	259,915
2013 Jan	North	223,910
2013 Feb	North	251,230
2013 Mar	North	352,872
2013 Apr	North	368,268
2013 May	North	488,126
2013 Jun	North	514,042
2013 Jul	North	558,767
2013 Aug	North	768,355
2013 Sep	North	602,107
2013 Oct	North	495,109
2013 Nov	North	338,029
2013 Dec	North	315,322
2014 Jan	North	262,539
2014 Feb	North	280,918
2014 Mar	North	369,207
2014 Apr	North	509,435
2014 May	North	566,519
2014 Jun	North	550,202
2014 Jul	North	666,483
2014 Aug	North	874,676
2014 Sep	North	665,442
2014 Oct	North	556,397
2014 Nov	North	377,451
2014 Dec	North	382,473
2015 Jan	North	320,372
2015 Feb	North	332,952
2015 Mar	North	446,649
2015 Apr	North	556,131
2015 May	North	666,687
2015 Jun	North	649,456
2015 Jul	North	766,392
2015 Aug	North	1,001,246
2015 Sep	North	780,721
2015 Oct	North	642,100
2015 Nov	North	416,009
2015 Dec	North	423,184
2016 Jan	North	370,496
2016 Feb	North	405,760
2016 Mar	North	563,335
2016 Apr	North	610,835
2016 May	North	730,640
2016 Jun	North	757,839
2016 Jul	North	885,199
2016 Aug	North	1,091,931
2016 Sep	North	868,941
2016 Oct	North	744,759
2016 Nov	North	482,179
2016 Dec	North	478,008
2017 Jan	North	406,014
2017 Feb	North	453,177
2017 Mar	North	554,730
2017 Apr	North	800,643
2017 May	North	809,927
2017 Jun	North	859,677
2017 Jul	North	976,597
2017 Aug	North	1,205,153
2017 Sep	North	976,846
2017 Oct	North	838,460
2017 Nov	North	552,908
2017 Dec	North	574,714
2018 Jan	North	448,867
2018 Feb	North	505,884
2018 Mar	North	677,600
2018 Apr	North	784,760
2018 May	North	910,431
2018 Jun	North	915,301
2018 Jul	North	1,027,991
2018 Aug	North	1,299,532
2018 Sep	North	1,045,460
2018 Oct	North	925,125
2018 Nov	North	643,384
2018 Dec	North	593,682
2019 Jan	North	506,234
2019 Feb	North	527,872
2019 Mar	North	720,805
2019 Apr	North	916,002
2019 May	North	1,003,703
2019 Jun	North	1,041,697
2019 Jul	North	1,171,400
2019 Aug	North	1,410,095
2019 Sep	North	1,144,562
2019 Oct	North	994,052
2019 Nov	North	713,057
2019 Dec	North	661,233
2020 Jan	North	578,609
2020 Feb	North	625,285
2020 Mar	North	265,615
2020 Apr	North	30,274
2020 May	North	70,636
2020 Jun	North	203,890
2020 Jul	North	466,450
2020 Aug	North	835,671
2020 Sep	North	557,919
2020 Oct	North	397,645
2020 Nov	North	160,674
2020 Dec	North	173,388
2021 Jan	North	134,458
2021 Feb	North	98,480
2021 Mar	North	124,151
2021 Apr	North	182,065
2021 May	North	395,133
2021 Jun	North	525,623
2021 Jul	North	697,914
2021 Aug	North	1,131,753
2021 Sep	North	835,537
2021 Oct	North	886,795
2021 Nov	North	624,508
2021 Dec	North	505,650
2022 Jan	North	347,324
2022 Feb	North	525,964
2022 Mar	North	663,862
2022 Apr	North	1,011,472
2022 May	North	1,070,923
2022 Jun	North	1,106,335
2000 Jan	Total Portugal	1,526,369
2000 Feb	Total Portugal	1,844,851
2000 Mar	Total Portugal	2,531,331
2000 Apr	Total Portugal	3,022,807
2000 May	Total Portugal	3,106,715
2000 Jun	Total Portugal	3,258,737
2000 Jul	Total Portugal	3,897,041
2000 Aug	Total Portugal	4,453,006
2000 Sep	Total Portugal	3,632,216
2000 Oct	Total Portugal	2,974,818
2000 Nov	Total Portugal	1,974,847
2000 Dec	Total Portugal	1,572,385
2001 Jan	Total Portugal	1,608,556
2001 Feb	Total Portugal	1,964,165
2001 Mar	Total Portugal	2,457,972
2001 Apr	Total Portugal	3,011,554
2001 May	Total Portugal	3,064,136
2001 Jun	Total Portugal	3,349,125
2001 Jul	Total Portugal	3,866,128
2001 Aug	Total Portugal	4,426,781
2001 Sep	Total Portugal	3,559,937
2001 Oct	Total Portugal	2,887,563
2001 Nov	Total Portugal	1,886,345
2001 Dec	Total Portugal	1,480,329
2002 Jan	Total Portugal	1,537,139
2002 Feb	Total Portugal	1,926,842
2002 Mar	Total Portugal	2,752,279
2002 Apr	Total Portugal	2,703,439
2002 May	Total Portugal	3,108,798
2002 Jun	Total Portugal	3,371,407
2002 Jul	Total Portugal	3,909,345
2002 Aug	Total Portugal	4,900,264
2002 Sep	Total Portugal	3,731,515
2002 Oct	Total Portugal	2,853,204
2002 Nov	Total Portugal	1,909,950
2002 Dec	Total Portugal	1,504,786
2003 Jan	Total Portugal	1,550,720
2003 Feb	Total Portugal	1,869,726
2003 Mar	Total Portugal	2,429,128
2003 Apr	Total Portugal	2,925,012
2003 May	Total Portugal	3,195,173
2003 Jun	Total Portugal	3,365,166
2003 Jul	Total Portugal	3,920,883
2003 Aug	Total Portugal	4,833,007
2003 Sep	Total Portugal	3,551,038
2003 Oct	Total Portugal	2,843,491
2003 Nov	Total Portugal	1,843,415
2003 Dec	Total Portugal	1,548,712
2004 Jan	Total Portugal	1,549,992
2004 Feb	Total Portugal	1,934,294
2004 Mar	Total Portugal	2,382,340
2004 Apr	Total Portugal	2,918,348
2004 May	Total Portugal	3,105,531
2004 Jun	Total Portugal	3,383,239
2004 Jul	Total Portugal	3,788,629
2004 Aug	Total Portugal	4,850,672
2004 Sep	Total Portugal	3,654,583
2004 Oct	Total Portugal	3,041,458
2004 Nov	Total Portugal	1,871,106
2004 Dec	Total Portugal	1,660,389
2005 Jan	Total Portugal	1,643,200
2005 Feb	Total Portugal	1,895,600
2005 Mar	Total Portugal	2,646,700
2005 Apr	Total Portugal	2,711,700
2005 May	Total Portugal	3,284,700
2005 Jun	Total Portugal	3,429,300
2005 Jul	Total Portugal	4,070,100
2005 Aug	Total Portugal	5,165,400
2005 Sep	Total Portugal	3,830,400
2005 Oct	Total Portugal	3,105,600
2005 Nov	Total Portugal	1,990,300
2005 Dec	Total Portugal	1,747,600
2006 Jan	Total Portugal	1,669,200
2006 Feb	Total Portugal	1,941,000
2006 Mar	Total Portugal	2,476,900
2006 Apr	Total Portugal	3,377,000
2006 May	Total Portugal	3,413,900
2006 Jun	Total Portugal	3,561,300
2006 Jul	Total Portugal	4,312,000
2006 Aug	Total Portugal	5,447,100
2006 Sep	Total Portugal	4,050,200
2006 Oct	Total Portugal	3,263,800
2006 Nov	Total Portugal	2,095,700
2006 Dec	Total Portugal	1,958,400
2007 Jan	Total Portugal	1,764,733
2007 Feb	Total Portugal	1,999,070
2007 Mar	Total Portugal	2,748,651
2007 Apr	Total Portugal	3,440,595
2007 May	Total Portugal	3,617,821
2007 Jun	Total Portugal	3,790,867
2007 Jul	Total Portugal	4,647,466
2007 Aug	Total Portugal	5,682,099
2007 Sep	Total Portugal	4,304,587
2007 Oct	Total Portugal	3,455,445
2007 Nov	Total Portugal	2,326,522
2007 Dec	Total Portugal	1,958,727
2008 Jan	Total Portugal	1,792,707
2008 Feb	Total Portugal	2,205,710
2008 Mar	Total Portugal	3,071,710
2008 Apr	Total Portugal	3,049,848
2008 May	Total Portugal	3,792,319
2008 Jun	Total Portugal	3,700,500
2008 Jul	Total Portugal	4,576,555
2008 Aug	Total Portugal	5,592,474
2008 Sep	Total Portugal	4,237,387
2008 Oct	Total Portugal	3,340,384
2008 Nov	Total Portugal	2,112,189
2008 Dec	Total Portugal	1,756,155
2009 Jan	Total Portugal	1,617,297
2009 Feb	Total Portugal	1,888,606
2009 Mar	Total Portugal	2,360,337
2009 Apr	Total Portugal	3,121,369
2009 May	Total Portugal	3,338,825
2009 Jun	Total Portugal	3,606,888
2009 Jul	Total Portugal	4,293,285
2009 Aug	Total Portugal	5,404,788
2009 Sep	Total Portugal	3,971,696
2009 Oct	Total Portugal	3,150,065
2009 Nov	Total Portugal	1,988,283
2009 Dec	Total Portugal	1,715,630
2010 Jan	Total Portugal	1,596,917
2010 Feb	Total Portugal	1,871,859
2010 Mar	Total Portugal	2,442,318
2010 Apr	Total Portugal	2,925,325
2010 May	Total Portugal	3,326,419
2010 Jun	Total Portugal	3,560,063
2010 Jul	Total Portugal	4,598,370
2010 Aug	Total Portugal	5,724,095
2010 Sep	Total Portugal	4,256,566
2010 Oct	Total Portugal	3,405,985
2010 Nov	Total Portugal	1,948,117
2010 Dec	Total Portugal	1,735,257
2011 Jan	Total Portugal	1,570,127
2011 Feb	Total Portugal	1,818,461
2011 Mar	Total Portugal	2,549,804
2011 Apr	Total Portugal	3,439,650
2011 May	Total Portugal	3,563,492
2011 Jun	Total Portugal	4,006,002
2011 Jul	Total Portugal	5,002,442
2011 Aug	Total Portugal	6,067,205
2011 Sep	Total Portugal	4,424,427
2011 Oct	Total Portugal	3,486,541
2011 Nov	Total Portugal	1,853,952
2011 Dec	Total Portugal	1,658,184
2012 Jan	Total Portugal	1,564,354
2012 Feb	Total Portugal	1,878,064
2012 Mar	Total Portugal	2,486,696
2012 Apr	Total Portugal	3,218,277
2012 May	Total Portugal	3,549,227
2012 Jun	Total Portugal	4,056,426
2012 Jul	Total Portugal	5,099,988
2012 Aug	Total Portugal	6,064,744
2012 Sep	Total Portugal	4,577,342
2012 Oct	Total Portugal	3,522,553
2012 Nov	Total Portugal	1,990,659
2012 Dec	Total Portugal	1,672,710
2013 Jan	Total Portugal	1,603,558
2013 Feb	Total Portugal	1,939,438
2013 Mar	Total Portugal	2,848,726
2013 Apr	Total Portugal	3,155,600
2013 May	Total Portugal	4,094,953
2013 Jun	Total Portugal	4,545,785
2013 Jul	Total Portugal	5,533,853
2013 Aug	Total Portugal	6,739,630
2013 Sep	Total Portugal	5,043,790
2013 Oct	Total Portugal	3,893,748
2013 Nov	Total Portugal	2,213,463
2013 Dec	Total Portugal	1,920,607
2014 Jan	Total Portugal	1,804,937
2014 Feb	Total Portugal	2,089,427
2014 Mar	Total Portugal	2,876,500
2014 Apr	Total Portugal	4,086,333
2014 May	Total Portugal	4,592,833
2014 Jun	Total Portugal	4,932,528
2014 Jul	Total Portugal	6,088,279
2014 Aug	Total Portugal	7,532,534
2014 Sep	Total Portugal	5,563,120
2014 Oct	Total Portugal	4,439,049
2014 Nov	Total Portugal	2,486,616
2014 Dec	Total Portugal	2,219,210
2015 Jan	Total Portugal	2,108,896
2015 Feb	Total Portugal	2,407,894
2015 Mar	Total Portugal	3,275,931
2015 Apr	Total Portugal	4,191,960
2015 May	Total Portugal	5,042,890
2015 Jun	Total Portugal	5,434,567
2015 Jul	Total Portugal	6,649,952
2015 Aug	Total Portugal	7,941,930
2015 Sep	Total Portugal	6,033,218
2015 Oct	Total Portugal	4,806,778
2015 Nov	Total Portugal	2,726,232
2015 Dec	Total Portugal	2,453,928
2016 Jan	Total Portugal	2,322,863
2016 Feb	Total Portugal	2,799,860
2016 Mar	Total Portugal	4,007,868
2016 Apr	Total Portugal	4,464,594
2016 May	Total Portugal	5,497,218
2016 Jun	Total Portugal	6,112,587
2016 Jul	Total Portugal	7,300,440
2016 Aug	Total Portugal	8,491,997
2016 Sep	Total Portugal	6,630,171
2016 Oct	Total Portugal	5,535,569
2016 Nov	Total Portugal	3,185,872
2016 Dec	Total Portugal	2,773,601
2017 Jan	Total Portugal	2,677,843
2017 Feb	Total Portugal	3,104,797
2017 Mar	Total Portugal	4,042,796
2017 Apr	Total Portugal	5,743,335
2017 May	Total Portugal	6,035,426
2017 Jun	Total Portugal	6,753,217
2017 Jul	Total Portugal	7,890,416
2017 Aug	Total Portugal	9,076,069
2017 Sep	Total Portugal	7,234,527
2017 Oct	Total Portugal	6,110,688
2017 Nov	Total Portugal	3,564,865
2017 Dec	Total Portugal	3,151,231
2018 Jan	Total Portugal	2,879,843
2018 Feb	Total Portugal	3,369,689
2018 Mar	Total Portugal	4,615,448
2018 Apr	Total Portugal	5,424,456
2018 May	Total Portugal	6,351,120
2018 Jun	Total Portugal	6,792,865
2018 Jul	Total Portugal	8,044,559
2018 Aug	Total Portugal	9,369,646
2018 Sep	Total Portugal	7,391,695
2018 Oct	Total Portugal	6,300,875
2018 Nov	Total Portugal	3,825,767
2018 Dec	Total Portugal	3,296,140
2019 Jan	Total Portugal	3,034,284
2019 Feb	Total Portugal	3,365,240
2019 Mar	Total Portugal	4,606,922
2019 Apr	Total Portugal	5,981,300
2019 May	Total Portugal	6,557,840
2019 Jun	Total Portugal	7,177,554
2019 Jul	Total Portugal	8,231,230
2019 Aug	Total Portugal	9,633,427
2019 Sep	Total Portugal	7,624,574
2019 Oct	Total Portugal	6,358,685
2019 Nov	Total Portugal	4,071,968
2019 Dec	Total Portugal	3,515,940
2020 Jan	Total Portugal	3,258,226
2020 Feb	Total Portugal	3,817,043
2020 Mar	Total Portugal	1,875,506
2020 Apr	Total Portugal	133,212
2020 May	Total Portugal	261,593
2020 Jun	Total Portugal	1,031,062
2020 Jul	Total Portugal	2,631,261
2020 Aug	Total Portugal	5,082,349
2020 Sep	Total Portugal	3,534,350
2020 Oct	Total Portugal	2,300,257
2020 Nov	Total Portugal	920,058
2020 Dec	Total Portugal	953,382
2021 Jan	Total Portugal	688,039
2021 Feb	Total Portugal	459,904
2021 Mar	Total Portugal	615,727
2021 Apr	Total Portugal	921,028
2021 May	Total Portugal	2,024,210
2021 Jun	Total Portugal	3,401,792
2021 Jul	Total Portugal	4,538,643
2021 Aug	Total Portugal	7,507,272
2021 Sep	Total Portugal	5,585,513
2021 Oct	Total Portugal	5,468,960
2021 Nov	Total Portugal	3,556,760
2021 Dec	Total Portugal	2,564,574
2022 Jan	Total Portugal	1,988,869
2022 Feb	Total Portugal	2,920,471
2022 Mar	Total Portugal	4,006,723
2022 Apr	Total Portugal	6,006,236
2022 May	Total Portugal	6,511,175
2022 Jun	Total Portugal	7,152,257

1.2 Time Series Plots

# Show time series of all regions in one plot
tourism %>%
  filter(Region != "Total Portugal") %>%
  autoplot(Overnight_Stays) +
  ggtitle("All Regions - Overnight Stays")

# Show all time series in a Facet Grid
tourism %>%
  filter(Region != "Total Portugal") %>%
  autoplot(Overnight_Stays) +
  facet_grid(Region~., scales = "free_y") +
  theme(strip.text.y = element_blank()) +
  ggtitle("All Regions - Overnight Stays")

# Show time series "Lisbon M.A."
tourism %>%
  filter(Region == "Lisbon M.A.") %>%
  autoplot(Overnight_Stays) +
  ggtitle("Lisbon M.A. - Overnight Stays")

# Show time series "Azores"
tourism %>%
  filter(Region == "Azores") %>%
  autoplot(Overnight_Stays) +
  ggtitle("Azores - Overnight Stays")

# Show time series "Alentejo"
tourism %>%
  filter(Region == "Alentejo") %>%
  autoplot(Overnight_Stays) +
  ggtitle("Alentejo - Overnight Stays")

# Show time series "Algarve"
tourism %>%
  filter(Region == "Algarve") %>%
  autoplot(Overnight_Stays) +
  ggtitle("Algarve - Overnight Stays")

# Show time series "Central"
tourism %>%
  filter(Region == "Central") %>%
  autoplot(Overnight_Stays) +
  ggtitle("Central - Overnight Stays")

# Show time series "Madeira"
tourism %>%
  filter(Region == "Madeira") %>%
  autoplot(Overnight_Stays) +
  ggtitle("Madeira - Overnight Stays")

# Show time series "North"
tourism %>%
  filter(Region == "North") %>%
  autoplot(Overnight_Stays) +
  ggtitle("North - Overnight Stays")

1.3 Seasonal Differencing for 2020

# Seasonal Difference March 2020
tourism %>%
  filter(Region != "Total Portugal") %>%
  mutate(SeasDiff_abs = difference(Overnight_Stays,12)) %>%
  filter_index("2020 Mar") %>%
  mutate(SeasDiff_rel = SeasDiff_abs/(Overnight_Stays-SeasDiff_abs)) %>%
  arrange(SeasDiff_rel) %>%
  as_tibble() %>%
  select(-Month) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Difference March 2020</span>", digits = 4, format.args = list(big.mark = ","), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Seasonal Difference March 2020

Region	Overnight_Stays	SeasDiff_abs	SeasDiff_rel
Central	158,354	-289,842	-0.6467
Lisbon M.A.	510,510	-932,820	-0.6463
North	265,615	-455,190	-0.6315
Alentejo	70,530	-101,882	-0.5909
Azores	59,488	-77,157	-0.5647
Algarve	513,360	-565,558	-0.5242
Madeira	297,649	-308,967	-0.5093

# Seasonal Difference April 2020
tourism %>%
  filter(Region != "Total Portugal") %>%
  mutate(SeasDiff_abs = difference(Overnight_Stays,12)) %>%
  filter_index("2020 Apr") %>%
  mutate(SeasDiff_rel = SeasDiff_abs/(Overnight_Stays-SeasDiff_abs)) %>%
  arrange(SeasDiff_rel) %>%
  as_tibble() %>%
  select(-Month) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Difference April 2020</span>", digits = 4, format.args = list(big.mark = ","), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Seasonal Difference April 2020

Region	Overnight_Stays	SeasDiff_abs	SeasDiff_rel
Azores	453	-192,486	-0.9977
Madeira	2,191	-606,131	-0.9964
Algarve	25,614	-1,769,880	-0.9857
Lisbon M.A.	40,771	-1,595,422	-0.9751
North	30,274	-885,728	-0.9669
Central	20,017	-570,543	-0.9661
Alentejo	13,892	-227,898	-0.9425

# Seasonal Difference May 2020
tourism %>%
  filter(Region != "Total Portugal") %>%
  mutate(SeasDiff_abs = difference(Overnight_Stays,12)) %>%
  filter_index("2020 May") %>%
  mutate(SeasDiff_rel = SeasDiff_abs/(Overnight_Stays-SeasDiff_abs)) %>%
  arrange(SeasDiff_rel) %>%
  as_tibble() %>%
  select(-Month) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Difference May 2020</span>", digits = 4, format.args = list(big.mark = ","), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Seasonal Difference May 2020

Region	Overnight_Stays	SeasDiff_abs	SeasDiff_rel
Azores	773	-220,800	-0.9965
Madeira	2,955	-662,769	-0.9956
Algarve	40,932	-1,949,597	-0.9794
Lisbon M.A.	66,383	-1,707,480	-0.9626
Central	41,571	-601,163	-0.9353
North	70,636	-933,067	-0.9296
Alentejo	38,343	-221,371	-0.8524

# Seasonal Difference June 2020
tourism %>%
  filter(Region != "Total Portugal") %>%
  mutate(SeasDiff_abs = difference(Overnight_Stays,12)) %>%
  filter_index("2020 Jun") %>%
  mutate(SeasDiff_rel = SeasDiff_abs/(Overnight_Stays-SeasDiff_abs)) %>%
  arrange(SeasDiff_rel) %>%
  as_tibble() %>%
  select(-Month) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Difference June 2020</span>", digits = 4, format.args = list(big.mark = ","), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Seasonal Difference June 2020

Region	Overnight_Stays	SeasDiff_abs	SeasDiff_rel
Madeira	14,932	-699,109	-0.9791
Azores	9,231	-246,179	-0.9639
Lisbon M.A.	138,646	-1,611,982	-0.9208
Algarve	330,393	-2,095,441	-0.8638
North	203,890	-837,807	-0.8043
Central	174,232	-509,664	-0.7452
Alentejo	159,738	-146,310	-0.4781

# Seasonal Difference July 2020
tourism %>%
  filter(Region != "Total Portugal") %>%
  mutate(SeasDiff_abs = difference(Overnight_Stays,12)) %>%
  filter_index("2020 Jul") %>%
  mutate(SeasDiff_rel = SeasDiff_abs/(Overnight_Stays-SeasDiff_abs)) %>%
  arrange(SeasDiff_rel) %>%
  as_tibble() %>%
  select(-Month) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Difference July 2020</span>", digits = 4, format.args = list(big.mark = ","), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Seasonal Difference July 2020

Region	Overnight_Stays	SeasDiff_abs	SeasDiff_rel
Madeira	95,576	-651,536	-0.8721
Azores	48,595	-262,651	-0.8439
Lisbon M.A.	319,160	-1,555,059	-0.8297
Algarve	1,035,732	-1,952,936	-0.6534
North	466,450	-704,950	-0.6018
Central	392,962	-385,057	-0.4949
Alentejo	272,786	-87,780	-0.2435

# Mean relative Seasonal Difference: April - December 2020
tourism %>%
  filter(Region != "Total Portugal") %>%
  mutate(SeasDiff_abs = difference(Overnight_Stays,12)) %>%
  filter_index("Apr 2020" ~ "Dec 2020") %>%
  mutate(SeasDiff_rel = SeasDiff_abs/(Overnight_Stays-SeasDiff_abs)) %>%
  features(SeasDiff_rel, features = list(mean = mean)) %>%
  rename(Mean_SeasDiff_rel = mean) %>%
  arrange(Mean_SeasDiff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean rel. Seas. Difference: <br> April - December 2020</span>", digits = 4, format.args = list(big.mark = ","), align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean rel. Seas. Difference:
April - December 2020

Region	Mean_SeasDiff_rel
Lisbon M.A.	-0.8344
Madeira	-0.8069
Azores	-0.7857
Algarve	-0.7197
North	-0.7039
Central	-0.6334
Alentejo	-0.4696

1.4 Analysis of Residence Countries of Tourists per Region

# Top 3 Residence Countries of Tourists in August 2019 per Region with Ratio

# Import data
residence_2019 <- read_excel("C:\\Users\\Rosan\\OneDrive - ISEG\\# Masterthesis\\My MFW\\MonthlyOvernightStays_ResidenceCountry_perRegion.xlsx",sheet = "2019_AllRegions") %>%
  select(c(Region, Residence_Country, August)) %>%
  arrange(desc(August)) %>%
  group_by(Region) %>%
  mutate(Ratio = August/sum(August)) %>%
  rename(Overnight_Stays = August) %>%
  slice(1:3)

# Change Region Names to English
residence_2019["Region"][residence_2019["Region"] == "Açores"] <- "Azores"
residence_2019["Region"][residence_2019["Region"] == "A.M. Lisboa"] <- "Lisbon M.A."
residence_2019["Region"][residence_2019["Region"] == "Centro"] <- "Central"
residence_2019["Region"][residence_2019["Region"] == "Norte"] <- "North"

# Change Residence Country Names to English
residence_2019["Residence_Country"][residence_2019["Residence_Country"] == "Outros Estrangeiros"] <- "Other Countries"
residence_2019["Residence_Country"][residence_2019["Residence_Country"] == "Espanha"] <- "Spain"
residence_2019["Residence_Country"][residence_2019["Residence_Country"] == "Alemanha"] <- "Germany"
residence_2019["Residence_Country"][residence_2019["Residence_Country"] == "EUA"] <- "USA"
residence_2019["Residence_Country"][residence_2019["Residence_Country"] == "França"] <- "France"
residence_2019["Residence_Country"][residence_2019["Residence_Country"] == "Reino Unido"] <- "United Kingdom"

# Output tibble in clear table
residence_2019 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Top 3 Residence Countries of Tourists in August 2019</span>", digits = 4, format.args = list(big.mark = ","), align = "cccc") %>%
  column_spec(2:4,border_left = T) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
  pack_rows("Lisbon M.A.", 1, 3) %>%
  pack_rows("Azores", 4, 6) %>%
    pack_rows("Alentejo", 7, 9) %>%
    pack_rows("Algarve", 10, 12) %>%
    pack_rows("Central", 13, 15) %>%
    pack_rows("Madeira", 16, 18) %>%
    pack_rows("North", 19, 21)

Top 3 Residence Countries of Tourists in August 2019

Region	Residence_Country	Overnight_Stays	Ratio
Lisbon M.A.
Lisbon M.A.	Portugal	397,267	0.1931
Lisbon M.A.	Other Countries	310,675	0.1510
Lisbon M.A.	Spain	279,011	0.1356
Azores
Azores	Portugal	111,747	0.3304
Azores	Germany	40,139	0.1187
Azores	USA	33,619	0.0994
Alentejo
Alentejo	Portugal	333,577	0.6886
Alentejo	Spain	53,789	0.1110
Alentejo	France	21,522	0.0444
Algarve
Algarve	Portugal	1,265,301	0.3679
Algarve	United Kingdom	741,086	0.2155
Algarve	Spain	275,366	0.0801
Central
Central	Portugal	612,429	0.5693
Central	Spain	168,353	0.1565
Central	France	75,448	0.0701
Madeira
Madeira	United Kingdom	172,621	0.2084
Madeira	Portugal	144,422	0.1743
Madeira	Germany	143,851	0.1736
North
North	Portugal	572,772	0.4062
North	Spain	265,021	0.1879
North	France	135,318	0.0960

# Ratio of Portuguese Tourists in Continental Regions in Aug 2019
residence_2019 %>%
  filter(!Region == ("Madeira"), !Region == ("Azores")) %>%
  filter(Residence_Country == "Portugal") %>%
  arrange(desc(Ratio)) %>%
  select(-Residence_Country) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Ratio of Portuguese Tourists in Continental Regions in Aug 2019</span>", digits = 4, format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2:3, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Ratio of Portuguese Tourists in Continental Regions in Aug 2019

Region	Overnight_Stays	Ratio
Alentejo	333,577	0.6886
Central	612,429	0.5693
North	572,772	0.4062
Algarve	1,265,301	0.3679
Lisbon M.A.	397,267	0.1931

# Top 3 Residence Countries of Tourists in August 2021 per Region with Ratio

# Import data
residence_2021 <- read_excel("C:\\Users\\Rosan\\OneDrive - ISEG\\# Masterthesis\\My MFW\\MonthlyOvernightStays_ResidenceCountry_perRegion.xlsx",sheet = "2021_AllRegions") %>%
  select(c(Region, Residence_Country, August)) %>%
  arrange(desc(August)) %>%
  group_by(Region) %>%
  mutate(Ratio = August/sum(August)) %>%
  rename(Overnight_Stays = August) %>%
  slice(1:3)

# Change Region Names to English
residence_2021["Region"][residence_2021["Region"] == "Açores"] <- "Azores"
residence_2021["Region"][residence_2021["Region"] == "A.M. Lisboa"] <- "Lisbon M.A."
residence_2021["Region"][residence_2021["Region"] == "Centro"] <- "Central"
residence_2021["Region"][residence_2021["Region"] == "Norte"] <- "North"

# Change Residence Country Names to English
residence_2021["Residence_Country"][residence_2021["Residence_Country"] == "Outros Estrangeiros"] <- "Other Countries"
residence_2021["Residence_Country"][residence_2021["Residence_Country"] == "Espanha"] <- "Spain"
residence_2021["Residence_Country"][residence_2021["Residence_Country"] == "Alemanha"] <- "Germany"
residence_2021["Residence_Country"][residence_2021["Residence_Country"] == "EUA"] <- "USA"
residence_2021["Residence_Country"][residence_2021["Residence_Country"] == "França"] <- "France"
residence_2021["Residence_Country"][residence_2021["Residence_Country"] == "Reino Unido"] <- "United Kingdom"

# Output tibble in clear table
residence_2021 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Top 3 Residence Countries of Tourists in August 2021</span>", digits = 4, format.args = list(big.mark = ","), align = "cccc") %>%
  column_spec(2:4,border_left = T) %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
  pack_rows("Lisbon M.A.", 1, 3) %>%
  pack_rows("Azores", 4, 6) %>%
  pack_rows("Alentejo", 7, 9) %>%
  pack_rows("Algarve", 10, 12) %>%
  pack_rows("Central", 13, 15) %>%
  pack_rows("Madeira", 16, 18) %>%
  pack_rows("North", 19, 21)

Top 3 Residence Countries of Tourists in August 2021

Region	Residence_Country	Overnight_Stays	Ratio
Lisbon M.A.
Lisbon M.A.	Portugal	371,740	0.3186
Lisbon M.A.	Spain	160,769	0.1378
Lisbon M.A.	France	149,282	0.1279
Azores
Azores	Portugal	160,074	0.5490
Azores	France	21,655	0.0743
Azores	Spain	20,515	0.0704
Alentejo
Alentejo	Portugal	379,872	0.8225
Alentejo	Spain	30,968	0.0671
Alentejo	France	13,301	0.0288
Algarve
Algarve	Portugal	1,733,447	0.6275
Algarve	United Kingdom	219,586	0.0795
Algarve	France	190,416	0.0689
Central
Central	Portugal	685,539	0.7511
Central	Spain	87,938	0.0963
Central	France	45,642	0.0500
Madeira
Madeira	Portugal	230,592	0.2956
Madeira	United Kingdom	171,145	0.2194
Madeira	Other Countries	83,416	0.1069
North
North	Portugal	636,323	0.5622
North	Spain	187,217	0.1654
North	France	107,777	0.0952

# Ratio of Portuguese Tourists in Continental Regions in Aug 2021
residence_2021 %>%
  filter(!Region == ("Madeira"), !Region == ("Azores")) %>%
  filter(Residence_Country == "Portugal") %>%
  arrange(desc(Ratio)) %>%
  select(-Residence_Country) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Ratio of Portuguese Tourists in Continental Regions in Aug 2021</span>", digits = 4, format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2:3, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Ratio of Portuguese Tourists in Continental Regions in Aug 2021

Region	Overnight_Stays	Ratio
Alentejo	379,872	0.8225
Central	685,539	0.7511
Algarve	1,733,447	0.6275
North	636,323	0.5622
Lisbon M.A.	371,740	0.3186

1.5 Seasonality and Trend of selected time series

# Save time series of interest
tourism_madeira_until2019 <- tourism %>%
  filter(Region == "Madeira") %>%
  filter(year(Month) <= 2019)

tourism_madeira_until2022 <- tourism %>% filter(Region == "Madeira")

tourism_algarve_until2019 <- tourism %>%
  filter(Region == "Algarve") %>%
  filter(year(Month) <= 2019)

tourism_algarve_until2022 <- tourism %>% filter(Region == "Algarve")

tourism_alentejo_until2019 <- tourism %>%
  filter(Region == "Alentejo") %>%
  filter(year(Month) <= 2019)

tourism_alentejo_until2022 <- tourism %>% filter(Region == "Alentejo")

1.5.1 Madeira

# Show tsibble
tourism_madeira_until2022 %>%
  select(Month, Overnight_Stays) %>% 
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Monthly Number of Overnight Stays in Madeira: 2000-2022</span>", format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Monthly Number of Overnight Stays in Madeira: 2000-2022

Month	Overnight_Stays
2000 Jan	343,435
2000 Feb	377,815
2000 Mar	482,568
2000 Apr	503,229
2000 May	423,632
2000 Jun	378,303
2000 Jul	425,313
2000 Aug	485,276
2000 Sep	409,729
2000 Oct	401,244
2000 Nov	397,636
2000 Dec	333,601
2001 Jan	368,946
2001 Feb	410,103
2001 Mar	429,832
2001 Apr	529,260
2001 May	468,422
2001 Jun	453,162
2001 Jul	502,384
2001 Aug	571,143
2001 Sep	478,452
2001 Oct	454,265
2001 Nov	416,310
2001 Dec	356,069
2002 Jan	362,185
2002 Feb	412,179
2002 Mar	527,093
2002 Apr	512,065
2002 May	433,851
2002 Jun	452,241
2002 Jul	482,783
2002 Aug	598,974
2002 Sep	486,537
2002 Oct	450,965
2002 Nov	398,179
2002 Dec	351,654
2003 Jan	384,462
2003 Feb	417,825
2003 Mar	513,219
2003 Apr	557,918
2003 May	481,655
2003 Jun	452,219
2003 Jul	492,289
2003 Aug	607,407
2003 Sep	494,775
2003 Oct	460,731
2003 Nov	385,485
2003 Dec	350,000
2004 Jan	360,594
2004 Feb	419,520
2004 Mar	480,002
2004 Apr	528,281
2004 May	480,137
2004 Jun	418,633
2004 Jul	479,276
2004 Aug	581,746
2004 Sep	500,631
2004 Oct	489,199
2004 Nov	400,182
2004 Dec	354,875
2005 Jan	403,100
2005 Feb	407,500
2005 Mar	483,000
2005 Apr	491,000
2005 May	467,100
2005 Jun	459,500
2005 Jul	510,500
2005 Aug	636,500
2005 Sep	520,700
2005 Oct	490,700
2005 Nov	407,900
2005 Dec	360,900
2006 Jan	382,300
2006 Feb	390,100
2006 Mar	492,100
2006 Apr	569,000
2006 May	511,400
2006 Jun	477,000
2006 Jul	517,500
2006 Aug	645,700
2006 Sep	524,700
2006 Oct	481,200
2006 Nov	386,400
2006 Dec	351,800
2007 Jan	363,880
2007 Feb	389,302
2007 Mar	511,248
2007 Apr	578,926
2007 May	542,489
2007 Jun	514,256
2007 Jul	576,100
2007 Aug	666,401
2007 Sep	552,536
2007 Oct	498,484
2007 Nov	432,492
2007 Dec	363,901
2008 Jan	385,313
2008 Feb	443,346
2008 Mar	560,943
2008 Apr	574,615
2008 May	578,922
2008 Jun	548,283
2008 Jul	605,631
2008 Aug	688,895
2008 Sep	577,442
2008 Oct	507,067
2008 Nov	395,395
2008 Dec	342,292
2009 Jan	337,043
2009 Feb	371,317
2009 Mar	473,879
2009 Apr	525,648
2009 May	510,850
2009 Jun	501,923
2009 Jul	523,383
2009 Aug	623,297
2009 Sep	517,222
2009 Oct	454,129
2009 Nov	350,155
2009 Dec	308,080
2010 Jan	319,379
2010 Feb	329,697
2010 Mar	388,978
2010 Apr	427,950
2010 May	431,385
2010 Jun	432,522
2010 Jul	492,382
2010 Aug	624,383
2010 Sep	496,609
2010 Oct	450,841
2010 Nov	327,330
2010 Dec	272,069
2011 Jan	286,010
2011 Feb	319,015
2011 Mar	448,224
2011 Apr	517,979
2011 May	575,401
2011 Jun	519,950
2011 Jul	589,288
2011 Aug	678,877
2011 Sep	577,108
2011 Oct	471,268
2011 Nov	319,900
2011 Dec	262,266
2012 Jan	289,312
2012 Feb	329,299
2012 Mar	399,988
2012 Apr	508,131
2012 May	521,638
2012 Jun	509,865
2012 Jul	602,837
2012 Aug	681,135
2012 Sep	562,007
2012 Oct	468,951
2012 Nov	350,902
2012 Dec	283,620
2013 Jan	322,235
2013 Feb	365,343
2013 Mar	462,258
2013 Apr	516,930
2013 May	608,081
2013 Jun	578,633
2013 Jul	677,083
2013 Aug	775,941
2013 Sep	639,271
2013 Oct	535,649
2013 Nov	390,742
2013 Dec	342,783
2014 Jan	374,568
2014 Feb	401,859
2014 Mar	503,533
2014 Apr	557,275
2014 May	610,148
2014 Jun	595,332
2014 Jul	687,207
2014 Aug	787,020
2014 Sep	652,671
2014 Oct	554,671
2014 Nov	415,750
2014 Dec	366,832
2015 Jan	399,040
2015 Feb	442,963
2015 Mar	545,523
2015 Apr	586,230
2015 May	628,998
2015 Jun	654,715
2015 Jul	766,557
2015 Aug	829,230
2015 Sep	696,849
2015 Oct	597,629
2015 Nov	475,257
2015 Dec	407,035
2016 Jan	448,784
2016 Feb	506,179
2016 Mar	611,987
2016 Apr	663,878
2016 May	726,980
2016 Jun	759,256
2016 Jul	849,148
2016 Aug	891,091
2016 Sep	768,042
2016 Oct	702,530
2016 Nov	545,468
2016 Dec	457,565
2017 Jan	503,654
2017 Feb	541,368
2017 Mar	647,679
2017 Apr	710,409
2017 May	745,096
2017 Jun	794,118
2017 Jul	864,476
2017 Aug	939,077
2017 Sep	818,705
2017 Oct	734,287
2017 Nov	582,743
2017 Dec	478,377
2018 Jan	534,281
2018 Feb	555,841
2018 Mar	652,082
2018 Apr	689,214
2018 May	755,491
2018 Jun	782,628
2018 Jul	837,740
2018 Aug	936,644
2018 Sep	806,267
2018 Oct	721,989
2018 Nov	575,096
2018 Dec	496,993
2019 Jan	486,306
2019 Feb	498,081
2019 Mar	606,616
2019 Apr	608,322
2019 May	665,724
2019 Jun	714,041
2019 Jul	747,112
2019 Aug	828,426
2019 Sep	719,254
2019 Oct	629,555
2019 Nov	508,290
2019 Dec	445,470
2020 Jan	488,461
2020 Feb	540,254
2020 Mar	297,649
2020 Apr	2,191
2020 May	2,955
2020 Jun	14,932
2020 Jul	95,576
2020 Aug	240,322
2020 Sep	251,221
2020 Oct	253,895
2020 Nov	116,634
2020 Dec	137,446
2021 Jan	93,013
2021 Feb	40,883
2021 Mar	60,163
2021 Apr	95,116
2021 May	179,599
2021 Jun	321,985
2021 Jul	552,399
2021 Aug	780,123
2021 Sep	697,572
2021 Oct	655,682
2021 Nov	521,638
2021 Dec	397,592
2022 Jan	341,744
2022 Feb	391,699
2022 Mar	569,482
2022 Apr	727,326
2022 May	779,426
2022 Jun	833,955

1.5.1.1 Seasonal Subseries Plot

# Plot Seasonal Subseries Plot
tourism_madeira_until2022 %>%
  gg_subseries(Overnight_Stays) +
  theme(strip.text.y = element_blank()) +
  ggtitle("Madeira - Seasonality of Overnight Stays")

1.5.1.2 Time Series Variation

# Difference from December 2000 to August 2000
diff_2000 <- tourism_madeira_until2022 %>%
  mutate(Diff_to_August = difference(Overnight_Stays, 4)) %>%
  filter_index("2000 Dec")

# Difference from December 2019 to August 2019
diff_2019 <- tourism_madeira_until2022 %>%
  mutate(Diff_to_August = difference(Overnight_Stays, 4)) %>%
  filter_index("2019 Dec")

# Show in one table
bind_rows(diff_2000, diff_2019) %>%
  select(Month, Overnight_Stays, Diff_to_August) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Madeira's Seasonal Variation: 2000 vs. 2019</span>", digits = 2, format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2:3, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
  footnote("Diff_to_August = Diff between Dec and Aug of the same year")

Madeira’s Seasonal Variation: 2000 vs. 2019

Month	Overnight_Stays	Diff_to_August
2000 Dec	333,601	-151,675
2019 Dec	445,470	-382,956
Note:
Diff_to_August = Diff between Dec and Aug of the same year

rm(diff_2000, diff_2019) # remove variables from R environment

1.5.1.3 Trend Calculation

# Absolute and relative annual Differences of Overnight Stays
tourism_madeira_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  mutate(across(c("Sum_Overnight_Stays", "Diff_abs", "Diff_rel"), ~ format(.x, big.mark = ",", digits = 2))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Abs. and rel. annual Differences of Overnight Stays in Madeira</span>", align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Abs. and rel. annual Differences of Overnight Stays in Madeira

Year	Sum_Overnight_Stays	Diff_abs	Diff_rel
2000	4,961,781	NA	NA
2001	5,438,348	476,567	0.0960
2002	5,468,706	30,358	0.0056
2003	5,597,985	129,279	0.0236
2004	5,493,076	-104,909	-0.0187
2005	5,638,400	145,324	0.0265
2006	5,729,200	90,800	0.0161
2007	5,990,015	260,815	0.0455
2008	6,208,144	218,129	0.0364
2009	5,496,926	-711,218	-0.1146
2010	4,993,525	-503,401	-0.0916
2011	5,565,286	571,761	0.1145
2012	5,507,685	-57,601	-0.0104
2013	6,214,949	707,264	0.1284
2014	6,506,866	291,917	0.0470
2015	7,030,026	523,160	0.0804
2016	7,930,908	900,882	0.1281
2017	8,359,989	429,081	0.0541
2018	8,344,266	-15,723	-0.0019
2019	7,457,197	-887,069	-0.1063
2020	2,441,536	-5,015,661	-0.6726
2021	4,395,765	1,954,229	0.8004
2022	3,643,632	-752,133	-0.1711

# Calculate Mean of relative annual Differences of Overnight Stays: 2001-2009
mean_diff_2001 <- tourism_madeira_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  filter_index("2001", "2002","2003","2004","2005","2006","2007","2008", "2009") %>%
  select(Year, Diff_rel) %>%
  features(.var = Diff_rel, list(Mean_Diff_rel = mean)) %>%
  mutate(Year = "2000-2009")

# Calculate Mean of relative annual Differences of Overnight Stays: 2010-2019
mean_diff_2010 <- tourism_madeira_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  filter_index("2010", "2011", "2012","2013","2014","2015","2016","2017","2018", "2019") %>%
  select(Year, Diff_rel) %>%
  features(.var = Diff_rel, list(Mean_Diff_rel = mean)) %>%
  mutate(Year = "2010-2019")

# Show results in one table
bind_rows(mean_diff_2001, mean_diff_2010) %>%
  select(Year, Mean_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean of rel. annual Differences of Overnight Stays</span>", digits = 4, format.args = list(big.mark = ","), align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Mean of rel. annual Differences of Overnight Stays

Year	Mean_Diff_rel
2000-2009	0.0129
2010-2019	0.0342

rm(mean_diff_2001, mean_diff_2010) # remove variables from R environment

# Calculate Seasonal Difference of months in 2022 to 2021 and 2019
tourism_madeira_until2022 %>%
  mutate(Year = year(Month)) %>%
  mutate(SeasDiff_to_2021_abs = difference(Overnight_Stays, 12)) %>%
  mutate(SeasDiff_to_2021_rel = SeasDiff_to_2021_abs/(Overnight_Stays-SeasDiff_to_2021_abs)) %>%
  mutate(SeasDiff_to_2019_abs = difference(Overnight_Stays, 36)) %>%
  mutate(SeasDiff_to_2019_rel = SeasDiff_to_2019_abs/(Overnight_Stays-SeasDiff_to_2019_abs)) %>%
  filter(Year == 2022) %>%
  select(Month, Overnight_Stays, SeasDiff_to_2021_abs, SeasDiff_to_2021_rel, SeasDiff_to_2019_abs, SeasDiff_to_2019_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Differences of 2022 to 2021 & 2019</span>", digits = 4, format.args = list(big.mark = ","), align = "lccccc") %>%
  column_spec(2:6, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Differences of 2022 to 2021 & 2019

Month	Overnight_Stays	SeasDiff_to_2021_abs	SeasDiff_to_2021_rel	SeasDiff_to_2019_abs	SeasDiff_to_2019_rel
2022 Jan	341,744	248,731	2.6742	-144,562	-0.2973
2022 Feb	391,699	350,816	8.5810	-106,382	-0.2136
2022 Mar	569,482	509,319	8.4657	-37,134	-0.0612
2022 Apr	727,326	632,210	6.6467	119,004	0.1956
2022 May	779,426	599,827	3.3398	113,702	0.1708
2022 Jun	833,955	511,970	1.5900	119,914	0.1679

1.5.1.4 STL Decomposition

# Fit STL decomposition to data
dcmp_madeira <- tourism_madeira_until2022 %>%
  model(STL(Overnight_Stays))

 # Plot components
dcmp_madeira %>%
  components() %>%
  autoplot() +
  ggtitle("Madeira - STL decomposition")

# Superimpose trend on top of time series
tourism_madeira_until2022 %>%
  autoplot(Overnight_Stays, color = "gray") +
  autolayer(components(dcmp_madeira), trend, color = "red") +
  ggtitle("Madeira - Overnight Stays with superimposed Trend")

1.5.1.5 Time Series Plot: Detailed View

# Create Time plot for period 2000-2022
tourism_madeira_until2022 %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Madeira: 2000-2022")

# Create Time plot for period 2000-2019
tourism_madeira_until2019 %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Madeira: 2000-2019")

# Create Time plot for period 2020-2022
tourism_madeira_until2022 %>%
  filter(year(Month) > 2019) %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Madeira: 2020-2022")

1.5.2 Algarve

# Show tsibble
tourism_algarve_until2022 %>%
  select(Month, Overnight_Stays) %>% 
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Monthly Number of Overnight Stays in Algarve: 2000-2022</span>", format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Monthly Number of Overnight Stays in Algarve: 2000-2022

Month	Overnight_Stays
2000 Jan	482,298
2000 Feb	668,668
2000 Mar	940,769
2000 Apr	1,204,711
2000 May	1,370,289
2000 Jun	1,635,456
2000 Jul	1,994,355
2000 Aug	2,155,769
2000 Sep	1,730,037
2000 Oct	1,308,086
2000 Nov	632,830
2000 Dec	448,204
2001 Jan	495,966
2001 Feb	731,372
2001 Mar	899,198
2001 Apr	1,155,935
2001 May	1,282,699
2001 Jun	1,586,267
2001 Jul	1,936,420
2001 Aug	2,067,675
2001 Sep	1,624,419
2001 Oct	1,164,255
2001 Nov	560,068
2001 Dec	395,918
2002 Jan	461,045
2002 Feb	699,389
2002 Mar	1,047,155
2002 Apr	994,476
2002 May	1,312,043
2002 Jun	1,629,825
2002 Jul	2,003,531
2002 Aug	2,326,464
2002 Sep	1,695,076
2002 Oct	1,141,575
2002 Nov	581,628
2002 Dec	402,096
2003 Jan	467,884
2003 Feb	686,326
2003 Mar	905,474
2003 Apr	1,124,760
2003 May	1,351,136
2003 Jun	1,651,162
2003 Jul	1,965,914
2003 Aug	2,309,345
2003 Sep	1,558,200
2003 Oct	1,087,039
2003 Nov	532,301
2003 Dec	398,038
2004 Jan	464,629
2004 Feb	675,615
2004 Mar	836,069
2004 Apr	1,049,221
2004 May	1,162,483
2004 Jun	1,408,698
2004 Jul	1,782,330
2004 Aug	2,262,316
2004 Sep	1,551,469
2004 Oct	1,118,943
2004 Nov	506,085
2004 Dec	435,015
2005 Jan	471,700
2005 Feb	667,300
2005 Mar	901,300
2005 Apr	919,100
2005 May	1,307,000
2005 Jun	1,535,200
2005 Jul	1,921,300
2005 Aug	2,345,800
2005 Sep	1,630,200
2005 Oct	1,150,200
2005 Nov	539,700
2005 Dec	425,300
2006 Jan	471,700
2006 Feb	631,400
2006 Mar	800,700
2006 Apr	1,164,700
2006 May	1,238,200
2006 Jun	1,563,700
2006 Jul	2,037,800
2006 Aug	2,419,500
2006 Sep	1,672,600
2006 Oct	1,136,000
2006 Nov	547,200
2006 Dec	480,100
2007 Jan	492,114
2007 Feb	641,596
2007 Mar	908,698
2007 Apr	1,173,146
2007 May	1,340,818
2007 Jun	1,627,451
2007 Jul	2,115,385
2007 Aug	2,439,108
2007 Sep	1,741,610
2007 Oct	1,185,860
2007 Nov	563,182
2007 Dec	475,416
2008 Jan	470,877
2008 Feb	674,063
2008 Mar	991,973
2008 Apr	946,986
2008 May	1,381,549
2008 Jun	1,558,966
2008 Jul	2,028,623
2008 Aug	2,436,162
2008 Sep	1,693,992
2008 Oct	1,140,194
2008 Nov	530,826
2008 Dec	410,953
2009 Jan	411,615
2009 Feb	557,401
2009 Mar	710,502
2009 Apr	1,017,779
2009 May	1,138,068
2009 Jun	1,489,130
2009 Jul	1,891,157
2009 Aug	2,315,586
2009 Sep	1,539,886
2009 Oct	1,010,273
2009 Nov	475,789
2009 Dec	370,417
2010 Jan	366,296
2010 Feb	533,056
2010 Mar	742,227
2010 Apr	902,745
2010 May	1,107,303
2010 Jun	1,464,695
2010 Jul	2,050,478
2010 Aug	2,468,924
2010 Sep	1,696,356
2010 Oct	1,104,659
2010 Nov	445,221
2010 Dec	365,490
2011 Jan	357,209
2011 Feb	503,831
2011 Mar	761,343
2011 Apr	1,177,115
2011 May	1,169,516
2011 Jun	1,576,730
2011 Jul	2,208,160
2011 Aug	2,572,404
2011 Sep	1,731,056
2011 Oct	1,161,751
2011 Nov	427,550
2011 Dec	333,201
2012 Jan	359,355
2012 Feb	531,709
2012 Mar	751,024
2012 Apr	1,017,976
2012 May	1,194,673
2012 Jun	1,678,327
2012 Jul	2,296,474
2012 Aug	2,622,801
2012 Sep	1,829,252
2012 Oct	1,244,751
2012 Nov	453,958
2012 Dec	346,474
2013 Jan	369,969
2013 Feb	520,055
2013 Mar	840,024
2013 Apr	986,191
2013 May	1,382,234
2013 Jun	1,814,108
2013 Jul	2,387,304
2013 Aug	2,764,686
2013 Sep	1,943,037
2013 Oct	1,291,360
2013 Nov	455,695
2013 Dec	358,062
2014 Jan	377,387
2014 Feb	543,470
2014 Mar	749,773
2014 Apr	1,337,145
2014 May	1,538,342
2014 Jun	1,994,167
2014 Jul	2,529,246
2014 Aug	3,069,865
2014 Sep	2,089,656
2014 Oct	1,477,481
2014 Nov	502,473
2014 Dec	382,543
2015 Jan	381,607
2015 Feb	544,777
2015 Mar	827,071
2015 Apr	1,242,844
2015 May	1,654,526
2015 Jun	2,079,484
2015 Jul	2,688,710
2015 Aug	3,108,357
2015 Sep	2,196,681
2015 Oct	1,553,142
2015 Nov	552,778
2015 Dec	426,419
2016 Jan	443,150
2016 Feb	664,278
2016 Mar	1,089,392
2016 Apr	1,335,308
2016 May	1,828,292
2016 Jun	2,288,337
2016 Jul	2,848,570
2016 Aug	3,204,047
2016 Sep	2,378,618
2016 Oct	1,793,822
2016 Nov	653,514
2016 Dec	478,510
2017 Jan	495,629
2017 Feb	704,532
2017 Mar	1,015,421
2017 Apr	1,765,170
2017 May	1,970,072
2017 Jun	2,417,100
2017 Jul	2,968,641
2017 Aug	3,295,406
2017 Sep	2,470,298
2017 Oct	1,911,961
2017 Nov	680,373
2017 Dec	512,548
2018 Jan	503,908
2018 Feb	731,090
2018 Mar	1,151,455
2018 Apr	1,575,078
2018 May	2,003,996
2018 Jun	2,381,154
2018 Jul	2,981,643
2018 Aug	3,371,918
2018 Sep	2,499,368
2018 Oct	1,956,693
2018 Nov	732,141
2018 Dec	554,803
2019 Jan	548,686
2019 Feb	739,981
2019 Mar	1,078,918
2019 Apr	1,795,494
2019 May	1,990,529
2019 Jun	2,425,834
2019 Jul	2,988,668
2019 Aug	3,439,271
2019 Sep	2,573,527
2019 Oct	1,930,852
2019 Nov	785,875
2019 Dec	602,860
2020 Jan	560,368
2020 Feb	844,247
2020 Mar	513,360
2020 Apr	25,614
2020 May	40,932
2020 Jun	330,393
2020 Jul	1,035,732
2020 Aug	2,090,569
2020 Sep	1,418,185
2020 Oct	696,087
2020 Nov	181,873
2020 Dec	153,351
2021 Jan	105,336
2021 Feb	66,194
2021 Mar	84,413
2021 Apr	138,661
2021 May	502,057
2021 Jun	1,182,009
2021 Jul	1,551,789
2021 Aug	2,762,537
2021 Sep	1,869,194
2021 Oct	1,584,764
2021 Nov	651,051
2021 Dec	376,031
2022 Jan	344,634
2022 Feb	590,122
2022 Mar	873,841
2022 Apr	1,629,377
2022 May	1,867,744
2022 Jun	2,230,207

1.5.2.1 Seasonal Subseries Plot

# Plot Seasonal Subseries Plot
tourism_algarve_until2022 %>%
  gg_subseries(Overnight_Stays) +
  theme(strip.text.y = element_blank()) +
  ggtitle("Algarve - Seasonality of Overnight Stays")

1.5.2.2 Time Series Variation

# Difference from December 2000 to August 2000
diff_2000 <- tourism_algarve_until2022 %>%
  mutate(Diff_to_August = difference(Overnight_Stays, 4)) %>%
  filter_index("2000 Dec")

# Difference from December 2019 to August 2019
diff_2019 <- tourism_algarve_until2022 %>%
  mutate(Diff_to_August = difference(Overnight_Stays, 4)) %>%
  filter_index("2019 Dec")

# Show in one table
bind_rows(diff_2000, diff_2019) %>%
  select(Month, Overnight_Stays, Diff_to_August) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Algarve's Seasonal Variation: 2000 vs. 2019</span>", digits = 2, format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2:3, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
  footnote("Diff_to_August = Diff between Dec and Aug of the same year")

Algarve’s Seasonal Variation: 2000 vs. 2019

Month	Overnight_Stays	Diff_to_August
2000 Dec	448,204	-1,707,565
2019 Dec	602,860	-2,836,411
Note:
Diff_to_August = Diff between Dec and Aug of the same year

rm(diff_2000, diff_2019) # remove variables from R environment

1.5.2.3 Trend Calculation

# Absolute and relative annual Differences of Overnight Stays
tourism_algarve_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  mutate(across(c("Sum_Overnight_Stays", "Diff_abs", "Diff_rel"), ~ format(.x, big.mark = ",", digits = 3))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Abs. and rel. annual Differences of Overnight Stays in Algarve</span>", align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Abs. and rel. annual Differences of Overnight Stays in Algarve

Year	Sum_Overnight_Stays	Diff_abs	Diff_rel
2000	14,571,472	NA	NA
2001	13,900,192	-671,280	-0.0461
2002	14,294,303	394,111	0.0284
2003	14,037,579	-256,724	-0.0180
2004	13,252,873	-784,706	-0.0559
2005	13,814,100	561,227	0.0423
2006	14,163,600	349,500	0.0253
2007	14,704,384	540,784	0.0382
2008	14,265,164	-439,220	-0.0299
2009	12,927,603	-1,337,561	-0.0938
2010	13,247,450	319,847	0.0247
2011	13,979,866	732,416	0.0553
2012	14,326,774	346,908	0.0248
2013	15,112,725	785,951	0.0549
2014	16,591,548	1,478,823	0.0979
2015	17,256,396	664,848	0.0401
2016	19,005,838	1,749,442	0.1014
2017	20,207,151	1,201,313	0.0632
2018	20,443,247	236,096	0.0117
2019	20,900,495	457,248	0.0224
2020	7,890,711	-13,009,784	-0.6225
2021	10,874,036	2,983,325	0.3781
2022	7,535,925	-3,338,111	-0.3070

# Calculate Mean of relative annual Differences of Overnight Stays: 2001-2009
mean_diff_2001 <- tourism_algarve_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  filter_index("2001", "2002","2003","2004","2005","2006","2007","2008", "2009") %>%
  select(Year, Diff_rel) %>%
  features(.var = Diff_rel, list(Mean_Diff_rel = mean)) %>%
  mutate(Year = "2000-2009")

# Calculate Mean of relative annual Differences of Overnight Stays: 2010-2019
mean_diff_2010 <- tourism_algarve_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  filter_index("2010", "2011", "2012","2013","2014","2015","2016","2017","2018", "2019") %>%
  select(Year, Diff_rel) %>%
  features(.var = Diff_rel, list(Mean_Diff_rel = mean)) %>%
  mutate(Year = "2010-2019")

# Show results in one table
bind_rows(mean_diff_2001, mean_diff_2010) %>%
  select(Year, Mean_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean of rel. annual Differences of Overnight Stays</span>", digits = 4, format.args = list(big.mark = ","), align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Mean of rel. annual Differences of Overnight Stays

Year	Mean_Diff_rel
2000-2009	-0.0122
2010-2019	0.0496

rm(mean_diff_2001, mean_diff_2010) # remove variables from R environment

# Calculate Seasonal Difference of months in 2022 to 2021 and 2019
tourism_algarve_until2022 %>%
  mutate(Year = year(Month)) %>%
  mutate(SeasDiff_to_2021_abs = difference(Overnight_Stays, 12)) %>%
  mutate(SeasDiff_to_2021_rel = SeasDiff_to_2021_abs/(Overnight_Stays-SeasDiff_to_2021_abs)) %>%
  mutate(SeasDiff_to_2019_abs = difference(Overnight_Stays, 36)) %>%
  mutate(SeasDiff_to_2019_rel = SeasDiff_to_2019_abs/(Overnight_Stays-SeasDiff_to_2019_abs)) %>%
  filter(Year == 2022) %>%
  select(Month, Overnight_Stays, SeasDiff_to_2021_abs, SeasDiff_to_2021_rel, SeasDiff_to_2019_abs, SeasDiff_to_2019_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Differences of 2022 to 2021 & 2019</span>", digits = 4, format.args = list(big.mark = ","), align = "lccccc") %>%
  column_spec(2:6, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Differences of 2022 to 2021 & 2019

Month	Overnight_Stays	SeasDiff_to_2021_abs	SeasDiff_to_2021_rel	SeasDiff_to_2019_abs	SeasDiff_to_2019_rel
2022 Jan	344,634	239,298	2.2718	-204,052	-0.3719
2022 Feb	590,122	523,928	7.9150	-149,859	-0.2025
2022 Mar	873,841	789,428	9.3520	-205,077	-0.1901
2022 Apr	1,629,377	1,490,716	10.7508	-166,117	-0.0925
2022 May	1,867,744	1,365,687	2.7202	-122,785	-0.0617
2022 Jun	2,230,207	1,048,198	0.8868	-195,627	-0.0806

1.5.2.4 STL Decomposition

# Fit STL decomposition to data
dcmp_algarve <- tourism_algarve_until2022 %>%
  model(STL(Overnight_Stays))

 # Plot components
dcmp_algarve %>%
  components() %>%
  autoplot() +
  ggtitle("Algarve - STL decomposition")

# Superimpose trend on top of time series
tourism_algarve_until2022 %>%
  autoplot(Overnight_Stays, color = "gray") +
  autolayer(components(dcmp_algarve), trend, color = "red") +
  ggtitle("Algarve - Overnight Stays with superimposed Trend")

1.5.2.5 Time Series Plot: Detailed View

# Create Time plot for period 2000-2022
tourism_algarve_until2022 %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Algarve: 2000-2022")

# Create Time plot for period 2000-2019
tourism_algarve_until2019 %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Algarve: 2000-2019")

# Create Time plot for period 2020-2022
tourism_algarve_until2022 %>%
  filter(year(Month) > 2019) %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Algarve: 2020-2022")

1.5.3 Alentejo

# Show tsibble
tourism_alentejo_until2022 %>%
  select(Month, Overnight_Stays) %>% 
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Monthly Number of Overnight Stays in Alentejo: 2000-2022</span>", format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Monthly Number of Overnight Stays in Alentejo: 2000-2022

Month	Overnight_Stays
2000 Jan	34,281
2000 Feb	42,287
2000 Mar	67,520
2000 Apr	85,884
2000 May	65,339
2000 Jun	71,263
2000 Jul	93,501
2000 Aug	132,360
2000 Sep	87,037
2000 Oct	64,620
2000 Nov	51,168
2000 Dec	49,890
2001 Jan	41,628
2001 Feb	52,517
2001 Mar	67,176
2001 Apr	91,294
2001 May	73,966
2001 Jun	83,290
2001 Jul	105,089
2001 Aug	136,296
2001 Sep	86,028
2001 Oct	66,974
2001 Nov	51,649
2001 Dec	41,657
2002 Jan	39,474
2002 Feb	55,105
2002 Mar	83,450
2002 Apr	72,810
2002 May	76,625
2002 Jun	83,525
2002 Jul	102,151
2002 Aug	139,476
2002 Sep	89,516
2002 Oct	63,692
2002 Nov	55,950
2002 Dec	42,334
2003 Jan	42,969
2003 Feb	47,839
2003 Mar	66,493
2003 Apr	88,707
2003 May	91,450
2003 Jun	89,474
2003 Jul	103,914
2003 Aug	138,159
2003 Sep	93,305
2003 Oct	72,716
2003 Nov	61,119
2003 Dec	51,236
2004 Jan	45,473
2004 Feb	63,350
2004 Mar	67,470
2004 Apr	89,156
2004 May	89,156
2004 Jun	90,271
2004 Jul	102,341
2004 Aug	155,529
2004 Sep	99,960
2004 Oct	83,283
2004 Nov	55,812
2004 Dec	51,215
2005 Jan	45,800
2005 Feb	51,200
2005 Mar	71,500
2005 Apr	75,700
2005 May	88,100
2005 Jun	80,200
2005 Jul	90,700
2005 Aug	147,300
2005 Sep	92,900
2005 Oct	73,000
2005 Nov	64,700
2005 Dec	58,100
2006 Jan	46,800
2006 Feb	56,500
2006 Mar	61,600
2006 Apr	93,100
2006 May	82,700
2006 Jun	79,100
2006 Jul	99,000
2006 Aug	136,600
2006 Sep	98,800
2006 Oct	83,500
2006 Nov	68,300
2006 Dec	72,600
2007 Jan	51,510
2007 Feb	60,557
2007 Mar	78,912
2007 Apr	99,059
2007 May	89,326
2007 Jun	96,349
2007 Jul	113,127
2007 Aug	164,837
2007 Sep	109,348
2007 Oct	89,006
2007 Nov	77,312
2007 Dec	69,226
2008 Jan	51,548
2008 Feb	63,947
2008 Mar	88,989
2008 Apr	84,580
2008 May	101,576
2008 Jun	91,173
2008 Jul	107,299
2008 Aug	153,743
2008 Sep	117,477
2008 Oct	94,237
2008 Nov	70,628
2008 Dec	60,476
2009 Jan	50,256
2009 Feb	63,694
2009 Mar	67,975
2009 Apr	96,647
2009 May	97,936
2009 Jun	107,295
2009 Jul	114,085
2009 Aug	176,426
2009 Sep	109,573
2009 Oct	92,353
2009 Nov	68,602
2009 Dec	59,473
2010 Jan	53,653
2010 Feb	62,257
2010 Mar	77,588
2010 Apr	99,982
2010 May	101,387
2010 Jun	108,611
2010 Jul	126,498
2010 Aug	178,380
2010 Sep	127,822
2010 Oct	104,174
2010 Nov	69,271
2010 Dec	62,935
2011 Jan	60,457
2011 Feb	67,260
2011 Mar	83,464
2011 Apr	102,958
2011 May	101,223
2011 Jun	120,148
2011 Jul	136,999
2011 Aug	212,668
2011 Sep	129,606
2011 Oct	101,185
2011 Nov	62,121
2011 Dec	65,563
2012 Jan	49,716
2012 Feb	58,638
2012 Mar	72,210
2012 Apr	87,406
2012 May	96,946
2012 Jun	115,885
2012 Jul	139,695
2012 Aug	194,368
2012 Sep	127,610
2012 Oct	89,649
2012 Nov	58,900
2012 Dec	51,122
2013 Jan	50,313
2013 Feb	58,615
2013 Mar	92,426
2013 Apr	100,996
2013 May	123,431
2013 Jun	143,946
2013 Jul	171,016
2013 Aug	252,423
2013 Sep	158,839
2013 Oct	109,956
2013 Nov	82,040
2013 Dec	72,692
2014 Jan	56,872
2014 Feb	64,346
2014 Mar	102,852
2014 Apr	151,151
2014 May	148,593
2014 Jun	154,231
2014 Jul	194,227
2014 Aug	303,902
2014 Sep	186,247
2014 Oct	133,884
2014 Nov	86,161
2014 Dec	81,830
2015 Jan	68,436
2015 Feb	84,417
2015 Mar	116,291
2015 Apr	145,183
2015 May	172,016
2015 Jun	182,765
2015 Jul	238,708
2015 Aug	358,044
2015 Sep	216,474
2015 Oct	148,376
2015 Nov	99,794
2015 Dec	93,804
2016 Jan	74,572
2016 Feb	97,522
2016 Mar	144,216
2016 Apr	153,386
2016 May	168,235
2016 Jun	215,800
2016 Jul	271,212
2016 Aug	380,776
2016 Sep	249,098
2016 Oct	175,862
2016 Nov	102,775
2016 Dec	100,859
2017 Jan	83,249
2017 Feb	105,210
2017 Mar	121,167
2017 Apr	217,906
2017 May	196,622
2017 Jun	248,582
2017 Jul	323,496
2017 Aug	431,571
2017 Sep	287,242
2017 Oct	212,357
2017 Nov	127,745
2017 Dec	132,238
2018 Jan	95,453
2018 Feb	120,303
2018 Mar	162,886
2018 Apr	187,186
2018 May	239,851
2018 Jun	264,588
2018 Jul	339,564
2018 Aug	446,375
2018 Sep	304,516
2018 Oct	230,827
2018 Nov	149,080
2018 Dec	135,316
2019 Jan	114,710
2019 Feb	122,635
2019 Mar	172,412
2019 Apr	241,790
2019 May	259,714
2019 Jun	306,048
2019 Jul	360,566
2019 Aug	484,403
2019 Sep	327,937
2019 Oct	238,677
2019 Nov	171,296
2019 Dec	138,642
2020 Jan	126,349
2020 Feb	167,411
2020 Mar	70,530
2020 Apr	13,892
2020 May	38,343
2020 Jun	159,738
2020 Jul	272,786
2020 Aug	407,020
2020 Sep	258,651
2020 Oct	167,448
2020 Nov	73,734
2020 Dec	73,353
2021 Jan	48,435
2021 Feb	40,443
2021 Mar	60,251
2021 Apr	85,179
2021 May	169,690
2021 Jun	254,243
2021 Jul	329,058
2021 Aug	461,844
2021 Sep	308,273
2021 Oct	250,949
2021 Nov	156,624
2021 Dec	115,100
2022 Jan	96,107
2022 Feb	141,508
2022 Mar	167,854
2022 Apr	248,959
2022 May	258,413
2022 Jun	300,520

1.5.3.1 Seasonal Subseries Plot

# Plot Seasonality Plot
tourism_alentejo_until2022 %>%
  gg_subseries(Overnight_Stays) +
  theme(strip.text.y = element_blank()) +
  ggtitle("Alentejo - Seasonality of Overnight Stays")

1.5.3.2 Time Series Variation

# Difference from January 2001 to August 2000
diff_2000 <- tourism_alentejo_until2022 %>%
  mutate(Diff_to_August = difference(Overnight_Stays, 5)) %>%
  filter_index("2001 Jan")

# Difference from January 2020 to August 2019
diff_2019 <- tourism_alentejo_until2022 %>%
  mutate(Diff_to_August = difference(Overnight_Stays, 5)) %>%
  filter_index("2020 Jan")

# Show in one table
bind_rows(diff_2000, diff_2019) %>%
  select(Month, Overnight_Stays, Diff_to_August) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Alentejo's Seasonal Variation: 2000/2001 vs. 2019/2020</span>", digits = 2, format.args = list(big.mark = ","), align = "lcc") %>%
  column_spec(2:3, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F) %>%
  footnote("Diff_to_August = Diff between Jan and Aug of the previous year")

Alentejo’s Seasonal Variation: 2000/2001 vs. 2019/2020

Month	Overnight_Stays	Diff_to_August
2001 Jan	41,628	-90,732
2020 Jan	126,349	-358,054
Note:
Diff_to_August = Diff between Jan and Aug of the previous year

rm(diff_2000, diff_2019) # remove variables from R environment

1.5.3.3 Trend Calculation

# Absolute and relative annual Differences of Overnight Stays
tourism_alentejo_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  mutate(across(c("Sum_Overnight_Stays", "Diff_abs", "Diff_rel"), ~ format(.x, big.mark = ",", digits = 2))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Abs. and rel. annual Differences of Overnight Stays in Alentejo</span>", align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Abs. and rel. annual Differences of Overnight Stays in Alentejo

Year	Sum_Overnight_Stays	Diff_abs	Diff_rel
2000	845,150	NA	NA
2001	897,564	52,414	0.0620
2002	904,108	6,544	0.0073
2003	947,381	43,273	0.0479
2004	993,016	45,635	0.0482
2005	939,200	-53,816	-0.0542
2006	978,600	39,400	0.0420
2007	1,098,569	119,969	0.1226
2008	1,085,673	-12,896	-0.0117
2009	1,104,315	18,642	0.0172
2010	1,172,558	68,243	0.0618
2011	1,243,652	71,094	0.0606
2012	1,142,145	-101,507	-0.0816
2013	1,416,693	274,548	0.2404
2014	1,664,296	247,603	0.1748
2015	1,924,308	260,012	0.1562
2016	2,134,313	210,005	0.1091
2017	2,487,385	353,072	0.1654
2018	2,675,945	188,560	0.0758
2019	2,938,830	262,885	0.0982
2020	1,829,255	-1,109,575	-0.3776
2021	2,280,089	450,834	0.2465
2022	1,213,361	-1,066,728	-0.4678

# Calculate Mean of relative annual Differences of Overnight Stays: 2001-2009
mean_diff_2001 <- tourism_alentejo_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  filter_index("2001", "2002","2003","2004","2005","2006","2007","2008", "2009") %>%
  select(Year, Diff_rel) %>%
  features(.var = Diff_rel,list(Mean_Diff_rel = mean)) %>%
  mutate(Year = "2000-2009")

# Calculate Mean of relative annual Differences of Overnight Stays: 2010-2019
mean_diff_2010 <- tourism_alentejo_until2022 %>%
  index_by(Year = year(Month)) %>%
  summarise(Sum_Overnight_Stays = sum(Overnight_Stays)) %>%
  mutate(Diff_abs = difference(Sum_Overnight_Stays, 1)) %>%
  mutate(Diff_rel = Diff_abs/(Sum_Overnight_Stays - Diff_abs)) %>%
  filter_index("2010", "2011", "2012","2013","2014","2015","2016","2017","2018", "2019") %>%
  select(Year, Diff_rel) %>%
  features(.var = Diff_rel,list(Mean_Diff_rel = mean)) %>%
  mutate(Year = "2010-2019")

# Show results in one table
bind_rows(mean_diff_2001, mean_diff_2010) %>%
  select(Year, Mean_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean of rel. annual Differences of Overnight Stays</span>", digits = 4, format.args = list(big.mark = ","), align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Mean of rel. annual Differences of Overnight Stays

Year	Mean_Diff_rel
2000-2009	0.0312
2010-2019	0.1061

rm(mean_diff_2001, mean_diff_2010) # remove variables from R environment

# Calculate Seasonal Difference of months in 2022 to 2021 and 2019
tourism_alentejo_until2022 %>%
  mutate(Year = year(Month)) %>%
  mutate(SeasDiff_to_2021_abs = difference(Overnight_Stays, 12)) %>%
  mutate(SeasDiff_to_2021_rel = SeasDiff_to_2021_abs/(Overnight_Stays-SeasDiff_to_2021_abs)) %>%
  mutate(SeasDiff_to_2019_abs = difference(Overnight_Stays, 36)) %>%
  mutate(SeasDiff_to_2019_rel = SeasDiff_to_2019_abs/(Overnight_Stays-SeasDiff_to_2019_abs)) %>%
  filter(Year == 2022) %>%
  select(Month, Overnight_Stays, SeasDiff_to_2021_abs, SeasDiff_to_2021_rel, SeasDiff_to_2019_abs, SeasDiff_to_2019_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Differences of 2022 to 2021 & 2019</span>", digits = 4, format.args = list(big.mark = ","), align = "lccccc") %>%
  column_spec(2:6, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Differences of 2022 to 2021 & 2019

Month	Overnight_Stays	SeasDiff_to_2021_abs	SeasDiff_to_2021_rel	SeasDiff_to_2019_abs	SeasDiff_to_2019_rel
2022 Jan	96,107	47,672	0.9842	-18,603	-0.1622
2022 Feb	141,508	101,065	2.4989	18,873	0.1539
2022 Mar	167,854	107,603	1.7859	-4,558	-0.0264
2022 Apr	248,959	163,780	1.9228	7,169	0.0296
2022 May	258,413	88,723	0.5229	-1,301	-0.0050
2022 Jun	300,520	46,277	0.1820	-5,528	-0.0181

1.5.3.4 STL Decomposition

# Fit STL decomposition to data
dcmp_alentejo <- tourism_alentejo_until2022 %>%
  model(STL(Overnight_Stays))

# Plot components
dcmp_alentejo %>%
  components() %>%
  autoplot() +
  ggtitle("Alentejo - STL decomposition")

# Superimpose trend on top of time series
tourism_alentejo_until2022 %>%
  autoplot(Overnight_Stays, color = "gray") +
  autolayer(components(dcmp_alentejo), trend, color = "red") +
  ggtitle("Alentejo - Overnight Stays with superimposed Trend")

1.5.3.5 Detailed Analysis of Time Plots

# Create Time plot for period 2000-2022
tourism_alentejo_until2022 %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Alentejo: 2000-2022")

# Create Time plot for period 2000-2019
tourism_alentejo_until2019 %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Alentejo: 2000-2019")

# Create Time plot for period 2020-2022
tourism_alentejo_until2022 %>%
  filter(year(Month) > 2019) %>%
  autoplot(Overnight_Stays) +
  ggtitle("Overnight Stays in Alentejo: 2020-2022")

2 Fitting and Evaluating Models

2.1 Madeira

2.1.1 Recursive Window Cross-Validation

2.1.1.1 Time series Cross-Validation & Seasonal Strength Test

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira <- tourism_madeira_until2022 %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Testing for Seasonal Strength
data_stretch_madeira %>%
  features(Overnight_Stays, unitroot_nsdiffs) %>%
  group_by(Region) %>%
  summarise(Mean_nsdiffs = (mean(nsdiffs))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Strength Test</span>", align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Strength Test

Region	Mean_nsdiffs
Madeira	1

2.1.1.2 Fitting Models and one-step ahead Forecasts

# Fit models
fit_madeira_stretch <- data_stretch_madeira %>%
  model(
    SNaive = SNAIVE(Overnight_Stays),
    Drift_STL = decomposition_model(STL(Overnight_Stays),RW(season_adjust ~ drift())),
    Naive = NAIVE(Overnight_Stays),
    TSLM = TSLM(Overnight_Stays ~ trend() + season()),
    ETS_auto = ETS(Overnight_Stays),
    HWA = ETS(Overnight_Stays ~ error("A") + trend("A") + season("A")),
    ARIMA_auto = ARIMA(Overnight_Stays),
    ARIMA_d1D1 = ARIMA(Overnight_Stays ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)),
    Prophet = fable.prophet::prophet(Overnight_Stays ~ season(period = 12)),
    SNaive_log = SNAIVE(log(Overnight_Stays)),
    Drift_STL_log = decomposition_model(STL(log(Overnight_Stays)),RW(season_adjust ~ drift())),
    Naive_log = NAIVE(log(Overnight_Stays)),
    TSLM_log = TSLM(log(Overnight_Stays) ~ trend() + season()),
    ETS_auto_log = ETS(log(Overnight_Stays)),
    HWA_log = ETS(log(Overnight_Stays) ~ error("A") + trend("A") + season("A")),
    ARIMA_auto_log = ARIMA(log(Overnight_Stays)),
    ARIMA_d1D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)),
    Prophet_log = fable.prophet::prophet(log(Overnight_Stays) ~ season(period = 12))
    )

# Perform a one-step ahead Forecast
fc_madeira_stretch <- fit_madeira_stretch %>% forecast(h=1)

2.1.1.3 Forecast Errors

# Calculate forecast error per observation and model
error_fc_madeira_stretch <- merge(tourism_madeira_until2022, fc_madeira_stretch, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# Show table
error_fc_madeira_stretch %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Forecast Error per Observation and Model</span>", digits = 2, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Forecast Error per Observation and Model

Month	Overnight_Stays	Model	Point_Forecast	Forecast_Error
2010 Jan	319,379	ARIMA_auto	336,040.22	-16,661.22
2010 Feb	329,697	ARIMA_auto	360,237.41	-30,540.41
2010 Mar	388,978	ARIMA_auto	446,194.07	-57,216.07
2010 Apr	427,950	ARIMA_auto	453,323.31	-25,373.31
2010 May	431,385	ARIMA_auto	424,694.98	6,690.02
2010 Jun	432,522	ARIMA_auto	418,843.54	13,678.46
2010 Jul	492,382	ARIMA_auto	474,033.80	18,348.20
2010 Aug	624,383	ARIMA_auto	587,104.83	37,278.17
2010 Sep	496,609	ARIMA_auto	505,657.48	-9,048.48
2010 Oct	450,841	ARIMA_auto	434,740.50	16,100.50
2010 Nov	327,330	ARIMA_auto	348,898.98	-21,568.98
2010 Dec	272,069	ARIMA_auto	279,968.26	-7,899.26
2011 Jan	286,010	ARIMA_auto	285,074.11	935.89
2011 Feb	319,015	ARIMA_auto	312,488.81	6,526.19
2011 Mar	448,224	ARIMA_auto	404,482.15	43,741.85
2011 Apr	517,979	ARIMA_auto	480,019.55	37,959.45
2011 May	575,401	ARIMA_auto	491,918.43	83,482.57
2011 Jun	519,950	ARIMA_auto	548,653.76	-28,703.76
2011 Jul	589,288	ARIMA_auto	559,857.17	29,430.83
2011 Aug	678,877	ARIMA_auto	688,687.33	-9,810.33
2011 Sep	577,108	ARIMA_auto	553,869.76	23,238.24
2011 Oct	471,268	ARIMA_auto	513,811.49	-42,543.49
2011 Nov	319,900	ARIMA_auto	363,504.37	-43,604.37
2011 Dec	262,266	ARIMA_auto	276,485.96	-14,219.96
2012 Jan	289,312	ARIMA_auto	283,241.63	6,070.37
2012 Feb	329,299	ARIMA_auto	323,846.58	5,452.42
2012 Mar	399,988	ARIMA_auto	437,479.94	-37,491.94
2012 Apr	508,131	ARIMA_auto	457,558.54	50,572.46
2012 May	521,638	ARIMA_auto	526,682.60	-5,044.60
2012 Jun	509,865	ARIMA_auto	492,064.87	17,800.13
2012 Jul	602,837	ARIMA_auto	564,020.18	38,816.82
2012 Aug	681,135	ARIMA_auto	694,868.23	-13,733.23
2012 Sep	562,007	ARIMA_auto	564,899.91	-2,892.91
2012 Oct	468,951	ARIMA_auto	482,451.99	-13,500.99
2012 Nov	350,902	ARIMA_auto	341,471.66	9,430.34
2012 Dec	283,620	ARIMA_auto	294,817.12	-11,197.12
2013 Jan	322,235	ARIMA_auto	302,852.31	19,382.69
2013 Feb	365,343	ARIMA_auto	352,145.29	13,197.71
2013 Mar	462,258	ARIMA_auto	449,728.92	12,529.08
2013 Apr	516,930	ARIMA_auto	532,372.52	-15,442.52
2013 May	608,081	ARIMA_auto	531,063.70	77,017.30
2013 Jun	578,633	ARIMA_auto	567,644.07	10,988.93
2013 Jul	677,083	ARIMA_auto	635,025.69	42,057.31
2013 Aug	775,941	ARIMA_auto	756,754.28	19,186.72
2013 Sep	639,271	ARIMA_auto	640,217.57	-946.57
2013 Oct	535,649	ARIMA_auto	543,604.35	-7,955.35
2013 Nov	390,742	ARIMA_auto	395,039.12	-4,297.12
2013 Dec	342,783	ARIMA_auto	320,902.53	21,880.47
2014 Jan	374,568	ARIMA_auto	358,970.38	15,597.62
2014 Feb	401,859	ARIMA_auto	401,977.09	-118.09
2014 Mar	503,533	ARIMA_auto	492,833.11	10,699.89
2014 Apr	557,275	ARIMA_auto	567,920.89	-10,645.89
2014 May	610,148	ARIMA_auto	610,066.75	81.25
2014 Jun	595,332	ARIMA_auto	570,761.33	24,570.67
2014 Jul	687,207	ARIMA_auto	674,147.19	13,059.81
2014 Aug	787,020	ARIMA_auto	768,493.46	18,526.54
2014 Sep	652,671	ARIMA_auto	656,367.29	-3,696.29
2014 Oct	554,671	ARIMA_auto	542,937.67	11,733.33
2014 Nov	415,750	ARIMA_auto	406,144.14	9,605.86
2014 Dec	366,832	ARIMA_auto	350,789.79	16,042.21
2015 Jan	399,040	ARIMA_auto	389,326.25	9,713.75
2015 Feb	442,963	ARIMA_auto	425,267.38	17,695.62
2015 Mar	545,523	ARIMA_auto	522,804.04	22,718.96
2015 Apr	586,230	ARIMA_auto	605,340.30	-19,110.30
2015 May	628,998	ARIMA_auto	629,769.76	-771.76
2015 Jun	654,715	ARIMA_auto	604,473.56	50,241.44
2015 Jul	766,557	ARIMA_auto	736,542.38	30,014.62
2015 Aug	829,230	ARIMA_auto	845,623.83	-16,393.83
2015 Sep	696,849	ARIMA_auto	688,722.65	8,126.35
2015 Oct	597,629	ARIMA_auto	588,970.39	8,658.61
2015 Nov	475,257	ARIMA_auto	454,073.75	21,183.25
2015 Dec	407,035	ARIMA_auto	409,923.30	-2,888.30
2016 Jan	448,784	ARIMA_auto	432,092.86	16,691.14
2016 Feb	506,179	ARIMA_auto	478,163.85	28,015.15
2016 Mar	611,987	ARIMA_auto	595,166.09	16,820.91
2016 Apr	663,878	ARIMA_auto	649,017.31	14,860.69
2016 May	726,980	ARIMA_auto	713,632.72	13,347.28
2016 Jun	759,256	ARIMA_auto	711,990.88	47,265.12
2016 Jul	849,148	ARIMA_auto	847,776.17	1,371.83
2016 Aug	891,091	ARIMA_auto	929,265.46	-38,174.46
2016 Sep	768,042	ARIMA_auto	759,111.26	8,930.74
2016 Oct	702,530	ARIMA_auto	669,770.28	32,759.72
2016 Nov	545,468	ARIMA_auto	566,784.42	-21,316.42
2016 Dec	457,565	ARIMA_auto	486,929.49	-29,364.49
2017 Jan	503,654	ARIMA_auto	498,293.66	5,360.34
2017 Feb	541,368	ARIMA_auto	550,323.83	-8,955.83
2017 Mar	647,679	ARIMA_auto	648,146.43	-467.43
2017 Apr	710,409	ARIMA_auto	699,470.24	10,938.76
2017 May	745,096	ARIMA_auto	764,475.71	-19,379.71
2017 Jun	794,118	ARIMA_auto	764,311.92	29,806.08
2017 Jul	864,476	ARIMA_auto	886,811.37	-22,335.37
2017 Aug	939,077	ARIMA_auto	931,439.56	7,637.44
2017 Sep	818,705	ARIMA_auto	810,040.60	8,664.40
2017 Oct	734,287	ARIMA_auto	732,744.00	1,543.00
2017 Nov	582,743	ARIMA_auto	590,106.79	-7,363.79
2017 Dec	478,377	ARIMA_auto	512,252.49	-33,875.49
2018 Jan	534,281	ARIMA_auto	526,479.80	7,801.20
2018 Feb	555,841	ARIMA_auto	582,112.27	-26,271.27
2018 Mar	652,082	ARIMA_auto	668,424.02	-16,342.02
2018 Apr	689,214	ARIMA_auto	713,744.75	-24,530.75
2018 May	755,491	ARIMA_auto	743,570.60	11,920.40
2018 Jun	782,628	ARIMA_auto	797,888.67	-15,260.67
2018 Jul	837,740	ARIMA_auto	876,628.23	-38,888.23
2018 Aug	936,644	ARIMA_auto	911,970.84	24,673.16
2018 Sep	806,267	ARIMA_auto	814,978.73	-8,711.73
2018 Oct	721,989	ARIMA_auto	725,602.85	-3,613.85
2018 Nov	575,096	ARIMA_auto	580,967.29	-5,871.29
2018 Dec	496,993	ARIMA_auto	488,726.91	8,266.09
2019 Jan	486,306	ARIMA_auto	546,714.23	-60,408.23
2019 Feb	498,081	ARIMA_auto	535,005.47	-36,924.47
2019 Mar	606,616	ARIMA_auto	614,236.83	-7,620.83
2019 Apr	608,322	ARIMA_auto	656,692.19	-48,370.19
2019 May	665,724	ARIMA_auto	679,542.24	-13,818.24
2019 Jun	714,041	ARIMA_auto	707,112.19	6,928.81
2019 Jul	747,112	ARIMA_auto	785,442.81	-38,330.81
2019 Aug	828,426	ARIMA_auto	838,151.80	-9,725.80
2019 Sep	719,254	ARIMA_auto	710,052.32	9,201.68
2019 Oct	629,555	ARIMA_auto	643,392.37	-13,837.37
2019 Nov	508,290	ARIMA_auto	486,785.77	21,504.23
2019 Dec	445,470	ARIMA_auto	421,360.19	24,109.81
2020 Jan	488,461	ARIMA_auto	464,252.20	24,208.80
2020 Feb	540,254	ARIMA_auto	506,906.75	33,347.25
2020 Mar	297,649	ARIMA_auto	643,673.54	-346,024.54
2020 Apr	2,191	ARIMA_auto	442,919.40	-440,728.40
2020 May	2,955	ARIMA_auto	14,911.13	-11,956.13
2020 Jun	14,932	ARIMA_auto	72,309.91	-57,377.91
2020 Jul	95,576	ARIMA_auto	75,735.94	19,840.06
2020 Aug	240,322	ARIMA_auto	212,387.04	27,934.96
2020 Sep	251,221	ARIMA_auto	170,954.31	80,266.69
2020 Oct	253,895	ARIMA_auto	197,615.44	56,279.56
2020 Nov	116,634	ARIMA_auto	135,589.90	-18,955.90
2020 Dec	137,446	ARIMA_auto	37,241.37	100,204.63
2021 Jan	93,013	ARIMA_auto	197,926.84	-104,913.84
2021 Feb	40,883	ARIMA_auto	102,640.52	-61,757.52
2021 Mar	60,163	ARIMA_auto	-35,958.51	96,121.51
2021 Apr	95,116	ARIMA_auto	-14,831.36	109,947.36
2021 May	179,599	ARIMA_auto	164,476.64	15,122.36
2021 Jun	321,985	ARIMA_auto	216,756.98	105,228.02
2021 Jul	552,399	ARIMA_auto	412,374.46	140,024.54
2021 Aug	780,123	ARIMA_auto	718,013.17	62,109.83
2021 Sep	697,572	ARIMA_auto	747,856.19	-50,284.19
2021 Oct	655,682	ARIMA_auto	630,088.72	25,593.28
2021 Nov	521,638	ARIMA_auto	515,750.52	5,887.48
2021 Dec	397,592	ARIMA_auto	469,547.45	-71,955.45
2022 Jan	341,744	ARIMA_auto	363,887.66	-22,143.66
2022 Feb	391,699	ARIMA_auto	327,452.92	64,246.08
2022 Mar	569,482	ARIMA_auto	395,442.49	174,039.51
2022 Apr	727,326	ARIMA_auto	596,506.89	130,819.11
2022 May	779,426	ARIMA_auto	823,615.73	-44,189.73
2022 Jun	833,955	ARIMA_auto	823,838.75	10,116.25
2010 Jan	319,379	ARIMA_auto_log	323,544.30	-4,165.30
2010 Feb	329,697	ARIMA_auto_log	356,913.49	-27,216.49
2010 Mar	388,978	ARIMA_auto_log	431,243.45	-42,265.45
2010 Apr	427,950	ARIMA_auto_log	442,193.90	-14,243.90
2010 May	431,385	ARIMA_auto_log	424,537.87	6,847.13
2010 Jun	432,522	ARIMA_auto_log	419,736.97	12,785.03
2010 Jul	492,382	ARIMA_auto_log	466,026.67	26,355.33
2010 Aug	624,383	ARIMA_auto_log	573,869.82	50,513.18
2010 Sep	496,609	ARIMA_auto_log	506,119.85	-9,510.85
2010 Oct	450,841	ARIMA_auto_log	438,643.28	12,197.72
2010 Nov	327,330	ARIMA_auto_log	355,473.17	-28,143.17
2010 Dec	272,069	ARIMA_auto_log	289,483.20	-17,414.20
2011 Jan	286,010	ARIMA_auto_log	286,920.27	-910.27
2011 Feb	319,015	ARIMA_auto_log	310,414.83	8,600.17
2011 Mar	448,224	ARIMA_auto_log	392,598.43	55,625.57
2011 Apr	517,979	ARIMA_auto_log	477,365.23	40,613.77
2011 May	575,401	ARIMA_auto_log	489,851.70	85,549.30
2011 Jun	519,950	ARIMA_auto_log	543,157.73	-23,207.73
2011 Jul	589,288	ARIMA_auto_log	559,017.95	30,270.05
2011 Aug	678,877	ARIMA_auto_log	701,509.05	-22,632.05
2011 Sep	577,108	ARIMA_auto_log	547,698.86	29,409.14
2011 Oct	471,268	ARIMA_auto_log	509,400.70	-38,132.70
2011 Nov	319,900	ARIMA_auto_log	361,578.50	-41,678.50
2011 Dec	262,266	ARIMA_auto_log	279,558.47	-17,292.47
2012 Jan	289,312	ARIMA_auto_log	280,848.48	8,463.52
2012 Feb	329,299	ARIMA_auto_log	321,164.68	8,134.32
2012 Mar	399,988	ARIMA_auto_log	434,063.59	-34,075.59
2012 Apr	508,131	ARIMA_auto_log	455,957.55	52,173.45
2012 May	521,638	ARIMA_auto_log	527,996.53	-6,358.53
2012 Jun	509,865	ARIMA_auto_log	493,629.93	16,235.07
2012 Jul	602,837	ARIMA_auto_log	566,586.85	36,250.15
2012 Aug	681,135	ARIMA_auto_log	703,926.05	-22,791.05
2012 Sep	562,007	ARIMA_auto_log	561,767.07	239.93
2012 Oct	468,951	ARIMA_auto_log	480,626.27	-11,675.27
2012 Nov	350,902	ARIMA_auto_log	339,037.14	11,864.86
2012 Dec	283,620	ARIMA_auto_log	292,541.53	-8,921.53
2013 Jan	322,235	ARIMA_auto_log	303,314.43	18,920.57
2013 Feb	365,343	ARIMA_auto_log	353,966.86	11,376.14
2013 Mar	462,258	ARIMA_auto_log	454,252.16	8,005.84
2013 Apr	516,930	ARIMA_auto_log	539,679.86	-22,749.86
2013 May	608,081	ARIMA_auto_log	532,040.45	76,040.55
2013 Jun	578,633	ARIMA_auto_log	572,200.61	6,432.39
2013 Jul	677,083	ARIMA_auto_log	642,239.50	34,843.50
2013 Aug	775,941	ARIMA_auto_log	771,105.66	4,835.34
2013 Sep	639,271	ARIMA_auto_log	622,195.92	17,075.08
2013 Oct	535,649	ARIMA_auto_log	529,020.43	6,628.57
2013 Nov	390,742	ARIMA_auto_log	376,885.85	13,856.15
2013 Dec	342,783	ARIMA_auto_log	311,882.37	30,900.63
2014 Jan	374,568	ARIMA_auto_log	364,448.52	10,119.48
2014 Feb	401,859	ARIMA_auto_log	409,686.06	-7,827.06
2014 Mar	503,533	ARIMA_auto_log	505,981.60	-2,448.60
2014 Apr	557,275	ARIMA_auto_log	578,461.32	-21,186.32
2014 May	610,148	ARIMA_auto_log	612,981.73	-2,833.73
2014 Jun	595,332	ARIMA_auto_log	570,851.77	24,480.23
2014 Jul	687,207	ARIMA_auto_log	682,468.00	4,739.00
2014 Aug	787,020	ARIMA_auto_log	775,536.23	11,483.77
2014 Sep	652,671	ARIMA_auto_log	646,261.76	6,409.24
2014 Oct	554,671	ARIMA_auto_log	535,310.17	19,360.83
2014 Nov	415,750	ARIMA_auto_log	392,669.20	23,080.80
2014 Dec	366,832	ARIMA_auto_log	341,762.29	25,069.71
2015 Jan	399,040	ARIMA_auto_log	395,358.39	3,681.61
2015 Feb	442,963	ARIMA_auto_log	431,435.52	11,527.48
2015 Mar	545,523	ARIMA_auto_log	538,486.74	7,036.26
2015 Apr	586,230	ARIMA_auto_log	615,352.67	-29,122.67
2015 May	628,998	ARIMA_auto_log	636,365.79	-7,367.79
2015 Jun	654,715	ARIMA_auto_log	603,731.56	50,983.44
2015 Jul	766,557	ARIMA_auto_log	748,890.05	17,666.95
2015 Aug	829,230	ARIMA_auto_log	857,769.60	-28,539.60
2015 Sep	696,849	ARIMA_auto_log	676,944.93	19,904.07
2015 Oct	597,629	ARIMA_auto_log	578,329.51	19,299.49
2015 Nov	475,257	ARIMA_auto_log	436,717.15	38,539.85
2015 Dec	407,035	ARIMA_auto_log	398,658.89	8,376.11
2016 Jan	448,784	ARIMA_auto_log	437,775.44	11,008.56
2016 Feb	506,179	ARIMA_auto_log	484,390.28	21,788.72
2016 Mar	611,987	ARIMA_auto_log	615,289.38	-3,302.38
2016 Apr	663,878	ARIMA_auto_log	656,133.64	7,744.36
2016 May	726,980	ARIMA_auto_log	720,046.66	6,933.34
2016 Jun	759,256	ARIMA_auto_log	711,214.99	48,041.01
2016 Jul	849,148	ARIMA_auto_log	864,734.59	-15,586.59
2016 Aug	891,091	ARIMA_auto_log	930,630.26	-39,539.26
2016 Sep	768,042	ARIMA_auto_log	733,500.66	34,541.34
2016 Oct	702,530	ARIMA_auto_log	642,828.06	59,701.94
2016 Nov	545,468	ARIMA_auto_log	531,833.90	13,634.10
2016 Dec	457,565	ARIMA_auto_log	468,441.71	-10,876.71
2017 Jan	503,654	ARIMA_auto_log	499,888.92	3,765.08
2017 Feb	541,368	ARIMA_auto_log	556,394.55	-15,026.55
2017 Mar	647,679	ARIMA_auto_log	666,263.82	-18,584.82
2017 Apr	710,409	ARIMA_auto_log	710,151.99	257.01
2017 May	745,096	ARIMA_auto_log	777,831.74	-32,735.74
2017 Jun	794,118	ARIMA_auto_log	773,630.03	20,487.97
2017 Jul	864,476	ARIMA_auto_log	910,231.01	-45,755.01
2017 Aug	939,077	ARIMA_auto_log	950,619.93	-11,542.93
2017 Sep	818,705	ARIMA_auto_log	803,171.87	15,533.13
2017 Oct	734,287	ARIMA_auto_log	725,043.16	9,243.84
2017 Nov	582,743	ARIMA_auto_log	569,887.88	12,855.12
2017 Dec	478,377	ARIMA_auto_log	495,787.17	-17,410.17
2018 Jan	534,281	ARIMA_auto_log	528,220.51	6,060.49
2018 Feb	555,841	ARIMA_auto_log	585,717.15	-29,876.15
2018 Mar	652,082	ARIMA_auto_log	680,891.77	-28,809.77
2018 Apr	689,214	ARIMA_auto_log	720,092.09	-30,878.09
2018 May	755,491	ARIMA_auto_log	750,739.47	4,751.53
2018 Jun	782,628	ARIMA_auto_log	805,882.89	-23,254.89
2018 Jul	837,740	ARIMA_auto_log	889,282.01	-51,542.01
2018 Aug	936,644	ARIMA_auto_log	920,035.36	16,608.64
2018 Sep	806,267	ARIMA_auto_log	814,074.62	-7,807.62
2018 Oct	721,989	ARIMA_auto_log	728,260.36	-6,271.36
2018 Nov	575,096	ARIMA_auto_log	570,765.11	4,330.89
2018 Dec	496,993	ARIMA_auto_log	480,038.91	16,954.09
2019 Jan	486,306	ARIMA_auto_log	548,741.98	-62,435.98
2019 Feb	498,081	ARIMA_auto_log	523,545.44	-25,464.44
2019 Mar	606,616	ARIMA_auto_log	598,055.25	8,560.75
2019 Apr	608,322	ARIMA_auto_log	656,994.46	-48,672.46
2019 May	665,724	ARIMA_auto_log	668,728.66	-3,004.66
2019 Jun	714,041	ARIMA_auto_log	706,454.77	7,586.23
2019 Jul	747,112	ARIMA_auto_log	784,968.89	-37,856.89
2019 Aug	828,426	ARIMA_auto_log	828,951.37	-525.37
2019 Sep	719,254	ARIMA_auto_log	725,884.22	-6,630.22
2019 Oct	629,555	ARIMA_auto_log	656,298.50	-26,743.50
2019 Nov	508,290	ARIMA_auto_log	506,056.15	2,233.85
2019 Dec	445,470	ARIMA_auto_log	435,940.08	9,529.92
2020 Jan	488,461	ARIMA_auto_log	469,904.43	18,556.57
2020 Feb	540,254	ARIMA_auto_log	510,786.67	29,467.33
2020 Mar	297,649	ARIMA_auto_log	646,771.84	-349,122.84
2020 Apr	2,191	ARIMA_auto_log	394,809.94	-392,618.94
2020 May	2,955	ARIMA_auto_log	3.33	2,951.67
2020 Jun	14,932	ARIMA_auto_log	50,393.20	-35,461.20
2020 Jul	95,576	ARIMA_auto_log	41,924.97	53,651.03
2020 Aug	240,322	ARIMA_auto_log	229,366.11	10,955.89
2020 Sep	251,221	ARIMA_auto_log	379,107.90	-127,886.90
2020 Oct	253,895	ARIMA_auto_log	295,997.25	-42,102.25
2020 Nov	116,634	ARIMA_auto_log	294,845.31	-178,211.31
2020 Dec	137,446	ARIMA_auto_log	130,758.19	6,687.81
2021 Jan	93,013	ARIMA_auto_log	225,307.59	-132,294.59
2021 Feb	40,883	ARIMA_auto_log	163,169.33	-122,286.33
2021 Mar	60,163	ARIMA_auto_log	36,834.49	23,328.51
2021 Apr	95,116	ARIMA_auto_log	13,973.97	81,142.03
2021 May	179,599	ARIMA_auto_log	162,464.96	17,134.04
2021 Jun	321,985	ARIMA_auto_log	275,116.06	46,868.94
2021 Jul	552,399	ARIMA_auto_log	459,858.38	92,540.62
2021 Aug	780,123	ARIMA_auto_log	659,698.91	120,424.09
2021 Sep	697,572	ARIMA_auto_log	752,931.11	-55,359.11
2021 Oct	655,682	ARIMA_auto_log	611,834.11	43,847.89
2021 Nov	521,638	ARIMA_auto_log	553,359.69	-31,721.69
2021 Dec	397,592	ARIMA_auto_log	494,868.01	-97,276.01
2022 Jan	341,744	ARIMA_auto_log	372,850.74	-31,106.74
2022 Feb	391,699	ARIMA_auto_log	340,616.11	51,082.89
2022 Mar	569,482	ARIMA_auto_log	365,154.07	204,327.93
2022 Apr	727,326	ARIMA_auto_log	167,698.24	559,627.76
2022 May	779,426	ARIMA_auto_log	726,820.61	52,605.39
2022 Jun	833,955	ARIMA_auto_log	740,437.55	93,517.45
2010 Jan	319,379	ARIMA_d0D1	336,040.22	-16,661.22
2010 Feb	329,697	ARIMA_d0D1	365,991.07	-36,294.07
2010 Mar	388,978	ARIMA_d0D1	451,689.18	-62,711.18
2010 Apr	427,950	ARIMA_d0D1	456,469.99	-28,519.99
2010 May	431,385	ARIMA_d0D1	427,407.52	3,977.48
2010 Jun	432,522	ARIMA_d0D1	427,500.20	5,021.80
2010 Jul	492,382	ARIMA_d0D1	487,620.01	4,761.99
2010 Aug	624,383	ARIMA_d0D1	601,124.35	23,258.65
2010 Sep	496,609	ARIMA_d0D1	518,894.39	-22,285.39
2010 Oct	450,841	ARIMA_d0D1	447,898.73	2,942.27
2010 Nov	327,330	ARIMA_d0D1	361,545.54	-34,215.54
2010 Dec	272,069	ARIMA_d0D1	289,516.77	-17,447.77
2011 Jan	286,010	ARIMA_d0D1	294,687.03	-8,677.03
2011 Feb	319,015	ARIMA_d0D1	322,635.89	-3,620.89
2011 Mar	448,224	ARIMA_d0D1	415,627.66	32,596.34
2011 Apr	517,979	ARIMA_d0D1	492,406.99	25,572.01
2011 May	575,401	ARIMA_d0D1	502,249.85	73,151.15
2011 Jun	519,950	ARIMA_d0D1	546,941.60	-26,991.60
2011 Jul	589,288	ARIMA_d0D1	559,857.17	29,430.83
2011 Aug	678,877	ARIMA_d0D1	688,687.33	-9,810.33
2011 Sep	577,108	ARIMA_d0D1	553,869.76	23,238.24
2011 Oct	471,268	ARIMA_d0D1	513,811.49	-42,543.49
2011 Nov	319,900	ARIMA_d0D1	363,504.37	-43,604.37
2011 Dec	262,266	ARIMA_d0D1	276,485.96	-14,219.96
2012 Jan	289,312	ARIMA_d0D1	283,241.63	6,070.37
2012 Feb	329,299	ARIMA_d0D1	323,846.58	5,452.42
2012 Mar	399,988	ARIMA_d0D1	437,479.94	-37,491.94
2012 Apr	508,131	ARIMA_d0D1	457,558.54	50,572.46
2012 May	521,638	ARIMA_d0D1	526,682.60	-5,044.60
2012 Jun	509,865	ARIMA_d0D1	492,064.87	17,800.13
2012 Jul	602,837	ARIMA_d0D1	564,020.18	38,816.82
2012 Aug	681,135	ARIMA_d0D1	694,868.23	-13,733.23
2012 Sep	562,007	ARIMA_d0D1	564,899.91	-2,892.91
2012 Oct	468,951	ARIMA_d0D1	482,451.99	-13,500.99
2012 Nov	350,902	ARIMA_d0D1	341,471.66	9,430.34
2012 Dec	283,620	ARIMA_d0D1	294,817.12	-11,197.12
2013 Jan	322,235	ARIMA_d0D1	302,852.31	19,382.69
2013 Feb	365,343	ARIMA_d0D1	352,145.29	13,197.71
2013 Mar	462,258	ARIMA_d0D1	449,728.92	12,529.08
2013 Apr	516,930	ARIMA_d0D1	532,372.52	-15,442.52
2013 May	608,081	ARIMA_d0D1	531,063.70	77,017.30
2013 Jun	578,633	ARIMA_d0D1	567,644.07	10,988.93
2013 Jul	677,083	ARIMA_d0D1	635,025.69	42,057.31
2013 Aug	775,941	ARIMA_d0D1	756,754.28	19,186.72
2013 Sep	639,271	ARIMA_d0D1	640,217.57	-946.57
2013 Oct	535,649	ARIMA_d0D1	543,604.35	-7,955.35
2013 Nov	390,742	ARIMA_d0D1	395,039.12	-4,297.12
2013 Dec	342,783	ARIMA_d0D1	320,902.53	21,880.47
2014 Jan	374,568	ARIMA_d0D1	358,970.38	15,597.62
2014 Feb	401,859	ARIMA_d0D1	401,977.09	-118.09
2014 Mar	503,533	ARIMA_d0D1	492,833.11	10,699.89
2014 Apr	557,275	ARIMA_d0D1	567,920.89	-10,645.89
2014 May	610,148	ARIMA_d0D1	610,066.75	81.25
2014 Jun	595,332	ARIMA_d0D1	570,761.33	24,570.67
2014 Jul	687,207	ARIMA_d0D1	674,147.19	13,059.81
2014 Aug	787,020	ARIMA_d0D1	768,493.46	18,526.54
2014 Sep	652,671	ARIMA_d0D1	656,367.29	-3,696.29
2014 Oct	554,671	ARIMA_d0D1	542,937.67	11,733.33
2014 Nov	415,750	ARIMA_d0D1	406,144.14	9,605.86
2014 Dec	366,832	ARIMA_d0D1	350,789.79	16,042.21
2015 Jan	399,040	ARIMA_d0D1	389,326.25	9,713.75
2015 Feb	442,963	ARIMA_d0D1	425,267.38	17,695.62
2015 Mar	545,523	ARIMA_d0D1	522,804.04	22,718.96
2015 Apr	586,230	ARIMA_d0D1	605,340.30	-19,110.30
2015 May	628,998	ARIMA_d0D1	629,769.76	-771.76
2015 Jun	654,715	ARIMA_d0D1	604,473.56	50,241.44
2015 Jul	766,557	ARIMA_d0D1	736,542.38	30,014.62
2015 Aug	829,230	ARIMA_d0D1	845,623.83	-16,393.83
2015 Sep	696,849	ARIMA_d0D1	688,722.65	8,126.35
2015 Oct	597,629	ARIMA_d0D1	588,970.39	8,658.61
2015 Nov	475,257	ARIMA_d0D1	454,073.75	21,183.25
2015 Dec	407,035	ARIMA_d0D1	409,923.30	-2,888.30
2016 Jan	448,784	ARIMA_d0D1	432,092.86	16,691.14
2016 Feb	506,179	ARIMA_d0D1	478,163.85	28,015.15
2016 Mar	611,987	ARIMA_d0D1	595,166.09	16,820.91
2016 Apr	663,878	ARIMA_d0D1	649,017.31	14,860.69
2016 May	726,980	ARIMA_d0D1	713,632.72	13,347.28
2016 Jun	759,256	ARIMA_d0D1	711,990.88	47,265.12
2016 Jul	849,148	ARIMA_d0D1	847,776.17	1,371.83
2016 Aug	891,091	ARIMA_d0D1	920,596.67	-29,505.67
2016 Sep	768,042	ARIMA_d0D1	747,541.13	20,500.87
2016 Oct	702,530	ARIMA_d0D1	657,612.78	44,917.22
2016 Nov	545,468	ARIMA_d0D1	556,306.80	-10,838.80
2016 Dec	457,565	ARIMA_d0D1	478,023.86	-20,458.86
2017 Jan	503,654	ARIMA_d0D1	485,726.29	17,927.71
2017 Feb	541,368	ARIMA_d0D1	540,451.85	916.15
2017 Mar	647,679	ARIMA_d0D1	638,126.56	9,552.44
2017 Apr	710,409	ARIMA_d0D1	690,213.28	20,195.72
2017 May	745,096	ARIMA_d0D1	756,843.78	-11,747.78
2017 Jun	794,118	ARIMA_d0D1	754,722.22	39,395.78
2017 Jul	864,476	ARIMA_d0D1	880,651.62	-16,175.62
2017 Aug	939,077	ARIMA_d0D1	922,153.06	16,923.94
2017 Sep	818,705	ARIMA_d0D1	802,448.18	16,256.82
2017 Oct	734,287	ARIMA_d0D1	726,283.19	8,003.81
2017 Nov	582,743	ARIMA_d0D1	583,075.49	-332.49
2017 Dec	478,377	ARIMA_d0D1	504,290.05	-25,913.05
2018 Jan	534,281	ARIMA_d0D1	515,489.17	18,791.83
2018 Feb	555,841	ARIMA_d0D1	571,840.26	-15,999.26
2018 Mar	652,082	ARIMA_d0D1	660,608.41	-8,526.41
2018 Apr	689,214	ARIMA_d0D1	704,912.48	-15,698.48
2018 May	755,491	ARIMA_d0D1	734,319.27	21,171.73
2018 Jun	782,628	ARIMA_d0D1	787,278.14	-4,650.14
2018 Jul	837,740	ARIMA_d0D1	867,812.60	-30,072.60
2018 Aug	936,644	ARIMA_d0D1	905,666.41	30,977.59
2018 Sep	806,267	ARIMA_d0D1	804,305.79	1,961.21
2018 Oct	721,989	ARIMA_d0D1	720,248.67	1,740.33
2018 Nov	575,096	ARIMA_d0D1	574,359.01	736.99
2018 Dec	496,993	ARIMA_d0D1	482,329.79	14,663.21
2019 Jan	486,306	ARIMA_d0D1	543,235.07	-56,929.07
2019 Feb	498,081	ARIMA_d0D1	533,019.81	-34,938.81
2019 Mar	606,616	ARIMA_d0D1	608,007.09	-1,391.09
2019 Apr	608,322	ARIMA_d0D1	656,692.19	-48,370.19
2019 May	665,724	ARIMA_d0D1	679,542.24	-13,818.24
2019 Jun	714,041	ARIMA_d0D1	707,112.19	6,928.81
2019 Jul	747,112	ARIMA_d0D1	785,442.81	-38,330.81
2019 Aug	828,426	ARIMA_d0D1	838,151.80	-9,725.80
2019 Sep	719,254	ARIMA_d0D1	710,052.32	9,201.68
2019 Oct	629,555	ARIMA_d0D1	643,392.37	-13,837.37
2019 Nov	508,290	ARIMA_d0D1	486,785.77	21,504.23
2019 Dec	445,470	ARIMA_d0D1	421,360.19	24,109.81
2020 Jan	488,461	ARIMA_d0D1	464,252.20	24,208.80
2020 Feb	540,254	ARIMA_d0D1	506,906.75	33,347.25
2020 Mar	297,649	ARIMA_d0D1	643,673.54	-346,024.54
2020 Apr	2,191	ARIMA_d0D1	442,919.40	-440,728.40
2020 May	2,955	ARIMA_d0D1	14,911.13	-11,956.13
2020 Jun	14,932	ARIMA_d0D1	72,309.91	-57,377.91
2020 Jul	95,576	ARIMA_d0D1	75,735.94	19,840.06
2020 Aug	240,322	ARIMA_d0D1	212,387.04	27,934.96
2020 Sep	251,221	ARIMA_d0D1	170,954.31	80,266.69
2020 Oct	253,895	ARIMA_d0D1	241,442.39	12,452.61
2020 Nov	116,634	ARIMA_d0D1	177,644.87	-61,010.87
2020 Dec	137,446	ARIMA_d0D1	61,187.49	76,258.51
2021 Jan	93,013	ARIMA_d0D1	222,633.01	-129,620.01
2021 Feb	40,883	ARIMA_d0D1	129,747.36	-88,864.36
2021 Mar	60,163	ARIMA_d0D1	-19,686.83	79,849.83
2021 Apr	95,116	ARIMA_d0D1	3,142.06	91,973.94
2021 May	179,599	ARIMA_d0D1	189,517.06	-9,918.06
2021 Jun	321,985	ARIMA_d0D1	237,909.75	84,075.25
2021 Jul	552,399	ARIMA_d0D1	432,684.84	119,714.16
2021 Aug	780,123	ARIMA_d0D1	718,013.17	62,109.83
2021 Sep	697,572	ARIMA_d0D1	747,856.19	-50,284.19
2021 Oct	655,682	ARIMA_d0D1	630,088.72	25,593.28
2021 Nov	521,638	ARIMA_d0D1	515,750.52	5,887.48
2021 Dec	397,592	ARIMA_d0D1	469,547.45	-71,955.45
2022 Jan	341,744	ARIMA_d0D1	363,887.66	-22,143.66
2022 Feb	391,699	ARIMA_d0D1	327,452.92	64,246.08
2022 Mar	569,482	ARIMA_d0D1	395,442.49	174,039.51
2022 Apr	727,326	ARIMA_d0D1	596,506.89	130,819.11
2022 May	779,426	ARIMA_d0D1	823,615.73	-44,189.73
2022 Jun	833,955	ARIMA_d0D1	823,838.75	10,116.25
2010 Jan	319,379	ARIMA_d0D1_log	328,145.67	-8,766.67
2010 Feb	329,697	ARIMA_d0D1_log	362,534.18	-32,837.18
2010 Mar	388,978	ARIMA_d0D1_log	437,688.54	-48,710.54
2010 Apr	427,950	ARIMA_d0D1_log	446,958.64	-19,008.64
2010 May	431,385	ARIMA_d0D1_log	428,822.03	2,562.97
2010 Jun	432,522	ARIMA_d0D1_log	429,340.87	3,181.13
2010 Jul	492,382	ARIMA_d0D1_log	482,110.92	10,271.08
2010 Aug	624,383	ARIMA_d0D1_log	594,255.30	30,127.70
2010 Sep	496,609	ARIMA_d0D1_log	521,875.44	-25,266.44
2010 Oct	450,841	ARIMA_d0D1_log	451,910.69	-1,069.69
2010 Nov	327,330	ARIMA_d0D1_log	366,119.51	-38,789.51
2010 Dec	272,069	ARIMA_d0D1_log	294,925.22	-22,856.22
2011 Jan	286,010	ARIMA_d0D1_log	291,293.62	-5,283.62
2011 Feb	319,015	ARIMA_d0D1_log	316,692.03	2,322.97
2011 Mar	448,224	ARIMA_d0D1_log	402,916.95	45,307.05
2011 Apr	517,979	ARIMA_d0D1_log	491,830.77	26,148.23
2011 May	575,401	ARIMA_d0D1_log	503,240.81	72,160.19
2011 Jun	519,950	ARIMA_d0D1_log	545,534.33	-25,584.33
2011 Jul	589,288	ARIMA_d0D1_log	564,384.49	24,903.51
2011 Aug	678,877	ARIMA_d0D1_log	701,509.05	-22,632.05
2011 Sep	577,108	ARIMA_d0D1_log	547,698.86	29,409.14
2011 Oct	471,268	ARIMA_d0D1_log	509,400.70	-38,132.70
2011 Nov	319,900	ARIMA_d0D1_log	361,578.50	-41,678.50
2011 Dec	262,266	ARIMA_d0D1_log	279,558.47	-17,292.47
2012 Jan	289,312	ARIMA_d0D1_log	280,848.48	8,463.52
2012 Feb	329,299	ARIMA_d0D1_log	321,164.68	8,134.32
2012 Mar	399,988	ARIMA_d0D1_log	434,063.59	-34,075.59
2012 Apr	508,131	ARIMA_d0D1_log	455,957.55	52,173.45
2012 May	521,638	ARIMA_d0D1_log	527,996.53	-6,358.53
2012 Jun	509,865	ARIMA_d0D1_log	493,629.93	16,235.07
2012 Jul	602,837	ARIMA_d0D1_log	566,586.85	36,250.15
2012 Aug	681,135	ARIMA_d0D1_log	703,926.05	-22,791.05
2012 Sep	562,007	ARIMA_d0D1_log	561,767.07	239.93
2012 Oct	468,951	ARIMA_d0D1_log	480,626.27	-11,675.27
2012 Nov	350,902	ARIMA_d0D1_log	339,037.14	11,864.86
2012 Dec	283,620	ARIMA_d0D1_log	292,541.53	-8,921.53
2013 Jan	322,235	ARIMA_d0D1_log	303,314.43	18,920.57
2013 Feb	365,343	ARIMA_d0D1_log	353,966.86	11,376.14
2013 Mar	462,258	ARIMA_d0D1_log	454,252.16	8,005.84
2013 Apr	516,930	ARIMA_d0D1_log	539,679.86	-22,749.86
2013 May	608,081	ARIMA_d0D1_log	532,040.45	76,040.55
2013 Jun	578,633	ARIMA_d0D1_log	572,200.61	6,432.39
2013 Jul	677,083	ARIMA_d0D1_log	642,239.50	34,843.50
2013 Aug	775,941	ARIMA_d0D1_log	771,105.66	4,835.34
2013 Sep	639,271	ARIMA_d0D1_log	622,195.92	17,075.08
2013 Oct	535,649	ARIMA_d0D1_log	529,020.43	6,628.57
2013 Nov	390,742	ARIMA_d0D1_log	376,885.85	13,856.15
2013 Dec	342,783	ARIMA_d0D1_log	311,882.37	30,900.63
2014 Jan	374,568	ARIMA_d0D1_log	364,448.52	10,119.48
2014 Feb	401,859	ARIMA_d0D1_log	409,686.06	-7,827.06
2014 Mar	503,533	ARIMA_d0D1_log	505,981.60	-2,448.60
2014 Apr	557,275	ARIMA_d0D1_log	578,461.32	-21,186.32
2014 May	610,148	ARIMA_d0D1_log	612,981.73	-2,833.73
2014 Jun	595,332	ARIMA_d0D1_log	570,851.77	24,480.23
2014 Jul	687,207	ARIMA_d0D1_log	682,468.00	4,739.00
2014 Aug	787,020	ARIMA_d0D1_log	775,536.23	11,483.77
2014 Sep	652,671	ARIMA_d0D1_log	646,261.76	6,409.24
2014 Oct	554,671	ARIMA_d0D1_log	535,310.17	19,360.83
2014 Nov	415,750	ARIMA_d0D1_log	392,669.20	23,080.80
2014 Dec	366,832	ARIMA_d0D1_log	341,762.29	25,069.71
2015 Jan	399,040	ARIMA_d0D1_log	395,358.39	3,681.61
2015 Feb	442,963	ARIMA_d0D1_log	431,435.52	11,527.48
2015 Mar	545,523	ARIMA_d0D1_log	538,486.74	7,036.26
2015 Apr	586,230	ARIMA_d0D1_log	615,352.67	-29,122.67
2015 May	628,998	ARIMA_d0D1_log	636,365.79	-7,367.79
2015 Jun	654,715	ARIMA_d0D1_log	603,731.56	50,983.44
2015 Jul	766,557	ARIMA_d0D1_log	748,890.05	17,666.95
2015 Aug	829,230	ARIMA_d0D1_log	857,769.60	-28,539.60
2015 Sep	696,849	ARIMA_d0D1_log	676,944.93	19,904.07
2015 Oct	597,629	ARIMA_d0D1_log	578,329.51	19,299.49
2015 Nov	475,257	ARIMA_d0D1_log	436,717.15	38,539.85
2015 Dec	407,035	ARIMA_d0D1_log	398,658.89	8,376.11
2016 Jan	448,784	ARIMA_d0D1_log	437,775.44	11,008.56
2016 Feb	506,179	ARIMA_d0D1_log	484,390.28	21,788.72
2016 Mar	611,987	ARIMA_d0D1_log	615,289.38	-3,302.38
2016 Apr	663,878	ARIMA_d0D1_log	656,133.64	7,744.36
2016 May	726,980	ARIMA_d0D1_log	720,046.66	6,933.34
2016 Jun	759,256	ARIMA_d0D1_log	711,214.99	48,041.01
2016 Jul	849,148	ARIMA_d0D1_log	864,734.59	-15,586.59
2016 Aug	891,091	ARIMA_d0D1_log	930,630.26	-39,539.26
2016 Sep	768,042	ARIMA_d0D1_log	733,500.66	34,541.34
2016 Oct	702,530	ARIMA_d0D1_log	642,828.06	59,701.94
2016 Nov	545,468	ARIMA_d0D1_log	524,663.75	20,804.25
2016 Dec	457,565	ARIMA_d0D1_log	462,643.76	-5,078.76
2017 Jan	503,654	ARIMA_d0D1_log	491,224.34	12,429.66
2017 Feb	541,368	ARIMA_d0D1_log	546,845.01	-5,477.01
2017 Mar	647,679	ARIMA_d0D1_log	652,697.10	-5,018.10
2017 Apr	710,409	ARIMA_d0D1_log	694,232.27	16,176.73
2017 May	745,096	ARIMA_d0D1_log	761,743.13	-16,647.13
2017 Jun	794,118	ARIMA_d0D1_log	755,198.09	38,919.91
2017 Jul	864,476	ARIMA_d0D1_log	893,283.09	-28,807.09
2017 Aug	939,077	ARIMA_d0D1_log	926,065.77	13,011.23
2017 Sep	818,705	ARIMA_d0D1_log	787,443.69	31,261.31
2017 Oct	734,287	ARIMA_d0D1_log	712,139.47	22,147.53
2017 Nov	582,743	ARIMA_d0D1_log	562,116.61	20,626.39
2017 Dec	478,377	ARIMA_d0D1_log	490,468.33	-12,091.33
2018 Jan	534,281	ARIMA_d0D1_log	520,225.95	14,055.05
2018 Feb	555,841	ARIMA_d0D1_log	579,834.85	-23,993.85
2018 Mar	652,082	ARIMA_d0D1_log	668,474.37	-16,392.37
2018 Apr	689,214	ARIMA_d0D1_log	705,260.98	-16,046.98
2018 May	755,491	ARIMA_d0D1_log	733,762.46	21,728.54
2018 Jun	782,628	ARIMA_d0D1_log	795,687.59	-13,059.59
2018 Jul	837,740	ARIMA_d0D1_log	870,641.10	-32,901.10
2018 Aug	936,644	ARIMA_d0D1_log	901,073.93	35,570.07
2018 Sep	806,267	ARIMA_d0D1_log	803,925.31	2,341.69
2018 Oct	721,989	ARIMA_d0D1_log	720,957.74	1,031.26
2018 Nov	575,096	ARIMA_d0D1_log	570,765.11	4,330.89
2018 Dec	496,993	ARIMA_d0D1_log	480,038.91	16,954.09
2019 Jan	486,306	ARIMA_d0D1_log	548,741.98	-62,435.98
2019 Feb	498,081	ARIMA_d0D1_log	523,545.44	-25,464.44
2019 Mar	606,616	ARIMA_d0D1_log	598,055.25	8,560.75
2019 Apr	608,322	ARIMA_d0D1_log	656,994.46	-48,672.46
2019 May	665,724	ARIMA_d0D1_log	668,728.66	-3,004.66
2019 Jun	714,041	ARIMA_d0D1_log	706,454.77	7,586.23
2019 Jul	747,112	ARIMA_d0D1_log	784,968.89	-37,856.89
2019 Aug	828,426	ARIMA_d0D1_log	828,951.37	-525.37
2019 Sep	719,254	ARIMA_d0D1_log	725,884.22	-6,630.22
2019 Oct	629,555	ARIMA_d0D1_log	656,298.50	-26,743.50
2019 Nov	508,290	ARIMA_d0D1_log	506,056.15	2,233.85
2019 Dec	445,470	ARIMA_d0D1_log	435,940.08	9,529.92
2020 Jan	488,461	ARIMA_d0D1_log	469,904.43	18,556.57
2020 Feb	540,254	ARIMA_d0D1_log	510,786.67	29,467.33
2020 Mar	297,649	ARIMA_d0D1_log	646,771.84	-349,122.84
2020 Apr	2,191	ARIMA_d0D1_log	394,809.94	-392,618.94
2020 May	2,955	ARIMA_d0D1_log	4.79	2,950.21
2020 Jun	14,932	ARIMA_d0D1_log	118,537.82	-103,605.82
2020 Jul	95,576	ARIMA_d0D1_log	43,058.04	52,517.96
2020 Aug	240,322	ARIMA_d0D1_log	270,799.66	-30,477.66
2020 Sep	251,221	ARIMA_d0D1_log	367,893.23	-116,672.23
2020 Oct	253,895	ARIMA_d0D1_log	300,164.72	-46,269.72
2020 Nov	116,634	ARIMA_d0D1_log	278,384.34	-161,750.34
2020 Dec	137,446	ARIMA_d0D1_log	123,177.11	14,268.89
2021 Jan	93,013	ARIMA_d0D1_log	236,521.90	-143,508.90
2021 Feb	40,883	ARIMA_d0D1_log	133,847.01	-92,964.01
2021 Mar	60,163	ARIMA_d0D1_log	28,247.43	31,915.57
2021 Apr	95,116	ARIMA_d0D1_log	2,751.66	92,364.34
2021 May	179,599	ARIMA_d0D1_log	178,978.14	620.86
2021 Jun	321,985	ARIMA_d0D1_log	299,790.95	22,194.05
2021 Jul	552,399	ARIMA_d0D1_log	548,685.11	3,713.89
2021 Aug	780,123	ARIMA_d0D1_log	773,511.86	6,611.14
2021 Sep	697,572	ARIMA_d0D1_log	710,258.35	-12,686.35
2021 Oct	655,682	ARIMA_d0D1_log	637,541.90	18,140.10
2021 Nov	521,638	ARIMA_d0D1_log	471,079.48	50,558.52
2021 Dec	397,592	ARIMA_d0D1_log	483,250.73	-85,658.73
2022 Jan	341,744	ARIMA_d0D1_log	368,065.94	-26,321.94
2022 Feb	391,699	ARIMA_d0D1_log	313,208.56	78,490.44
2022 Mar	569,482	ARIMA_d0D1_log	485,308.34	84,173.66
2022 Apr	727,326	ARIMA_d0D1_log	321,501.56	405,824.44
2022 May	779,426	ARIMA_d0D1_log	895,794.48	-116,368.48
2022 Jun	833,955	ARIMA_d0D1_log	795,739.00	38,216.00
2010 Jan	319,379	ARIMA_d1D1	324,272.23	-4,893.23
2010 Feb	329,697	ARIMA_d1D1	360,237.41	-30,540.41
2010 Mar	388,978	ARIMA_d1D1	446,194.07	-57,216.07
2010 Apr	427,950	ARIMA_d1D1	453,323.31	-25,373.31
2010 May	431,385	ARIMA_d1D1	424,694.98	6,690.02
2010 Jun	432,522	ARIMA_d1D1	418,843.54	13,678.46
2010 Jul	492,382	ARIMA_d1D1	474,033.80	18,348.20
2010 Aug	624,383	ARIMA_d1D1	587,104.83	37,278.17
2010 Sep	496,609	ARIMA_d1D1	505,657.48	-9,048.48
2010 Oct	450,841	ARIMA_d1D1	434,740.50	16,100.50
2010 Nov	327,330	ARIMA_d1D1	348,898.98	-21,568.98
2010 Dec	272,069	ARIMA_d1D1	279,968.26	-7,899.26
2011 Jan	286,010	ARIMA_d1D1	285,074.11	935.89
2011 Feb	319,015	ARIMA_d1D1	312,488.81	6,526.19
2011 Mar	448,224	ARIMA_d1D1	404,482.15	43,741.85
2011 Apr	517,979	ARIMA_d1D1	480,019.55	37,959.45
2011 May	575,401	ARIMA_d1D1	491,918.43	83,482.57
2011 Jun	519,950	ARIMA_d1D1	548,653.76	-28,703.76
2011 Jul	589,288	ARIMA_d1D1	557,022.67	32,265.33
2011 Aug	678,877	ARIMA_d1D1	689,501.19	-10,624.19
2011 Sep	577,108	ARIMA_d1D1	553,533.85	23,574.15
2011 Oct	471,268	ARIMA_d1D1	515,451.77	-44,183.77
2011 Nov	319,900	ARIMA_d1D1	361,999.98	-42,099.98
2011 Dec	262,266	ARIMA_d1D1	274,745.03	-12,479.03
2012 Jan	289,312	ARIMA_d1D1	277,826.48	11,485.52
2012 Feb	329,299	ARIMA_d1D1	321,767.22	7,531.78
2012 Mar	399,988	ARIMA_d1D1	435,460.18	-35,472.18
2012 Apr	508,131	ARIMA_d1D1	453,698.08	54,432.92
2012 May	521,638	ARIMA_d1D1	524,628.58	-2,990.58
2012 Jun	509,865	ARIMA_d1D1	489,834.86	20,030.14
2012 Jul	602,837	ARIMA_d1D1	558,591.98	44,245.02
2012 Aug	681,135	ARIMA_d1D1	697,723.68	-16,588.68
2012 Sep	562,007	ARIMA_d1D1	564,376.89	-2,369.89
2012 Oct	468,951	ARIMA_d1D1	481,683.30	-12,732.30
2012 Nov	350,902	ARIMA_d1D1	340,434.20	10,467.80
2012 Dec	283,620	ARIMA_d1D1	294,164.71	-10,544.71
2013 Jan	322,235	ARIMA_d1D1	302,104.11	20,130.89
2013 Feb	365,343	ARIMA_d1D1	351,793.49	13,549.51
2013 Mar	462,258	ARIMA_d1D1	449,647.83	12,610.17
2013 Apr	516,930	ARIMA_d1D1	533,047.44	-16,117.44
2013 May	608,081	ARIMA_d1D1	531,300.92	76,780.08
2013 Jun	578,633	ARIMA_d1D1	568,841.27	9,791.73
2013 Jul	677,083	ARIMA_d1D1	639,945.74	37,137.26
2013 Aug	775,941	ARIMA_d1D1	758,632.60	17,308.40
2013 Sep	639,271	ARIMA_d1D1	657,886.40	-18,615.40
2013 Oct	535,649	ARIMA_d1D1	561,992.94	-26,343.94
2013 Nov	390,742	ARIMA_d1D1	411,247.79	-20,505.79
2013 Dec	342,783	ARIMA_d1D1	330,450.05	12,332.95
2014 Jan	374,568	ARIMA_d1D1	368,733.50	5,834.50
2014 Feb	401,859	ARIMA_d1D1	412,608.16	-10,749.16
2014 Mar	503,533	ARIMA_d1D1	503,435.44	97.56
2014 Apr	557,275	ARIMA_d1D1	578,060.68	-20,785.68
2014 May	610,148	ARIMA_d1D1	620,034.50	-9,886.50
2014 Jun	595,332	ARIMA_d1D1	575,860.65	19,471.35
2014 Jul	687,207	ARIMA_d1D1	680,355.74	6,851.26
2014 Aug	787,020	ARIMA_d1D1	776,165.08	10,854.92
2014 Sep	652,671	ARIMA_d1D1	664,236.66	-11,565.66
2014 Oct	554,671	ARIMA_d1D1	553,381.09	1,289.91
2014 Nov	415,750	ARIMA_d1D1	415,177.94	572.06
2014 Dec	366,832	ARIMA_d1D1	359,240.55	7,591.45
2015 Jan	399,040	ARIMA_d1D1	397,761.92	1,278.08
2015 Feb	442,963	ARIMA_d1D1	434,480.21	8,482.79
2015 Mar	545,523	ARIMA_d1D1	532,278.44	13,244.56
2015 Apr	586,230	ARIMA_d1D1	613,743.63	-27,513.63
2015 May	628,998	ARIMA_d1D1	642,374.45	-13,376.45
2015 Jun	654,715	ARIMA_d1D1	613,437.57	41,277.43
2015 Jul	766,557	ARIMA_d1D1	740,573.36	25,983.64
2015 Aug	829,230	ARIMA_d1D1	854,135.56	-24,905.56
2015 Sep	696,849	ARIMA_d1D1	695,612.38	1,236.62
2015 Oct	597,629	ARIMA_d1D1	596,998.12	630.88
2015 Nov	475,257	ARIMA_d1D1	466,862.56	8,394.44
2015 Dec	407,035	ARIMA_d1D1	418,993.57	-11,958.57
2016 Jan	448,784	ARIMA_d1D1	442,879.42	5,904.58
2016 Feb	506,179	ARIMA_d1D1	486,154.25	20,024.75
2016 Mar	611,987	ARIMA_d1D1	603,840.71	8,146.29
2016 Apr	663,878	ARIMA_d1D1	656,196.57	7,681.43
2016 May	726,980	ARIMA_d1D1	718,888.84	8,091.16
2016 Jun	759,256	ARIMA_d1D1	720,719.87	38,536.13
2016 Jul	849,148	ARIMA_d1D1	851,988.37	-2,840.37
2016 Aug	891,091	ARIMA_d1D1	929,265.46	-38,174.46
2016 Sep	768,042	ARIMA_d1D1	759,111.26	8,930.74
2016 Oct	702,530	ARIMA_d1D1	669,770.28	32,759.72
2016 Nov	545,468	ARIMA_d1D1	566,784.42	-21,316.42
2016 Dec	457,565	ARIMA_d1D1	486,929.49	-29,364.49
2017 Jan	503,654	ARIMA_d1D1	498,293.66	5,360.34
2017 Feb	541,368	ARIMA_d1D1	550,323.83	-8,955.83
2017 Mar	647,679	ARIMA_d1D1	648,146.43	-467.43
2017 Apr	710,409	ARIMA_d1D1	699,470.24	10,938.76
2017 May	745,096	ARIMA_d1D1	764,475.71	-19,379.71
2017 Jun	794,118	ARIMA_d1D1	764,311.92	29,806.08
2017 Jul	864,476	ARIMA_d1D1	886,811.37	-22,335.37
2017 Aug	939,077	ARIMA_d1D1	931,439.56	7,637.44
2017 Sep	818,705	ARIMA_d1D1	810,040.60	8,664.40
2017 Oct	734,287	ARIMA_d1D1	732,744.00	1,543.00
2017 Nov	582,743	ARIMA_d1D1	590,106.79	-7,363.79
2017 Dec	478,377	ARIMA_d1D1	512,252.49	-33,875.49
2018 Jan	534,281	ARIMA_d1D1	526,479.80	7,801.20
2018 Feb	555,841	ARIMA_d1D1	582,112.27	-26,271.27
2018 Mar	652,082	ARIMA_d1D1	668,424.02	-16,342.02
2018 Apr	689,214	ARIMA_d1D1	713,744.75	-24,530.75
2018 May	755,491	ARIMA_d1D1	743,570.60	11,920.40
2018 Jun	782,628	ARIMA_d1D1	797,888.67	-15,260.67
2018 Jul	837,740	ARIMA_d1D1	876,628.23	-38,888.23
2018 Aug	936,644	ARIMA_d1D1	911,970.84	24,673.16
2018 Sep	806,267	ARIMA_d1D1	814,978.73	-8,711.73
2018 Oct	721,989	ARIMA_d1D1	725,602.85	-3,613.85
2018 Nov	575,096	ARIMA_d1D1	580,967.29	-5,871.29
2018 Dec	496,993	ARIMA_d1D1	488,726.91	8,266.09
2019 Jan	486,306	ARIMA_d1D1	546,714.23	-60,408.23
2019 Feb	498,081	ARIMA_d1D1	535,005.47	-36,924.47
2019 Mar	606,616	ARIMA_d1D1	614,236.83	-7,620.83
2019 Apr	608,322	ARIMA_d1D1	665,065.79	-56,743.79
2019 May	665,724	ARIMA_d1D1	675,394.06	-9,670.06
2019 Jun	714,041	ARIMA_d1D1	701,624.78	12,416.22
2019 Jul	747,112	ARIMA_d1D1	779,901.17	-32,789.17
2019 Aug	828,426	ARIMA_d1D1	831,723.05	-3,297.05
2019 Sep	719,254	ARIMA_d1D1	703,167.16	16,086.84
2019 Oct	629,555	ARIMA_d1D1	636,509.44	-6,954.44
2019 Nov	508,290	ARIMA_d1D1	480,278.30	28,011.70
2019 Dec	445,470	ARIMA_d1D1	415,038.73	30,431.27
2020 Jan	488,461	ARIMA_d1D1	459,985.38	28,475.62
2020 Feb	540,254	ARIMA_d1D1	504,469.53	35,784.47
2020 Mar	297,649	ARIMA_d1D1	638,659.11	-341,010.11
2020 Apr	2,191	ARIMA_d1D1	409,800.97	-407,609.97
2020 May	2,955	ARIMA_d1D1	-29,423.41	32,378.41
2020 Jun	14,932	ARIMA_d1D1	118,649.95	-103,717.95
2020 Jul	95,576	ARIMA_d1D1	59,671.55	35,904.45
2020 Aug	240,322	ARIMA_d1D1	187,120.12	53,201.88
2020 Sep	251,221	ARIMA_d1D1	136,354.94	114,866.06
2020 Oct	253,895	ARIMA_d1D1	197,615.44	56,279.56
2020 Nov	116,634	ARIMA_d1D1	135,589.90	-18,955.90
2020 Dec	137,446	ARIMA_d1D1	37,241.37	100,204.63
2021 Jan	93,013	ARIMA_d1D1	197,926.84	-104,913.84
2021 Feb	40,883	ARIMA_d1D1	102,640.52	-61,757.52
2021 Mar	60,163	ARIMA_d1D1	-35,958.51	96,121.51
2021 Apr	95,116	ARIMA_d1D1	-14,831.36	109,947.36
2021 May	179,599	ARIMA_d1D1	164,476.64	15,122.36
2021 Jun	321,985	ARIMA_d1D1	216,756.98	105,228.02
2021 Jul	552,399	ARIMA_d1D1	412,374.46	140,024.54
2021 Aug	780,123	ARIMA_d1D1	698,217.06	81,905.94
2021 Sep	697,572	ARIMA_d1D1	744,497.42	-46,925.42
2021 Oct	655,682	ARIMA_d1D1	635,529.18	20,152.82
2021 Nov	521,638	ARIMA_d1D1	526,965.01	-5,327.01
2021 Dec	397,592	ARIMA_d1D1	472,810.91	-75,218.91
2022 Jan	341,744	ARIMA_d1D1	383,061.46	-41,317.46
2022 Feb	391,699	ARIMA_d1D1	330,038.63	61,660.37
2022 Mar	569,482	ARIMA_d1D1	372,984.65	196,497.35
2022 Apr	727,326	ARIMA_d1D1	609,441.60	117,884.40
2022 May	779,426	ARIMA_d1D1	828,723.78	-49,297.78
2022 Jun	833,955	ARIMA_d1D1	822,151.77	11,803.23
2010 Jan	319,379	ARIMA_d1D1_log	323,544.30	-4,165.30
2010 Feb	329,697	ARIMA_d1D1_log	356,913.49	-27,216.49
2010 Mar	388,978	ARIMA_d1D1_log	431,243.45	-42,265.45
2010 Apr	427,950	ARIMA_d1D1_log	442,193.90	-14,243.90
2010 May	431,385	ARIMA_d1D1_log	424,537.87	6,847.13
2010 Jun	432,522	ARIMA_d1D1_log	419,736.97	12,785.03
2010 Jul	492,382	ARIMA_d1D1_log	466,026.67	26,355.33
2010 Aug	624,383	ARIMA_d1D1_log	573,869.82	50,513.18
2010 Sep	496,609	ARIMA_d1D1_log	506,119.85	-9,510.85
2010 Oct	450,841	ARIMA_d1D1_log	438,643.28	12,197.72
2010 Nov	327,330	ARIMA_d1D1_log	355,473.17	-28,143.17
2010 Dec	272,069	ARIMA_d1D1_log	289,483.20	-17,414.20
2011 Jan	286,010	ARIMA_d1D1_log	286,920.27	-910.27
2011 Feb	319,015	ARIMA_d1D1_log	310,414.83	8,600.17
2011 Mar	448,224	ARIMA_d1D1_log	392,598.43	55,625.57
2011 Apr	517,979	ARIMA_d1D1_log	477,365.23	40,613.77
2011 May	575,401	ARIMA_d1D1_log	489,851.70	85,549.30
2011 Jun	519,950	ARIMA_d1D1_log	543,157.73	-23,207.73
2011 Jul	589,288	ARIMA_d1D1_log	559,017.95	30,270.05
2011 Aug	678,877	ARIMA_d1D1_log	699,017.86	-20,140.86
2011 Sep	577,108	ARIMA_d1D1_log	544,711.31	32,396.69
2011 Oct	471,268	ARIMA_d1D1_log	508,602.34	-37,334.34
2011 Nov	319,900	ARIMA_d1D1_log	360,291.17	-40,391.17
2011 Dec	262,266	ARIMA_d1D1_log	277,964.45	-15,698.45
2012 Jan	289,312	ARIMA_d1D1_log	279,078.21	10,233.79
2012 Feb	329,299	ARIMA_d1D1_log	318,922.97	10,376.03
2012 Mar	399,988	ARIMA_d1D1_log	430,914.19	-30,926.19
2012 Apr	508,131	ARIMA_d1D1_log	449,803.49	58,327.51
2012 May	521,638	ARIMA_d1D1_log	523,908.44	-2,270.44
2012 Jun	509,865	ARIMA_d1D1_log	489,904.69	19,960.31
2012 Jul	602,837	ARIMA_d1D1_log	562,942.01	39,894.99
2012 Aug	681,135	ARIMA_d1D1_log	700,814.22	-19,679.22
2012 Sep	562,007	ARIMA_d1D1_log	559,276.42	2,730.58
2012 Oct	468,951	ARIMA_d1D1_log	478,461.18	-9,510.18
2012 Nov	350,902	ARIMA_d1D1_log	337,425.82	13,476.18
2012 Dec	283,620	ARIMA_d1D1_log	291,422.22	-7,802.22
2013 Jan	322,235	ARIMA_d1D1_log	302,228.62	20,006.38
2013 Feb	365,343	ARIMA_d1D1_log	353,067.76	12,275.24
2013 Mar	462,258	ARIMA_d1D1_log	453,493.01	8,764.99
2013 Apr	516,930	ARIMA_d1D1_log	539,509.49	-22,579.49
2013 May	608,081	ARIMA_d1D1_log	531,457.06	76,623.94
2013 Jun	578,633	ARIMA_d1D1_log	573,680.91	4,952.09
2013 Jul	677,083	ARIMA_d1D1_log	644,653.86	32,429.14
2013 Aug	775,941	ARIMA_d1D1_log	800,966.50	-25,025.50
2013 Sep	639,271	ARIMA_d1D1_log	639,250.86	20.14
2013 Oct	535,649	ARIMA_d1D1_log	545,680.05	-10,031.05
2013 Nov	390,742	ARIMA_d1D1_log	386,028.90	4,713.10
2013 Dec	342,783	ARIMA_d1D1_log	319,599.25	23,183.75
2014 Jan	374,568	ARIMA_d1D1_log	376,917.28	-2,349.28
2014 Feb	401,859	ARIMA_d1D1_log	423,543.70	-21,684.70
2014 Mar	503,533	ARIMA_d1D1_log	520,901.02	-17,368.02
2014 Apr	557,275	ARIMA_d1D1_log	592,509.58	-35,234.58
2014 May	610,148	ARIMA_d1D1_log	619,544.23	-9,396.23
2014 Jun	595,332	ARIMA_d1D1_log	576,211.06	19,120.94
2014 Jul	687,207	ARIMA_d1D1_log	692,661.92	-5,454.92
2014 Aug	787,020	ARIMA_d1D1_log	786,769.10	250.90
2014 Sep	652,671	ARIMA_d1D1_log	656,284.80	-3,613.80
2014 Oct	554,671	ARIMA_d1D1_log	542,477.99	12,193.01
2014 Nov	415,750	ARIMA_d1D1_log	398,908.86	16,841.14
2014 Dec	366,832	ARIMA_d1D1_log	348,804.29	18,027.71
2015 Jan	399,040	ARIMA_d1D1_log	407,327.94	-8,287.94
2015 Feb	442,963	ARIMA_d1D1_log	443,956.42	-993.42
2015 Mar	545,523	ARIMA_d1D1_log	552,054.29	-6,531.29
2015 Apr	586,230	ARIMA_d1D1_log	633,360.20	-47,130.20
2015 May	628,998	ARIMA_d1D1_log	644,875.87	-15,877.87
2015 Jun	654,715	ARIMA_d1D1_log	610,314.52	44,400.48
2015 Jul	766,557	ARIMA_d1D1_log	765,422.03	1,134.97
2015 Aug	829,230	ARIMA_d1D1_log	875,789.12	-46,559.12
2015 Sep	696,849	ARIMA_d1D1_log	686,289.66	10,559.34
2015 Oct	597,629	ARIMA_d1D1_log	587,334.55	10,294.45
2015 Nov	475,257	ARIMA_d1D1_log	444,779.99	30,477.01
2015 Dec	407,035	ARIMA_d1D1_log	408,208.00	-1,173.00
2016 Jan	448,784	ARIMA_d1D1_log	449,915.67	-1,131.67
2016 Feb	506,179	ARIMA_d1D1_log	497,151.37	9,027.63
2016 Mar	611,987	ARIMA_d1D1_log	632,619.39	-20,632.39
2016 Apr	663,878	ARIMA_d1D1_log	672,357.48	-8,479.48
2016 May	726,980	ARIMA_d1D1_log	737,944.35	-10,964.35
2016 Jun	759,256	ARIMA_d1D1_log	723,721.76	35,534.24
2016 Jul	849,148	ARIMA_d1D1_log	877,149.15	-28,001.15
2016 Aug	891,091	ARIMA_d1D1_log	952,306.59	-61,215.59
2016 Sep	768,042	ARIMA_d1D1_log	751,276.23	16,765.77
2016 Oct	702,530	ARIMA_d1D1_log	654,325.60	48,204.40
2016 Nov	545,468	ARIMA_d1D1_log	531,833.90	13,634.10
2016 Dec	457,565	ARIMA_d1D1_log	468,441.71	-10,876.71
2017 Jan	503,654	ARIMA_d1D1_log	499,888.92	3,765.08
2017 Feb	541,368	ARIMA_d1D1_log	556,394.55	-15,026.55
2017 Mar	647,679	ARIMA_d1D1_log	666,263.82	-18,584.82
2017 Apr	710,409	ARIMA_d1D1_log	710,151.99	257.01
2017 May	745,096	ARIMA_d1D1_log	777,831.74	-32,735.74
2017 Jun	794,118	ARIMA_d1D1_log	773,630.03	20,487.97
2017 Jul	864,476	ARIMA_d1D1_log	910,231.01	-45,755.01
2017 Aug	939,077	ARIMA_d1D1_log	950,619.93	-11,542.93
2017 Sep	818,705	ARIMA_d1D1_log	803,171.87	15,533.13
2017 Oct	734,287	ARIMA_d1D1_log	725,043.16	9,243.84
2017 Nov	582,743	ARIMA_d1D1_log	569,887.88	12,855.12
2017 Dec	478,377	ARIMA_d1D1_log	495,787.17	-17,410.17
2018 Jan	534,281	ARIMA_d1D1_log	528,220.51	6,060.49
2018 Feb	555,841	ARIMA_d1D1_log	585,717.15	-29,876.15
2018 Mar	652,082	ARIMA_d1D1_log	680,891.77	-28,809.77
2018 Apr	689,214	ARIMA_d1D1_log	720,092.09	-30,878.09
2018 May	755,491	ARIMA_d1D1_log	750,739.47	4,751.53
2018 Jun	782,628	ARIMA_d1D1_log	805,882.89	-23,254.89
2018 Jul	837,740	ARIMA_d1D1_log	889,282.01	-51,542.01
2018 Aug	936,644	ARIMA_d1D1_log	920,035.36	16,608.64
2018 Sep	806,267	ARIMA_d1D1_log	814,074.62	-7,807.62
2018 Oct	721,989	ARIMA_d1D1_log	728,260.36	-6,271.36
2018 Nov	575,096	ARIMA_d1D1_log	574,503.97	592.03
2018 Dec	496,993	ARIMA_d1D1_log	482,433.24	14,559.76
2019 Jan	486,306	ARIMA_d1D1_log	549,917.74	-63,611.74
2019 Feb	498,081	ARIMA_d1D1_log	535,036.10	-36,955.10
2019 Mar	606,616	ARIMA_d1D1_log	609,083.08	-2,467.08
2019 Apr	608,322	ARIMA_d1D1_log	665,123.16	-56,801.16
2019 May	665,724	ARIMA_d1D1_log	678,441.90	-12,717.90
2019 Jun	714,041	ARIMA_d1D1_log	712,747.44	1,293.56
2019 Jul	747,112	ARIMA_d1D1_log	787,798.68	-40,686.68
2019 Aug	828,426	ARIMA_d1D1_log	832,498.49	-4,072.49
2019 Sep	719,254	ARIMA_d1D1_log	725,779.70	-6,525.70
2019 Oct	629,555	ARIMA_d1D1_log	654,552.70	-24,997.70
2019 Nov	508,290	ARIMA_d1D1_log	505,074.76	3,215.24
2019 Dec	445,470	ARIMA_d1D1_log	433,516.80	11,953.20
2020 Jan	488,461	ARIMA_d1D1_log	465,039.82	23,421.18
2020 Feb	540,254	ARIMA_d1D1_log	504,350.43	35,903.57
2020 Mar	297,649	ARIMA_d1D1_log	637,873.12	-340,224.12
2020 Apr	2,191	ARIMA_d1D1_log	386,344.23	-384,153.23
2020 May	2,955	ARIMA_d1D1_log	0.88	2,954.12
2020 Jun	14,932	ARIMA_d1D1_log	51,957.88	-37,025.88
2020 Jul	95,576	ARIMA_d1D1_log	68,002.70	27,573.30
2020 Aug	240,322	ARIMA_d1D1_log	85,063.99	155,258.01
2020 Sep	251,221	ARIMA_d1D1_log	215,981.64	35,239.36
2020 Oct	253,895	ARIMA_d1D1_log	175,022.87	78,872.13
2020 Nov	116,634	ARIMA_d1D1_log	176,914.57	-60,280.57
2020 Dec	137,446	ARIMA_d1D1_log	75,348.03	62,097.97
2021 Jan	93,013	ARIMA_d1D1_log	162,520.10	-69,507.10
2021 Feb	40,883	ARIMA_d1D1_log	90,650.00	-49,767.00
2021 Mar	60,163	ARIMA_d1D1_log	21,782.60	38,380.40
2021 Apr	95,116	ARIMA_d1D1_log	2,561.18	92,554.82
2021 May	179,599	ARIMA_d1D1_log	147,379.64	32,219.36
2021 Jun	321,985	ARIMA_d1D1_log	218,151.80	103,833.20
2021 Jul	552,399	ARIMA_d1D1_log	336,740.04	215,658.96
2021 Aug	780,123	ARIMA_d1D1_log	551,450.64	228,672.36
2021 Sep	697,572	ARIMA_d1D1_log	535,560.80	162,011.20
2021 Oct	655,682	ARIMA_d1D1_log	469,741.51	185,940.49
2021 Nov	521,638	ARIMA_d1D1_log	407,596.36	114,041.64
2021 Dec	397,592	ARIMA_d1D1_log	381,799.88	15,792.12
2022 Jan	341,744	ARIMA_d1D1_log	332,219.71	9,524.29
2022 Feb	391,699	ARIMA_d1D1_log	293,418.62	98,280.38
2022 Mar	569,482	ARIMA_d1D1_log	343,064.95	226,417.05
2022 Apr	727,326	ARIMA_d1D1_log	107,227.94	620,098.06
2022 May	779,426	ARIMA_d1D1_log	842,400.17	-62,974.17
2022 Jun	833,955	ARIMA_d1D1_log	745,603.52	88,351.48
2010 Jan	319,379	Drift_STL	330,843.27	-11,464.27
2010 Feb	329,697	Drift_STL	354,519.50	-24,822.50
2010 Mar	388,978	Drift_STL	435,024.77	-46,046.77
2010 Apr	427,950	Drift_STL	440,441.70	-12,491.70
2010 May	431,385	Drift_STL	402,016.31	29,368.69
2010 Jun	432,522	Drift_STL	404,134.02	28,387.98
2010 Jul	492,382	Drift_STL	473,579.02	18,802.98
2010 Aug	624,383	Drift_STL	590,749.07	33,633.93
2010 Sep	496,609	Drift_STL	506,271.45	-9,662.45
2010 Oct	450,841	Drift_STL	445,058.82	5,782.18
2010 Nov	327,330	Drift_STL	358,811.14	-31,481.14
2010 Dec	272,069	Drift_STL	282,836.80	-10,767.80
2011 Jan	286,010	Drift_STL	294,841.89	-8,831.89
2011 Feb	319,015	Drift_STL	321,227.23	-2,212.23
2011 Mar	448,224	Drift_STL	419,653.39	28,570.61
2011 Apr	517,979	Drift_STL	492,415.05	25,563.95
2011 May	575,401	Drift_STL	490,786.30	84,614.70
2011 Jun	519,950	Drift_STL	540,318.94	-20,368.94
2011 Jul	589,288	Drift_STL	561,530.87	27,757.13
2011 Aug	678,877	Drift_STL	689,922.40	-11,045.40
2011 Sep	577,108	Drift_STL	562,987.61	14,120.39
2011 Oct	471,268	Drift_STL	526,794.53	-55,526.53
2011 Nov	319,900	Drift_STL	382,948.09	-63,048.09
2011 Dec	262,266	Drift_STL	285,867.30	-23,601.30
2012 Jan	289,312	Drift_STL	291,459.51	-2,147.51
2012 Feb	329,299	Drift_STL	329,192.53	106.47
2012 Mar	399,988	Drift_STL	437,282.37	-37,294.37
2012 Apr	508,131	Drift_STL	455,827.17	52,303.83
2012 May	521,638	Drift_STL	497,996.75	23,641.25
2012 Jun	509,865	Drift_STL	486,480.47	23,384.53
2012 Jul	602,837	Drift_STL	551,065.46	51,771.54
2012 Aug	681,135	Drift_STL	693,387.18	-12,252.18
2012 Sep	562,007	Drift_STL	561,249.26	757.74
2012 Oct	468,951	Drift_STL	497,658.38	-28,707.38
2012 Nov	350,902	Drift_STL	365,119.66	-14,217.66
2012 Dec	283,620	Drift_STL	307,405.54	-23,785.54
2013 Jan	322,235	Drift_STL	309,416.53	12,818.47
2013 Feb	365,343	Drift_STL	359,587.31	5,755.69
2013 Mar	462,258	Drift_STL	466,834.44	-4,576.44
2013 Apr	516,930	Drift_STL	525,004.39	-8,074.39
2013 May	608,081	Drift_STL	519,628.77	88,452.23
2013 Jun	578,633	Drift_STL	572,310.01	6,322.99
2013 Jul	677,083	Drift_STL	627,507.69	49,575.31
2013 Aug	775,941	Drift_STL	763,005.10	12,935.90
2013 Sep	639,271	Drift_STL	652,818.91	-13,547.91
2013 Oct	535,649	Drift_STL	567,527.09	-31,878.09
2013 Nov	390,742	Drift_STL	428,507.85	-37,765.85
2013 Dec	342,783	Drift_STL	348,046.15	-5,263.15
2014 Jan	374,568	Drift_STL	372,274.76	2,293.24
2014 Feb	401,859	Drift_STL	415,315.43	-13,456.43
2014 Mar	503,533	Drift_STL	505,464.89	-1,931.89
2014 Apr	557,275	Drift_STL	569,149.04	-11,874.04
2014 May	610,148	Drift_STL	580,430.43	29,717.57
2014 Jun	595,332	Drift_STL	580,147.92	15,184.08
2014 Jul	687,207	Drift_STL	654,545.16	32,661.84
2014 Aug	787,020	Drift_STL	773,900.85	13,119.15
2014 Sep	652,671	Drift_STL	659,809.64	-7,138.64
2014 Oct	554,671	Drift_STL	570,256.63	-15,585.63
2014 Nov	415,750	Drift_STL	435,538.26	-19,788.26
2014 Dec	366,832	Drift_STL	368,301.60	-1,469.60
2015 Jan	399,040	Drift_STL	394,305.22	4,734.78
2015 Feb	442,963	Drift_STL	435,497.24	7,465.76
2015 Mar	545,523	Drift_STL	541,716.64	3,806.36
2015 Apr	586,230	Drift_STL	608,498.31	-22,268.31
2015 May	628,998	Drift_STL	620,028.69	8,969.31
2015 Jun	654,715	Drift_STL	603,333.07	51,381.93
2015 Jul	766,557	Drift_STL	718,452.64	48,104.36
2015 Aug	829,230	Drift_STL	849,248.85	-20,018.85
2015 Sep	696,849	Drift_STL	700,635.68	-3,786.68
2015 Oct	597,629	Drift_STL	609,333.53	-11,704.53
2015 Nov	475,257	Drift_STL	472,590.19	2,666.81
2015 Dec	407,035	Drift_STL	425,587.68	-18,552.68
2016 Jan	448,784	Drift_STL	437,469.58	11,314.42
2016 Feb	506,179	Drift_STL	486,008.91	20,170.09
2016 Mar	611,987	Drift_STL	602,398.18	9,588.82
2016 Apr	663,878	Drift_STL	670,297.71	-6,419.71
2016 May	726,980	Drift_STL	701,892.86	25,087.14
2016 Jun	759,256	Drift_STL	706,289.07	52,966.93
2016 Jul	849,148	Drift_STL	829,781.00	19,367.00
2016 Aug	891,091	Drift_STL	927,193.32	-36,102.32
2016 Sep	768,042	Drift_STL	763,296.56	4,745.44
2016 Oct	702,530	Drift_STL	676,908.79	25,621.21
2016 Nov	545,468	Drift_STL	571,621.57	-26,153.57
2016 Dec	457,565	Drift_STL	493,539.42	-35,974.42
2017 Jan	503,654	Drift_STL	494,568.78	9,085.22
2017 Feb	541,368	Drift_STL	546,004.69	-4,636.69
2017 Mar	647,679	Drift_STL	641,213.35	6,465.65
2017 Apr	710,409	Drift_STL	706,119.38	4,289.62
2017 May	745,096	Drift_STL	755,697.00	-10,601.00
2017 Jun	794,118	Drift_STL	736,279.19	57,838.81
2017 Jul	864,476	Drift_STL	869,001.35	-4,525.35
2017 Aug	939,077	Drift_STL	935,557.31	3,519.69
2017 Sep	818,705	Drift_STL	806,855.38	11,849.62
2017 Oct	734,287	Drift_STL	724,977.45	9,309.55
2017 Nov	582,743	Drift_STL	594,911.04	-12,168.04
2017 Dec	478,377	Drift_STL	521,411.97	-43,034.97
2018 Jan	534,281	Drift_STL	518,435.87	15,845.13
2018 Feb	555,841	Drift_STL	575,139.84	-19,298.84
2018 Mar	652,082	Drift_STL	657,354.93	-5,272.93
2018 Apr	689,214	Drift_STL	711,792.29	-22,578.29
2018 May	755,491	Drift_STL	739,886.68	15,604.32
2018 Jun	782,628	Drift_STL	758,045.36	24,582.64
2018 Jul	837,740	Drift_STL	860,522.87	-22,782.87
2018 Aug	936,644	Drift_STL	909,781.47	26,862.53
2018 Sep	806,267	Drift_STL	803,712.83	2,554.17
2018 Oct	721,989	Drift_STL	711,610.50	10,378.50
2018 Nov	575,096	Drift_STL	576,849.98	-1,753.98
2018 Dec	496,993	Drift_STL	502,293.39	-5,300.39
2019 Jan	486,306	Drift_STL	535,809.92	-49,503.92
2019 Feb	498,081	Drift_STL	528,458.31	-30,377.31
2019 Mar	606,616	Drift_STL	603,567.26	3,048.74
2019 Apr	608,322	Drift_STL	663,281.07	-54,959.07
2019 May	665,724	Drift_STL	668,873.49	-3,149.49
2019 Jun	714,041	Drift_STL	681,412.32	32,628.68
2019 Jul	747,112	Drift_STL	790,356.39	-43,244.39
2019 Aug	828,426	Drift_STL	825,148.70	3,277.30
2019 Sep	719,254	Drift_STL	698,838.02	20,415.98
2019 Oct	629,555	Drift_STL	624,822.34	4,732.66
2019 Nov	508,290	Drift_STL	481,146.52	27,143.48
2019 Dec	445,470	Drift_STL	426,763.33	18,706.67
2020 Jan	488,461	Drift_STL	471,074.88	17,386.12
2020 Feb	540,254	Drift_STL	515,419.51	24,834.49
2020 Mar	297,649	Drift_STL	635,479.21	-337,830.21
2020 Apr	2,191	Drift_STL	378,242.14	-376,051.14
2020 May	2,955	Drift_STL	125,737.09	-122,782.09
2020 Jun	14,932	Drift_STL	80,673.08	-65,741.08
2020 Jul	95,576	Drift_STL	123,402.65	-27,826.65
2020 Aug	240,322	Drift_STL	195,216.51	45,105.49
2020 Sep	251,221	Drift_STL	114,997.17	136,223.83
2020 Oct	253,895	Drift_STL	136,829.03	117,065.97
2020 Nov	116,634	Drift_STL	78,308.07	38,325.93
2020 Dec	137,446	Drift_STL	9,352.94	128,093.06
2021 Jan	93,013	Drift_STL	132,161.34	-39,148.34
2021 Feb	40,883	Drift_STL	106,165.16	-65,282.16
2021 Mar	60,163	Drift_STL	82,771.82	-22,608.82
2021 Apr	95,116	Drift_STL	56,482.60	38,633.40
2021 May	179,599	Drift_STL	153,477.13	26,121.87
2021 Jun	321,985	Drift_STL	217,417.04	104,567.96
2021 Jul	552,399	Drift_STL	394,668.17	157,730.83
2021 Aug	780,123	Drift_STL	627,969.33	152,153.67
2021 Sep	697,572	Drift_STL	655,978.68	41,593.32
2021 Oct	655,682	Drift_STL	607,745.54	47,936.46
2021 Nov	521,638	Drift_STL	499,761.14	21,876.86
2021 Dec	397,592	Drift_STL	452,737.00	-55,145.00
2022 Jan	341,744	Drift_STL	423,132.02	-81,388.02
2022 Feb	391,699	Drift_STL	379,081.11	12,617.89
2022 Mar	569,482	Drift_STL	441,299.84	128,182.16
2022 Apr	727,326	Drift_STL	560,806.70	166,519.30
2022 May	779,426	Drift_STL	775,255.17	4,170.83
2022 Jun	833,955	Drift_STL	831,088.96	2,866.04
2010 Jan	319,379	Drift_STL_log	328,457.48	-9,078.48
2010 Feb	329,697	Drift_STL_log	350,624.01	-20,927.01
2010 Mar	388,978	Drift_STL_log	417,519.94	-28,541.94
2010 Apr	427,950	Drift_STL_log	429,274.14	-1,324.14
2010 May	431,385	Drift_STL_log	406,256.89	25,128.11
2010 Jun	432,522	Drift_STL_log	407,633.81	24,888.19
2010 Jul	492,382	Drift_STL_log	467,666.27	24,715.73
2010 Aug	624,383	Drift_STL_log	580,773.25	43,609.75
2010 Sep	496,609	Drift_STL_log	508,351.90	-11,742.90
2010 Oct	450,841	Drift_STL_log	448,841.24	1,999.76
2010 Nov	327,330	Drift_STL_log	365,507.86	-38,177.86
2010 Dec	272,069	Drift_STL_log	291,770.29	-19,701.29
2011 Jan	286,010	Drift_STL_log	291,536.89	-5,526.89
2011 Feb	319,015	Drift_STL_log	314,862.18	4,152.82
2011 Mar	448,224	Drift_STL_log	401,619.56	46,604.44
2011 Apr	517,979	Drift_STL_log	486,809.11	31,169.89
2011 May	575,401	Drift_STL_log	489,360.90	86,040.10
2011 Jun	519,950	Drift_STL_log	535,241.01	-15,291.01
2011 Jul	589,288	Drift_STL_log	562,817.71	26,470.29
2011 Aug	678,877	Drift_STL_log	699,645.77	-20,768.77
2011 Sep	577,108	Drift_STL_log	556,635.96	20,472.04
2011 Oct	471,268	Drift_STL_log	522,350.82	-51,082.82
2011 Nov	319,900	Drift_STL_log	381,208.09	-61,308.09
2011 Dec	262,266	Drift_STL_log	289,298.82	-27,032.82
2012 Jan	289,312	Drift_STL_log	285,494.29	3,817.71
2012 Feb	329,299	Drift_STL_log	322,615.16	6,683.84
2012 Mar	399,988	Drift_STL_log	424,514.66	-24,526.66
2012 Apr	508,131	Drift_STL_log	446,514.25	61,616.75
2012 May	521,638	Drift_STL_log	495,727.92	25,910.08
2012 Jun	509,865	Drift_STL_log	485,548.58	24,316.42
2012 Jul	602,837	Drift_STL_log	550,161.61	52,675.39
2012 Aug	681,135	Drift_STL_log	700,305.03	-19,170.03
2012 Sep	562,007	Drift_STL_log	555,101.29	6,905.71
2012 Oct	468,951	Drift_STL_log	495,030.22	-26,079.22
2012 Nov	350,902	Drift_STL_log	364,202.20	-13,300.20
2012 Dec	283,620	Drift_STL_log	307,649.11	-24,029.11
2013 Jan	322,235	Drift_STL_log	307,167.21	15,067.79
2013 Feb	365,343	Drift_STL_log	358,493.31	6,849.69
2013 Mar	462,258	Drift_STL_log	467,197.97	-4,939.97
2013 Apr	516,930	Drift_STL_log	526,556.25	-9,626.25
2013 May	608,081	Drift_STL_log	519,238.45	88,842.55
2013 Jun	578,633	Drift_STL_log	568,677.31	9,955.69
2013 Jul	677,083	Drift_STL_log	634,190.82	42,892.18
2013 Aug	775,941	Drift_STL_log	782,045.60	-6,104.60
2013 Sep	639,271	Drift_STL_log	633,429.97	5,841.03
2013 Oct	535,649	Drift_STL_log	555,014.97	-19,365.97
2013 Nov	390,742	Drift_STL_log	409,913.39	-19,171.39
2013 Dec	342,783	Drift_STL_log	338,129.33	4,653.67
2014 Jan	374,568	Drift_STL_log	371,919.17	2,648.83
2014 Feb	401,859	Drift_STL_log	418,655.44	-16,796.44
2014 Mar	503,533	Drift_STL_log	516,958.42	-13,425.42
2014 Apr	557,275	Drift_STL_log	578,899.55	-21,624.55
2014 May	610,148	Drift_STL_log	582,908.12	27,239.88
2014 Jun	595,332	Drift_STL_log	579,477.03	15,854.97
2014 Jul	687,207	Drift_STL_log	664,130.73	23,076.27
2014 Aug	787,020	Drift_STL_log	793,079.75	-6,059.75
2014 Sep	652,671	Drift_STL_log	643,512.79	9,158.21
2014 Oct	554,671	Drift_STL_log	558,221.75	-3,550.75
2014 Nov	415,750	Drift_STL_log	415,082.18	667.82
2014 Dec	366,832	Drift_STL_log	355,538.86	11,293.14
2015 Jan	399,040	Drift_STL_log	395,406.71	3,633.29
2015 Feb	442,963	Drift_STL_log	440,473.03	2,489.97
2015 Mar	545,523	Drift_STL_log	562,213.35	-16,690.35
2015 Apr	586,230	Drift_STL_log	623,945.16	-37,715.16
2015 May	628,998	Drift_STL_log	625,531.84	3,466.16
2015 Jun	654,715	Drift_STL_log	603,559.44	51,155.56
2015 Jul	766,557	Drift_STL_log	735,157.38	31,399.62
2015 Aug	829,230	Drift_STL_log	878,030.03	-48,800.03
2015 Sep	696,849	Drift_STL_log	682,650.35	14,198.65
2015 Oct	597,629	Drift_STL_log	593,230.48	4,398.52
2015 Nov	475,257	Drift_STL_log	443,337.84	31,919.16
2015 Dec	407,035	Drift_STL_log	403,395.94	3,639.06
2016 Jan	448,784	Drift_STL_log	438,732.93	10,051.07
2016 Feb	506,179	Drift_STL_log	493,215.36	12,963.64
2016 Mar	611,987	Drift_STL_log	634,701.74	-22,714.74
2016 Apr	663,878	Drift_STL_log	693,925.41	-30,047.41
2016 May	726,980	Drift_STL_log	715,386.31	11,593.69
2016 Jun	759,256	Drift_STL_log	706,710.20	52,545.80
2016 Jul	849,148	Drift_STL_log	860,762.88	-11,614.88
2016 Aug	891,091	Drift_STL_log	965,943.98	-74,852.98
2016 Sep	768,042	Drift_STL_log	742,643.04	25,398.96
2016 Oct	702,530	Drift_STL_log	654,041.57	48,488.43
2016 Nov	545,468	Drift_STL_log	520,531.68	24,936.32
2016 Dec	457,565	Drift_STL_log	460,239.90	-2,674.90
2017 Jan	503,654	Drift_STL_log	494,991.42	8,662.58
2017 Feb	541,368	Drift_STL_log	553,936.16	-12,568.16
2017 Mar	647,679	Drift_STL_log	674,680.77	-27,001.77
2017 Apr	710,409	Drift_STL_log	731,240.73	-20,831.73
2017 May	745,096	Drift_STL_log	773,992.64	-28,896.64
2017 Jun	794,118	Drift_STL_log	739,018.78	55,099.22
2017 Jul	864,476	Drift_STL_log	902,217.95	-37,741.95
2017 Aug	939,077	Drift_STL_log	970,805.20	-31,728.20
2017 Sep	818,705	Drift_STL_log	787,159.64	31,545.36
2017 Oct	734,287	Drift_STL_log	700,890.57	33,396.43
2017 Nov	582,743	Drift_STL_log	545,567.55	37,175.45
2017 Dec	478,377	Drift_STL_log	486,499.20	-8,122.20
2018 Jan	534,281	Drift_STL_log	517,403.81	16,877.19
2018 Feb	555,841	Drift_STL_log	581,450.27	-25,609.27
2018 Mar	652,082	Drift_STL_log	684,911.67	-32,829.67
2018 Apr	689,214	Drift_STL_log	732,162.60	-42,948.60
2018 May	755,491	Drift_STL_log	754,961.42	529.58
2018 Jun	782,628	Drift_STL_log	762,104.22	20,523.78
2018 Jul	837,740	Drift_STL_log	887,517.20	-49,777.20
2018 Aug	936,644	Drift_STL_log	935,636.46	1,007.54
2018 Sep	806,267	Drift_STL_log	792,128.03	14,138.97
2018 Oct	721,989	Drift_STL_log	695,899.08	26,089.92
2018 Nov	575,096	Drift_STL_log	542,360.11	32,735.89
2018 Dec	496,993	Drift_STL_log	476,204.73	20,788.27
2019 Jan	486,306	Drift_STL_log	535,200.63	-48,894.63
2019 Feb	498,081	Drift_STL_log	528,643.49	-30,562.49
2019 Mar	606,616	Drift_STL_log	611,124.51	-4,508.51
2019 Apr	608,322	Drift_STL_log	672,533.13	-64,211.13
2019 May	665,724	Drift_STL_log	673,132.50	-7,408.50
2019 Jun	714,041	Drift_STL_log	683,040.81	31,000.19
2019 Jul	747,112	Drift_STL_log	801,631.03	-54,519.03
2019 Aug	828,426	Drift_STL_log	833,179.40	-4,753.40
2019 Sep	719,254	Drift_STL_log	706,397.07	12,856.93
2019 Oct	629,555	Drift_STL_log	625,911.52	3,643.48
2019 Nov	508,290	Drift_STL_log	480,055.89	28,234.11
2019 Dec	445,470	Drift_STL_log	422,244.32	23,225.68
2020 Jan	488,461	Drift_STL_log	470,016.36	18,444.64
2020 Feb	540,254	Drift_STL_log	516,462.15	23,791.85
2020 Mar	297,649	Drift_STL_log	646,643.06	-348,994.06
2020 Apr	2,191	Drift_STL_log	350,547.34	-348,356.34
2020 May	2,955	Drift_STL_log	4,827.06	-1,872.06
2020 Jun	14,932	Drift_STL_log	4,982.29	9,949.71
2020 Jul	95,576	Drift_STL_log	19,165.49	76,410.51
2020 Aug	240,322	Drift_STL_log	94,242.10	146,079.90
2020 Sep	251,221	Drift_STL_log	164,560.37	86,660.63
2020 Oct	253,895	Drift_STL_log	177,064.39	76,830.61
2020 Nov	116,634	Drift_STL_log	164,845.11	-48,211.11
2020 Dec	137,446	Drift_STL_log	92,263.77	45,182.23
2021 Jan	93,013	Drift_STL_log	136,582.02	-43,569.02
2021 Feb	40,883	Drift_STL_log	100,121.01	-59,238.01
2021 Mar	60,163	Drift_STL_log	50,102.84	10,060.16
2021 Apr	95,116	Drift_STL_log	32,671.18	62,444.82
2021 May	179,599	Drift_STL_log	117,844.40	61,754.60
2021 Jun	321,985	Drift_STL_log	257,747.03	64,237.97
2021 Jul	552,399	Drift_STL_log	486,964.27	65,434.73
2021 Aug	780,123	Drift_STL_log	702,816.46	77,306.54
2021 Sep	697,572	Drift_STL_log	698,978.84	-1,406.84
2021 Oct	655,682	Drift_STL_log	646,396.04	9,285.96
2021 Nov	521,638	Drift_STL_log	484,536.99	37,101.01
2021 Dec	397,592	Drift_STL_log	486,126.58	-88,534.58
2022 Jan	341,744	Drift_STL_log	423,675.66	-81,931.66
2022 Feb	391,699	Drift_STL_log	350,601.16	41,097.84
2022 Mar	569,482	Drift_STL_log	473,749.67	95,732.33
2022 Apr	727,326	Drift_STL_log	316,684.30	410,641.70
2022 May	779,426	Drift_STL_log	966,040.95	-186,614.95
2022 Jun	833,955	Drift_STL_log	1,272,200.24	-438,245.24
2010 Jan	319,379	ETS_auto	325,493.63	-6,114.63
2010 Feb	329,697	ETS_auto	349,358.98	-19,661.98
2010 Mar	388,978	ETS_auto	423,844.10	-34,866.10
2010 Apr	427,950	ETS_auto	426,321.85	1,628.15
2010 May	431,385	ETS_auto	391,959.85	39,425.15
2010 Jun	432,522	ETS_auto	402,588.11	29,933.89
2010 Jul	492,382	ETS_auto	473,579.88	18,802.12
2010 Aug	624,383	ETS_auto	584,096.62	40,286.38
2010 Sep	496,609	ETS_auto	512,566.59	-15,957.59
2010 Oct	450,841	ETS_auto	463,567.97	-12,726.97
2010 Nov	327,330	ETS_auto	385,364.85	-58,034.85
2010 Dec	272,069	ETS_auto	280,937.87	-8,868.87
2011 Jan	286,010	ETS_auto	290,743.18	-4,733.18
2011 Feb	319,015	ETS_auto	321,729.93	-2,714.93
2011 Mar	448,224	ETS_auto	407,942.97	40,281.03
2011 Apr	517,979	ETS_auto	489,854.87	28,124.13
2011 May	575,401	ETS_auto	475,126.30	100,274.70
2011 Jun	519,950	ETS_auto	551,426.09	-31,476.09
2011 Jul	589,288	ETS_auto	565,404.33	23,883.67
2011 Aug	678,877	ETS_auto	690,409.67	-11,532.67
2011 Sep	577,108	ETS_auto	573,427.48	3,680.52
2011 Oct	471,268	ETS_auto	538,751.59	-67,483.59
2011 Nov	319,900	ETS_auto	398,031.10	-78,131.10
2011 Dec	262,266	ETS_auto	268,716.54	-6,450.54
2012 Jan	289,312	ETS_auto	279,248.78	10,063.22
2012 Feb	329,299	ETS_auto	324,226.06	5,072.94
2012 Mar	399,988	ETS_auto	421,417.43	-21,429.43
2012 Apr	508,131	ETS_auto	448,223.67	59,907.33
2012 May	521,638	ETS_auto	474,180.36	47,457.64
2012 Jun	509,865	ETS_auto	498,956.63	10,908.37
2012 Jul	602,837	ETS_auto	555,749.37	47,087.63
2012 Aug	681,135	ETS_auto	703,616.76	-22,481.76
2012 Sep	562,007	ETS_auto	575,578.06	-13,571.06
2012 Oct	468,951	ETS_auto	518,415.47	-49,464.47
2012 Nov	350,902	ETS_auto	385,872.49	-34,970.49
2012 Dec	283,620	ETS_auto	299,286.73	-15,666.73
2013 Jan	322,235	ETS_auto	301,375.89	20,859.11
2013 Feb	365,343	ETS_auto	357,081.61	8,261.39
2013 Mar	462,258	ETS_auto	455,952.68	6,305.32
2013 Apr	516,930	ETS_auto	511,501.68	5,428.32
2013 May	608,081	ETS_auto	490,391.57	117,689.43
2013 Jun	578,633	ETS_auto	547,197.06	31,435.94
2013 Jul	677,083	ETS_auto	627,688.57	49,394.43
2013 Aug	775,941	ETS_auto	726,660.91	49,280.09
2013 Sep	639,271	ETS_auto	668,824.59	-29,553.59
2013 Oct	535,649	ETS_auto	591,647.88	-55,998.88
2013 Nov	390,742	ETS_auto	380,996.97	9,745.03
2013 Dec	342,783	ETS_auto	318,280.85	24,502.15
2014 Jan	374,568	ETS_auto	378,641.99	-4,073.99
2014 Feb	401,859	ETS_auto	425,683.28	-23,824.28
2014 Mar	503,533	ETS_auto	528,197.77	-24,664.77
2014 Apr	557,275	ETS_auto	604,727.28	-47,452.28
2014 May	610,148	ETS_auto	664,704.32	-54,556.32
2014 Jun	595,332	ETS_auto	599,197.30	-3,865.30
2014 Jul	687,207	ETS_auto	677,707.22	9,499.78
2014 Aug	787,020	ETS_auto	761,253.91	25,766.09
2014 Sep	652,671	ETS_auto	627,080.22	25,590.78
2014 Oct	554,671	ETS_auto	525,810.53	28,860.47
2014 Nov	415,750	ETS_auto	390,497.29	25,252.71
2014 Dec	366,832	ETS_auto	337,583.93	29,248.07
2015 Jan	399,040	ETS_auto	381,576.71	17,463.29
2015 Feb	442,963	ETS_auto	427,309.49	15,653.51
2015 Mar	545,523	ETS_auto	549,355.56	-3,832.56
2015 Apr	586,230	ETS_auto	629,087.95	-42,857.95
2015 May	628,998	ETS_auto	691,631.39	-62,633.39
2015 Jun	654,715	ETS_auto	649,402.54	5,312.46
2015 Jul	766,557	ETS_auto	757,550.54	9,006.46
2015 Aug	829,230	ETS_auto	862,262.69	-33,032.69
2015 Sep	696,849	ETS_auto	693,018.78	3,830.22
2015 Oct	597,629	ETS_auto	575,822.66	21,806.34
2015 Nov	475,257	ETS_auto	425,543.05	49,713.95
2015 Dec	407,035	ETS_auto	380,305.05	26,729.95
2016 Jan	448,784	ETS_auto	415,755.48	33,028.52
2016 Feb	506,179	ETS_auto	466,009.76	40,169.24
2016 Mar	611,987	ETS_auto	596,254.08	15,732.92
2016 Apr	663,878	ETS_auto	677,755.70	-13,877.70
2016 May	726,980	ETS_auto	649,593.73	77,386.27
2016 Jun	759,256	ETS_auto	762,194.60	-2,938.60
2016 Jul	849,148	ETS_auto	883,928.74	-34,780.74
2016 Aug	891,091	ETS_auto	952,944.83	-61,853.83
2016 Sep	768,042	ETS_auto	776,113.46	-8,071.46
2016 Oct	702,530	ETS_auto	660,922.08	41,607.92
2016 Nov	545,468	ETS_auto	517,673.04	27,794.96
2016 Dec	457,565	ETS_auto	438,258.58	19,306.42
2017 Jan	503,654	ETS_auto	481,851.23	21,802.77
2017 Feb	541,368	ETS_auto	538,903.28	2,464.72
2017 Mar	647,679	ETS_auto	646,353.76	1,325.24
2017 Apr	710,409	ETS_auto	701,702.89	8,706.11
2017 May	745,096	ETS_auto	771,769.26	-26,673.26
2017 Jun	794,118	ETS_auto	794,293.14	-175.14
2017 Jul	864,476	ETS_auto	900,496.51	-36,020.51
2017 Aug	939,077	ETS_auto	961,905.75	-22,828.75
2017 Sep	818,705	ETS_auto	824,298.71	-5,593.71
2017 Oct	734,287	ETS_auto	732,857.96	1,429.04
2017 Nov	582,743	ETS_auto	556,689.66	26,053.34
2017 Dec	478,377	ETS_auto	467,595.75	10,781.25
2018 Jan	534,281	ETS_auto	511,020.94	23,260.06
2018 Feb	555,841	ETS_auto	555,370.74	470.26
2018 Mar	652,082	ETS_auto	667,169.84	-15,087.84
2018 Apr	689,214	ETS_auto	715,924.03	-26,710.03
2018 May	755,491	ETS_auto	754,283.73	1,207.27
2018 Jun	782,628	ETS_auto	803,927.96	-21,299.96
2018 Jul	837,740	ETS_auto	874,340.63	-36,600.63
2018 Aug	936,644	ETS_auto	939,918.98	-3,274.98
2018 Sep	806,267	ETS_auto	823,555.08	-17,288.08
2018 Oct	721,989	ETS_auto	733,635.34	-11,646.34
2018 Nov	575,096	ETS_auto	568,373.32	6,722.68
2018 Dec	496,993	ETS_auto	465,152.96	31,840.04
2019 Jan	486,306	ETS_auto	523,320.21	-37,014.21
2019 Feb	498,081	ETS_auto	529,097.35	-31,016.35
2019 Mar	606,616	ETS_auto	620,085.49	-13,469.49
2019 Apr	608,322	ETS_auto	654,491.80	-46,169.80
2019 May	665,724	ETS_auto	700,843.01	-35,119.01
2019 Jun	714,041	ETS_auto	717,482.17	-3,441.17
2019 Jul	747,112	ETS_auto	783,426.40	-36,314.40
2019 Aug	828,426	ETS_auto	863,980.04	-35,554.04
2019 Sep	719,254	ETS_auto	738,641.14	-19,387.14
2019 Oct	629,555	ETS_auto	659,756.89	-30,201.89
2019 Nov	508,290	ETS_auto	512,275.68	-3,985.68
2019 Dec	445,470	ETS_auto	434,492.52	10,977.48
2020 Jan	488,461	ETS_auto	441,538.23	46,922.77
2020 Feb	540,254	ETS_auto	481,439.56	58,814.44
2020 Mar	297,649	ETS_auto	612,975.40	-315,326.40
2020 Apr	2,191	ETS_auto	520,664.18	-518,473.18
2020 May	2,955	ETS_auto	6,250.23	-3,295.23
2020 Jun	14,932	ETS_auto	-4,134.24	19,066.24
2020 Jul	95,576	ETS_auto	72,402.04	23,173.96
2020 Aug	240,322	ETS_auto	175,628.92	64,693.08
2020 Sep	251,221	ETS_auto	126,480.11	124,740.89
2020 Oct	253,895	ETS_auto	190,426.86	63,468.14
2020 Nov	116,634	ETS_auto	152,472.59	-35,838.59
2020 Dec	137,446	ETS_auto	60,006.30	77,439.70
2021 Jan	93,013	ETS_auto	163,971.47	-70,958.47
2021 Feb	40,883	ETS_auto	138,144.76	-97,261.76
2021 Mar	60,163	ETS_auto	122,139.67	-61,976.67
2021 Apr	95,116	ETS_auto	97,869.50	-2,753.50
2021 May	179,599	ETS_auto	100,576.28	79,022.72
2021 Jun	321,985	ETS_auto	174,913.70	147,071.30
2021 Jul	552,399	ETS_auto	383,867.68	168,531.32
2021 Aug	780,123	ETS_auto	651,223.84	128,899.16
2021 Sep	697,572	ETS_auto	673,673.79	23,898.21
2021 Oct	655,682	ETS_auto	640,098.93	15,583.07
2021 Nov	521,638	ETS_auto	550,737.80	-29,099.80
2021 Dec	397,592	ETS_auto	467,255.63	-69,663.63
2022 Jan	341,744	ETS_auto	415,094.08	-73,350.08
2022 Feb	391,699	ETS_auto	376,204.84	15,494.16
2022 Mar	569,482	ETS_auto	465,800.11	103,681.89
2022 Apr	727,326	ETS_auto	596,144.65	131,181.35
2022 May	779,426	ETS_auto	726,470.77	52,955.23
2022 Jun	833,955	ETS_auto	783,221.02	50,733.98
2010 Jan	319,379	ETS_auto_log	324,404.68	-5,025.68
2010 Feb	329,697	ETS_auto_log	352,190.30	-22,493.30
2010 Mar	388,978	ETS_auto_log	411,886.15	-22,908.15
2010 Apr	427,950	ETS_auto_log	429,134.93	-1,184.93
2010 May	431,385	ETS_auto_log	390,802.50	40,582.50
2010 Jun	432,522	ETS_auto_log	407,096.53	25,425.47
2010 Jul	492,382	ETS_auto_log	471,221.26	21,160.74
2010 Aug	624,383	ETS_auto_log	584,042.53	40,340.47
2010 Sep	496,609	ETS_auto_log	514,233.38	-17,624.38
2010 Oct	450,841	ETS_auto_log	462,235.75	-11,394.75
2010 Nov	327,330	ETS_auto_log	384,011.57	-56,681.57
2010 Dec	272,069	ETS_auto_log	291,868.59	-19,799.59
2011 Jan	286,010	ETS_auto_log	290,327.45	-4,317.45
2011 Feb	319,015	ETS_auto_log	312,231.09	6,783.91
2011 Mar	448,224	ETS_auto_log	387,732.16	60,491.84
2011 Apr	517,979	ETS_auto_log	486,026.95	31,952.05
2011 May	575,401	ETS_auto_log	475,614.28	99,786.72
2011 Jun	519,950	ETS_auto_log	548,061.97	-28,111.97
2011 Jul	589,288	ETS_auto_log	573,769.90	15,518.10
2011 Aug	678,877	ETS_auto_log	706,059.31	-27,182.31
2011 Sep	577,108	ETS_auto_log	561,427.46	15,680.54
2011 Oct	471,268	ETS_auto_log	533,626.05	-62,358.05
2011 Nov	319,900	ETS_auto_log	396,446.54	-76,546.54
2011 Dec	262,266	ETS_auto_log	279,221.07	-16,955.07
2012 Jan	289,312	ETS_auto_log	275,517.23	13,794.77
2012 Feb	329,299	ETS_auto_log	314,025.78	15,273.22
2012 Mar	399,988	ETS_auto_log	405,860.52	-5,872.52
2012 Apr	508,131	ETS_auto_log	437,612.31	70,518.69
2012 May	521,638	ETS_auto_log	472,673.81	48,964.19
2012 Jun	509,865	ETS_auto_log	496,234.63	13,630.37
2012 Jul	602,837	ETS_auto_log	565,597.96	37,239.04
2012 Aug	681,135	ETS_auto_log	720,211.06	-39,076.06
2012 Sep	562,007	ETS_auto_log	564,345.67	-2,338.67
2012 Oct	468,951	ETS_auto_log	515,701.66	-46,750.66
2012 Nov	350,902	ETS_auto_log	387,491.79	-36,589.79
2012 Dec	283,620	ETS_auto_log	305,409.44	-21,789.44
2013 Jan	322,235	ETS_auto_log	299,209.24	23,025.76
2013 Feb	365,343	ETS_auto_log	353,878.14	11,464.86
2013 Mar	462,258	ETS_auto_log	451,214.91	11,043.09
2013 Apr	516,930	ETS_auto_log	506,526.72	10,403.28
2013 May	608,081	ETS_auto_log	483,776.28	124,304.72
2013 Jun	578,633	ETS_auto_log	543,677.34	34,955.66
2013 Jul	677,083	ETS_auto_log	633,604.48	43,478.52
2013 Aug	775,941	ETS_auto_log	812,691.71	-36,750.71
2013 Sep	639,271	ETS_auto_log	610,512.21	28,758.79
2013 Oct	535,649	ETS_auto_log	514,493.51	21,155.49
2013 Nov	390,742	ETS_auto_log	382,748.87	7,993.13
2013 Dec	342,783	ETS_auto_log	316,409.18	26,373.82
2014 Jan	374,568	ETS_auto_log	392,679.67	-18,111.67
2014 Feb	401,859	ETS_auto_log	425,763.27	-23,904.27
2014 Mar	503,533	ETS_auto_log	525,220.01	-21,687.01
2014 Apr	557,275	ETS_auto_log	556,016.79	1,258.21
2014 May	610,148	ETS_auto_log	534,723.17	75,424.83
2014 Jun	595,332	ETS_auto_log	602,936.75	-7,604.75
2014 Jul	687,207	ETS_auto_log	677,948.33	9,258.67
2014 Aug	787,020	ETS_auto_log	759,744.72	27,275.28
2014 Sep	652,671	ETS_auto_log	630,859.01	21,811.99
2014 Oct	554,671	ETS_auto_log	527,580.80	27,090.20
2014 Nov	415,750	ETS_auto_log	387,867.97	27,882.03
2014 Dec	366,832	ETS_auto_log	357,544.89	9,287.11
2015 Jan	399,040	ETS_auto_log	376,908.45	22,131.55
2015 Feb	442,963	ETS_auto_log	435,124.36	7,838.64
2015 Mar	545,523	ETS_auto_log	546,963.07	-1,440.07
2015 Apr	586,230	ETS_auto_log	627,394.99	-41,164.99
2015 May	628,998	ETS_auto_log	691,389.77	-62,391.77
2015 Jun	654,715	ETS_auto_log	603,571.62	51,143.38
2015 Jul	766,557	ETS_auto_log	751,630.48	14,926.52
2015 Aug	829,230	ETS_auto_log	855,304.27	-26,074.27
2015 Sep	696,849	ETS_auto_log	685,032.68	11,816.32
2015 Oct	597,629	ETS_auto_log	578,908.38	18,720.62
2015 Nov	475,257	ETS_auto_log	434,043.46	41,213.54
2015 Dec	407,035	ETS_auto_log	410,933.57	-3,898.57
2016 Jan	448,784	ETS_auto_log	430,775.33	18,008.67
2016 Feb	506,179	ETS_auto_log	488,954.34	17,224.66
2016 Mar	611,987	ETS_auto_log	622,329.98	-10,342.98
2016 Apr	663,878	ETS_auto_log	673,390.90	-9,512.90
2016 May	726,980	ETS_auto_log	640,603.36	86,376.64
2016 Jun	759,256	ETS_auto_log	700,671.71	58,584.29
2016 Jul	849,148	ETS_auto_log	848,465.44	682.56
2016 Aug	891,091	ETS_auto_log	958,416.51	-67,325.51
2016 Sep	768,042	ETS_auto_log	779,081.04	-11,039.04
2016 Oct	702,530	ETS_auto_log	657,028.48	45,501.52
2016 Nov	545,468	ETS_auto_log	518,598.96	26,869.04
2016 Dec	457,565	ETS_auto_log	469,529.77	-11,964.77
2017 Jan	503,654	ETS_auto_log	488,737.29	14,916.71
2017 Feb	541,368	ETS_auto_log	538,915.88	2,452.12
2017 Mar	647,679	ETS_auto_log	646,791.84	887.16
2017 Apr	710,409	ETS_auto_log	715,625.32	-5,216.32
2017 May	745,096	ETS_auto_log	770,429.12	-25,333.12
2017 Jun	794,118	ETS_auto_log	722,844.31	71,273.69
2017 Jul	864,476	ETS_auto_log	892,105.21	-27,629.21
2017 Aug	939,077	ETS_auto_log	960,010.44	-20,933.44
2017 Sep	818,705	ETS_auto_log	819,423.14	-718.14
2017 Oct	734,287	ETS_auto_log	728,037.89	6,249.11
2017 Nov	582,743	ETS_auto_log	558,961.12	23,781.88
2017 Dec	478,377	ETS_auto_log	471,407.65	6,969.35
2018 Jan	534,281	ETS_auto_log	512,864.91	21,416.09
2018 Feb	555,841	ETS_auto_log	559,919.21	-4,078.21
2018 Mar	652,082	ETS_auto_log	668,730.58	-16,648.58
2018 Apr	689,214	ETS_auto_log	723,326.87	-34,112.87
2018 May	755,491	ETS_auto_log	763,576.40	-8,085.40
2018 Jun	782,628	ETS_auto_log	799,357.20	-16,729.20
2018 Jul	837,740	ETS_auto_log	877,495.81	-39,755.81
2018 Aug	936,644	ETS_auto_log	946,896.36	-10,252.36
2018 Sep	806,267	ETS_auto_log	819,183.22	-12,916.22
2018 Oct	721,989	ETS_auto_log	733,381.83	-11,392.83
2018 Nov	575,096	ETS_auto_log	567,984.95	7,111.05
2018 Dec	496,993	ETS_auto_log	466,804.42	30,188.58
2019 Jan	486,306	ETS_auto_log	523,966.30	-37,660.30
2019 Feb	498,081	ETS_auto_log	533,013.47	-34,932.47
2019 Mar	606,616	ETS_auto_log	614,960.13	-8,344.13
2019 Apr	608,322	ETS_auto_log	660,747.56	-52,425.56
2019 May	665,724	ETS_auto_log	706,140.37	-40,416.37
2019 Jun	714,041	ETS_auto_log	726,582.06	-12,541.06
2019 Jul	747,112	ETS_auto_log	785,942.38	-38,830.38
2019 Aug	828,426	ETS_auto_log	862,262.94	-33,836.94
2019 Sep	719,254	ETS_auto_log	739,076.24	-19,822.24
2019 Oct	629,555	ETS_auto_log	658,685.65	-29,130.65
2019 Nov	508,290	ETS_auto_log	513,589.97	-5,299.97
2019 Dec	445,470	ETS_auto_log	433,590.72	11,879.28
2020 Jan	488,461	ETS_auto_log	441,963.52	46,497.48
2020 Feb	540,254	ETS_auto_log	478,720.75	61,533.25
2020 Mar	297,649	ETS_auto_log	613,327.08	-315,678.08
2020 Apr	2,191	ETS_auto_log	507,161.73	-504,970.73
2020 May	2,955	ETS_auto_log	17.00	2,938.00
2020 Jun	14,932	ETS_auto_log	1,868.52	13,063.48
2020 Jul	95,576	ETS_auto_log	15,915.45	79,660.55
2020 Aug	240,322	ETS_auto_log	116,316.71	124,005.29
2020 Sep	251,221	ETS_auto_log	200,503.08	50,717.92
2020 Oct	253,895	ETS_auto_log	269,794.10	-15,899.10
2020 Nov	116,634	ETS_auto_log	225,069.20	-108,435.20
2020 Dec	137,446	ETS_auto_log	106,866.38	30,579.62
2021 Jan	93,013	ETS_auto_log	159,239.25	-66,226.25
2021 Feb	40,883	ETS_auto_log	107,936.27	-67,053.27
2021 Mar	60,163	ETS_auto_log	56,619.36	3,543.64
2021 Apr	95,116	ETS_auto_log	57,156.11	37,959.89
2021 May	179,599	ETS_auto_log	103,024.43	76,574.57
2021 Jun	321,985	ETS_auto_log	207,531.28	114,453.72
2021 Jul	552,399	ETS_auto_log	346,546.77	205,852.23
2021 Aug	780,123	ETS_auto_log	736,451.39	43,671.61
2021 Sep	697,572	ETS_auto_log	714,335.03	-16,763.03
2021 Oct	655,682	ETS_auto_log	672,236.26	-16,554.26
2021 Nov	521,638	ETS_auto_log	544,114.09	-22,476.09
2021 Dec	397,592	ETS_auto_log	463,789.93	-66,197.93
2022 Jan	341,744	ETS_auto_log	443,519.37	-101,775.37
2022 Feb	391,699	ETS_auto_log	372,485.13	19,213.87
2022 Mar	569,482	ETS_auto_log	507,698.06	61,783.94
2022 Apr	727,326	ETS_auto_log	554,533.60	172,792.40
2022 May	779,426	ETS_auto_log	851,639.41	-72,213.41
2022 Jun	833,955	ETS_auto_log	894,655.95	-60,700.95
2010 Jan	319,379	HWA	327,508.10	-8,129.10
2010 Feb	329,697	HWA	356,851.40	-27,154.40
2010 Mar	388,978	HWA	424,276.25	-35,298.25
2010 Apr	427,950	HWA	437,541.96	-9,591.96
2010 May	431,385	HWA	385,001.61	46,383.39
2010 Jun	432,522	HWA	406,455.61	26,066.39
2010 Jul	492,382	HWA	474,652.40	17,729.60
2010 Aug	624,383	HWA	592,428.18	31,954.82
2010 Sep	496,609	HWA	521,255.15	-24,646.15
2010 Oct	450,841	HWA	463,584.13	-12,743.13
2010 Nov	327,330	HWA	382,066.42	-54,736.42
2010 Dec	272,069	HWA	281,656.03	-9,587.03
2011 Jan	286,010	HWA	291,700.50	-5,690.50
2011 Feb	319,015	HWA	322,766.92	-3,751.92
2011 Mar	448,224	HWA	409,132.64	39,091.36
2011 Apr	517,979	HWA	491,523.00	26,456.00
2011 May	575,401	HWA	477,798.53	97,602.47
2011 Jun	519,950	HWA	534,502.15	-14,552.15
2011 Jul	589,288	HWA	567,681.19	21,606.81
2011 Aug	678,877	HWA	692,824.98	-13,947.98
2011 Sep	577,108	HWA	575,700.48	1,407.52
2011 Oct	471,268	HWA	541,022.91	-69,754.91
2011 Nov	319,900	HWA	399,972.48	-80,072.48
2011 Dec	262,266	HWA	270,296.96	-8,030.96
2012 Jan	289,312	HWA	280,220.47	9,091.53
2012 Feb	329,299	HWA	325,161.71	4,137.29
2012 Mar	399,988	HWA	423,097.95	-23,109.95
2012 Apr	508,131	HWA	448,044.76	60,086.24
2012 May	521,638	HWA	477,216.34	44,421.66
2012 Jun	509,865	HWA	501,450.27	8,414.73
2012 Jul	602,837	HWA	557,961.50	44,875.50
2012 Aug	681,135	HWA	706,001.73	-24,866.73
2012 Sep	562,007	HWA	577,710.97	-15,703.97
2012 Oct	468,951	HWA	520,509.76	-51,558.76
2012 Nov	350,902	HWA	387,958.25	-37,056.25
2012 Dec	283,620	HWA	301,377.17	-17,757.17
2013 Jan	322,235	HWA	303,152.87	19,082.13
2013 Feb	365,343	HWA	357,127.96	8,215.04
2013 Mar	462,258	HWA	456,431.96	5,826.04
2013 Apr	516,930	HWA	513,209.99	3,720.01
2013 May	608,081	HWA	492,456.94	115,624.06
2013 Jun	578,633	HWA	587,803.43	-9,170.43
2013 Jul	677,083	HWA	629,843.67	47,239.33
2013 Aug	775,941	HWA	778,184.64	-2,243.64
2013 Sep	639,271	HWA	671,112.46	-31,841.46
2013 Oct	535,649	HWA	593,712.01	-58,063.01
2013 Nov	390,742	HWA	451,617.15	-60,875.15
2013 Dec	342,783	HWA	339,475.14	3,307.86
2014 Jan	374,568	HWA	363,173.07	11,394.93
2014 Feb	401,859	HWA	409,474.84	-7,615.84
2014 Mar	503,533	HWA	492,286.72	11,246.28
2014 Apr	557,275	HWA	554,295.64	2,979.36
2014 May	610,148	HWA	541,458.74	68,689.26
2014 Jun	595,332	HWA	589,639.96	5,692.04
2014 Jul	687,207	HWA	649,394.19	37,812.81
2014 Aug	787,020	HWA	788,306.90	-1,286.90
2014 Sep	652,671	HWA	679,782.48	-27,111.48
2014 Oct	554,671	HWA	602,822.23	-48,151.23
2014 Nov	415,750	HWA	466,269.36	-50,519.36
2014 Dec	366,832	HWA	364,763.78	2,068.22
2015 Jan	399,040	HWA	387,510.37	11,529.63
2015 Feb	442,963	HWA	433,374.79	9,588.21
2015 Mar	545,523	HWA	533,495.78	12,027.22
2015 Apr	586,230	HWA	595,673.36	-9,443.36
2015 May	628,998	HWA	575,296.61	53,701.39
2015 Jun	654,715	HWA	608,856.73	45,858.27
2015 Jul	766,557	HWA	711,074.76	55,482.24
2015 Aug	829,230	HWA	867,484.76	-38,254.76
2015 Sep	696,849	HWA	720,058.18	-23,209.18
2015 Oct	597,629	HWA	643,697.06	-46,068.06
2015 Nov	475,257	HWA	505,828.63	-30,571.63
2015 Dec	407,035	HWA	424,288.93	-17,253.93
2016 Jan	448,784	HWA	429,035.34	19,748.66
2016 Feb	506,179	HWA	483,454.38	22,724.62
2016 Mar	611,987	HWA	596,859.35	15,127.65
2016 Apr	663,878	HWA	661,896.05	1,981.95
2016 May	726,980	HWA	656,379.40	70,600.60
2016 Jun	759,256	HWA	709,760.38	49,495.62
2016 Jul	849,148	HWA	818,773.84	30,374.16
2016 Aug	891,091	HWA	909,893.87	-18,802.87
2016 Sep	768,042	HWA	767,277.00	765.00
2016 Oct	702,530	HWA	664,452.94	38,077.06
2016 Nov	545,468	HWA	547,103.46	-1,635.46
2016 Dec	457,565	HWA	479,350.16	-21,785.16
2017 Jan	503,654	HWA	509,855.92	-6,201.92
2017 Feb	541,368	HWA	556,907.51	-15,539.51
2017 Mar	647,679	HWA	650,207.42	-2,528.42
2017 Apr	710,409	HWA	695,842.72	14,566.28
2017 May	745,096	HWA	758,818.70	-13,722.70
2017 Jun	794,118	HWA	776,630.80	17,487.20
2017 Jul	864,476	HWA	870,879.44	-6,403.44
2017 Aug	939,077	HWA	917,724.73	21,352.27
2017 Sep	818,705	HWA	802,833.58	15,871.42
2017 Oct	734,287	HWA	728,895.04	5,391.96
2017 Nov	582,743	HWA	574,649.59	8,093.41
2017 Dec	478,377	HWA	498,374.23	-19,997.23
2018 Jan	534,281	HWA	539,187.75	-4,906.75
2018 Feb	555,841	HWA	581,070.43	-25,229.43
2018 Mar	652,082	HWA	678,678.72	-26,596.72
2018 Apr	689,214	HWA	725,509.88	-36,295.88
2018 May	755,491	HWA	751,388.52	4,102.48
2018 Jun	782,628	HWA	795,236.60	-12,608.60
2018 Jul	837,740	HWA	863,183.74	-25,443.74
2018 Aug	936,644	HWA	919,645.73	16,998.27
2018 Sep	806,267	HWA	799,695.05	6,571.95
2018 Oct	721,989	HWA	715,721.46	6,267.54
2018 Nov	575,096	HWA	563,450.76	11,645.24
2018 Dec	496,993	HWA	471,250.60	25,742.40
2019 Jan	486,306	HWA	538,966.91	-52,660.91
2019 Feb	498,081	HWA	549,921.35	-51,840.35
2019 Mar	606,616	HWA	636,483.49	-29,867.49
2019 Apr	608,322	HWA	676,101.46	-67,779.46
2019 May	665,724	HWA	714,336.13	-48,612.13
2019 Jun	714,041	HWA	726,842.20	-12,801.20
2019 Jul	747,112	HWA	786,509.85	-39,397.85
2019 Aug	828,426	HWA	862,748.44	-34,322.44
2019 Sep	719,254	HWA	715,558.28	3,695.72
2019 Oct	629,555	HWA	629,770.34	-215.34
2019 Nov	508,290	HWA	477,648.81	30,641.19
2019 Dec	445,470	HWA	401,292.42	44,177.58
2020 Jan	488,461	HWA	428,485.42	59,975.58
2020 Feb	540,254	HWA	484,797.68	55,456.32
2020 Mar	297,649	HWA	628,010.01	-330,361.01
2020 Apr	2,191	HWA	534,480.80	-532,289.80
2020 May	2,955	HWA	-77,847.41	80,802.41
2020 Jun	14,932	HWA	-43,373.56	58,305.56
2020 Jul	95,576	HWA	44,023.18	51,552.82
2020 Aug	240,322	HWA	175,754.79	64,567.21
2020 Sep	251,221	HWA	123,478.71	127,742.29
2020 Oct	253,895	HWA	190,553.69	63,341.31
2020 Nov	116,634	HWA	153,306.21	-36,672.21
2020 Dec	137,446	HWA	61,173.47	76,272.53
2021 Jan	93,013	HWA	165,863.27	-72,850.27
2021 Feb	40,883	HWA	131,959.57	-91,076.57
2021 Mar	60,163	HWA	122,118.04	-61,955.04
2021 Apr	95,116	HWA	97,729.08	-2,613.08
2021 May	179,599	HWA	98,560.37	81,038.63
2021 Jun	321,985	HWA	174,428.81	147,556.19
2021 Jul	552,399	HWA	383,867.68	168,531.32
2021 Aug	780,123	HWA	651,223.84	128,899.16
2021 Sep	697,572	HWA	676,663.98	20,908.02
2021 Oct	655,682	HWA	643,067.36	12,614.64
2021 Nov	521,638	HWA	553,683.21	-32,045.21
2021 Dec	397,592	HWA	470,179.02	-72,587.02
2022 Jan	341,744	HWA	419,784.24	-78,040.24
2022 Feb	391,699	HWA	376,765.25	14,933.75
2022 Mar	569,482	HWA	467,903.48	101,578.52
2022 Apr	727,326	HWA	598,921.36	128,404.64
2022 May	779,426	HWA	732,157.49	47,268.51
2022 Jun	833,955	HWA	783,221.02	50,733.98
2010 Jan	319,379	HWA_log	326,441.44	-7,062.44
2010 Feb	329,697	HWA_log	367,033.44	-37,336.44
2010 Mar	388,978	HWA_log	430,256.09	-41,278.09
2010 Apr	427,950	HWA_log	454,738.20	-26,788.20
2010 May	431,385	HWA_log	402,094.07	29,290.93
2010 Jun	432,522	HWA_log	394,809.59	37,712.41
2010 Jul	492,382	HWA_log	470,249.35	22,132.65
2010 Aug	624,383	HWA_log	577,913.29	46,469.71
2010 Sep	496,609	HWA_log	469,440.88	27,168.12
2010 Oct	450,841	HWA_log	422,132.67	28,708.33
2010 Nov	327,330	HWA_log	338,880.16	-11,550.16
2010 Dec	272,069	HWA_log	297,341.01	-25,272.01
2011 Jan	286,010	HWA_log	297,463.84	-11,453.84
2011 Feb	319,015	HWA_log	316,214.51	2,800.49
2011 Mar	448,224	HWA_log	401,082.01	47,141.99
2011 Apr	517,979	HWA_log	457,797.81	60,181.19
2011 May	575,401	HWA_log	466,165.57	109,235.43
2011 Jun	519,950	HWA_log	510,364.92	9,585.08
2011 Jul	589,288	HWA_log	554,887.45	34,400.55
2011 Aug	678,877	HWA_log	682,484.36	-3,607.36
2011 Sep	577,108	HWA_log	539,167.23	37,940.77
2011 Oct	471,268	HWA_log	492,018.54	-20,750.54
2011 Nov	319,900	HWA_log	367,449.71	-47,549.71
2011 Dec	262,266	HWA_log	306,880.76	-44,614.76
2012 Jan	289,312	HWA_log	305,951.46	-16,639.46
2012 Feb	329,299	HWA_log	334,635.50	-5,336.50
2012 Mar	399,988	HWA_log	446,385.04	-46,397.04
2012 Apr	508,131	HWA_log	472,590.58	35,540.42
2012 May	521,638	HWA_log	514,181.10	7,456.90
2012 Jun	509,865	HWA_log	472,839.51	37,025.49
2012 Jul	602,837	HWA_log	543,751.69	59,085.31
2012 Aug	681,135	HWA_log	649,519.61	31,615.39
2012 Sep	562,007	HWA_log	555,233.98	6,773.02
2012 Oct	468,951	HWA_log	461,784.06	7,166.94
2012 Nov	350,902	HWA_log	330,872.61	20,029.39
2012 Dec	283,620	HWA_log	288,718.11	-5,098.11
2013 Jan	322,235	HWA_log	324,648.86	-2,413.86
2013 Feb	365,343	HWA_log	368,880.08	-3,537.08
2013 Mar	462,258	HWA_log	469,863.06	-7,605.06
2013 Apr	516,930	HWA_log	571,056.41	-54,126.41
2013 May	608,081	HWA_log	564,628.62	43,452.38
2013 Jun	578,633	HWA_log	546,771.92	31,861.08
2013 Jul	677,083	HWA_log	636,809.58	40,273.42
2013 Aug	775,941	HWA_log	726,741.64	49,199.36
2013 Sep	639,271	HWA_log	609,053.08	30,217.92
2013 Oct	535,649	HWA_log	515,744.51	19,904.49
2013 Nov	390,742	HWA_log	381,961.94	8,780.06
2013 Dec	342,783	HWA_log	317,675.88	25,107.12
2014 Jan	374,568	HWA_log	368,503.21	6,064.79
2014 Feb	401,859	HWA_log	427,891.28	-26,032.28
2014 Mar	503,533	HWA_log	525,220.01	-21,687.01
2014 Apr	557,275	HWA_log	607,908.55	-50,633.55
2014 May	610,148	HWA_log	665,346.54	-55,198.54
2014 Jun	595,332	HWA_log	602,936.75	-7,604.75
2014 Jul	687,207	HWA_log	686,273.34	933.66
2014 Aug	787,020	HWA_log	777,043.12	9,976.88
2014 Sep	652,671	HWA_log	630,859.01	21,811.99
2014 Oct	554,671	HWA_log	527,580.80	27,090.20
2014 Nov	415,750	HWA_log	389,325.70	26,424.30
2014 Dec	366,832	HWA_log	337,695.43	29,136.57
2015 Jan	399,040	HWA_log	380,269.38	18,770.62
2015 Feb	442,963	HWA_log	423,793.83	19,169.17
2015 Mar	545,523	HWA_log	552,209.70	-6,686.70
2015 Apr	586,230	HWA_log	627,394.99	-41,164.99
2015 May	628,998	HWA_log	688,796.26	-59,798.26
2015 Jun	654,715	HWA_log	651,373.19	3,341.81
2015 Jul	766,557	HWA_log	751,630.48	14,926.52
2015 Aug	829,230	HWA_log	858,273.23	-29,043.23
2015 Sep	696,849	HWA_log	694,940.96	1,908.04
2015 Oct	597,629	HWA_log	578,908.38	18,720.62
2015 Nov	475,257	HWA_log	434,043.46	41,213.54
2015 Dec	407,035	HWA_log	381,613.58	25,421.42
2016 Jan	448,784	HWA_log	418,164.48	30,619.52
2016 Feb	506,179	HWA_log	466,714.25	39,464.75
2016 Mar	611,987	HWA_log	586,542.68	25,444.32
2016 Apr	663,878	HWA_log	650,047.05	13,830.95
2016 May	726,980	HWA_log	719,540.39	7,439.61
2016 Jun	759,256	HWA_log	747,442.30	11,813.70
2016 Jul	849,148	HWA_log	877,286.69	-28,138.69
2016 Aug	891,091	HWA_log	958,416.51	-67,325.51
2016 Sep	768,042	HWA_log	777,432.62	-9,390.62
2016 Oct	702,530	HWA_log	657,028.48	45,501.52
2016 Nov	545,468	HWA_log	518,598.96	26,869.04
2016 Dec	457,565	HWA_log	441,216.34	16,348.66
2017 Jan	503,654	HWA_log	481,203.16	22,450.84
2017 Feb	541,368	HWA_log	538,463.84	2,904.16
2017 Mar	647,679	HWA_log	648,843.47	-1,164.47
2017 Apr	710,409	HWA_log	705,806.05	4,602.95
2017 May	745,096	HWA_log	774,629.25	-29,533.25
2017 Jun	794,118	HWA_log	795,460.90	-1,342.90
2017 Jul	864,476	HWA_log	902,522.82	-38,046.82
2017 Aug	939,077	HWA_log	961,009.66	-21,932.66
2017 Sep	818,705	HWA_log	819,620.12	-915.12
2017 Oct	734,287	HWA_log	733,156.08	1,130.92
2017 Nov	582,743	HWA_log	558,961.12	23,781.88
2017 Dec	478,377	HWA_log	471,407.65	6,969.35
2018 Jan	534,281	HWA_log	512,864.91	21,416.09
2018 Feb	555,841	HWA_log	559,919.21	-4,078.21
2018 Mar	652,082	HWA_log	668,730.58	-16,648.58
2018 Apr	689,214	HWA_log	723,326.87	-34,112.87
2018 May	755,491	HWA_log	763,576.40	-8,085.40
2018 Jun	782,628	HWA_log	812,348.77	-29,720.77
2018 Jul	837,740	HWA_log	893,157.38	-55,417.38
2018 Aug	936,644	HWA_log	946,896.36	-10,252.36
2018 Sep	806,267	HWA_log	824,998.64	-18,731.64
2018 Oct	721,989	HWA_log	733,381.83	-11,392.83
2018 Nov	575,096	HWA_log	567,984.95	7,111.05
2018 Dec	496,993	HWA_log	466,804.42	30,188.58
2019 Jan	486,306	HWA_log	523,529.07	-37,223.07
2019 Feb	498,081	HWA_log	535,352.13	-37,271.13
2019 Mar	606,616	HWA_log	621,637.00	-15,021.00
2019 Apr	608,322	HWA_log	666,325.03	-58,003.03
2019 May	665,724	HWA_log	701,370.61	-35,646.61
2019 Jun	714,041	HWA_log	721,618.44	-7,577.44
2019 Jul	747,112	HWA_log	785,942.38	-38,830.38
2019 Aug	828,426	HWA_log	862,262.94	-33,836.94
2019 Sep	719,254	HWA_log	739,076.24	-19,822.24
2019 Oct	629,555	HWA_log	658,054.70	-28,499.70
2019 Nov	508,290	HWA_log	510,813.07	-2,523.07
2019 Dec	445,470	HWA_log	433,590.72	11,879.28
2020 Jan	488,461	HWA_log	441,963.52	46,497.48
2020 Feb	540,254	HWA_log	479,452.53	60,801.47
2020 Mar	297,649	HWA_log	611,949.43	-314,300.43
2020 Apr	2,191	HWA_log	490,049.25	-487,858.25
2020 May	2,955	HWA_log	29,868.92	-26,913.92
2020 Jun	14,932	HWA_log	1,538.89	13,393.11
2020 Jul	95,576	HWA_log	12,918.90	82,657.10
2020 Aug	240,322	HWA_log	76,226.30	164,095.70
2020 Sep	251,221	HWA_log	176,605.54	74,615.46
2020 Oct	253,895	HWA_log	229,057.21	24,837.79
2020 Nov	116,634	HWA_log	225,069.20	-108,435.20
2020 Dec	137,446	HWA_log	102,785.94	34,660.06
2021 Jan	93,013	HWA_log	161,123.39	-68,110.39
2021 Feb	40,883	HWA_log	111,026.00	-70,143.00
2021 Mar	60,163	HWA_log	47,903.06	12,259.94
2021 Apr	95,116	HWA_log	45,237.04	49,878.96
2021 May	179,599	HWA_log	102,150.87	77,448.13
2021 Jun	321,985	HWA_log	201,446.48	120,538.52
2021 Jul	552,399	HWA_log	390,501.14	161,897.86
2021 Aug	780,123	HWA_log	724,407.12	55,715.88
2021 Sep	697,572	HWA_log	634,078.38	63,493.62
2021 Oct	655,682	HWA_log	631,669.40	24,012.60
2021 Nov	521,638	HWA_log	521,439.83	198.17
2021 Dec	397,592	HWA_log	501,187.52	-103,595.52
2022 Jan	341,744	HWA_log	420,807.77	-79,063.77
2022 Feb	391,699	HWA_log	364,692.28	27,006.72
2022 Mar	569,482	HWA_log	513,195.54	56,286.46
2022 Apr	727,326	HWA_log	531,482.09	195,843.91
2022 May	779,426	HWA_log	795,005.73	-15,579.73
2022 Jun	833,955	HWA_log	951,109.60	-117,154.60
2010 Jan	319,379	Naive	308,080.00	11,299.00
2010 Feb	329,697	Naive	319,379.00	10,318.00
2010 Mar	388,978	Naive	329,697.00	59,281.00
2010 Apr	427,950	Naive	388,978.00	38,972.00
2010 May	431,385	Naive	427,950.00	3,435.00
2010 Jun	432,522	Naive	431,385.00	1,137.00
2010 Jul	492,382	Naive	432,522.00	59,860.00
2010 Aug	624,383	Naive	492,382.00	132,001.00
2010 Sep	496,609	Naive	624,383.00	-127,774.00
2010 Oct	450,841	Naive	496,609.00	-45,768.00
2010 Nov	327,330	Naive	450,841.00	-123,511.00
2010 Dec	272,069	Naive	327,330.00	-55,261.00
2011 Jan	286,010	Naive	272,069.00	13,941.00
2011 Feb	319,015	Naive	286,010.00	33,005.00
2011 Mar	448,224	Naive	319,015.00	129,209.00
2011 Apr	517,979	Naive	448,224.00	69,755.00
2011 May	575,401	Naive	517,979.00	57,422.00
2011 Jun	519,950	Naive	575,401.00	-55,451.00
2011 Jul	589,288	Naive	519,950.00	69,338.00
2011 Aug	678,877	Naive	589,288.00	89,589.00
2011 Sep	577,108	Naive	678,877.00	-101,769.00
2011 Oct	471,268	Naive	577,108.00	-105,840.00
2011 Nov	319,900	Naive	471,268.00	-151,368.00
2011 Dec	262,266	Naive	319,900.00	-57,634.00
2012 Jan	289,312	Naive	262,266.00	27,046.00
2012 Feb	329,299	Naive	289,312.00	39,987.00
2012 Mar	399,988	Naive	329,299.00	70,689.00
2012 Apr	508,131	Naive	399,988.00	108,143.00
2012 May	521,638	Naive	508,131.00	13,507.00
2012 Jun	509,865	Naive	521,638.00	-11,773.00
2012 Jul	602,837	Naive	509,865.00	92,972.00
2012 Aug	681,135	Naive	602,837.00	78,298.00
2012 Sep	562,007	Naive	681,135.00	-119,128.00
2012 Oct	468,951	Naive	562,007.00	-93,056.00
2012 Nov	350,902	Naive	468,951.00	-118,049.00
2012 Dec	283,620	Naive	350,902.00	-67,282.00
2013 Jan	322,235	Naive	283,620.00	38,615.00
2013 Feb	365,343	Naive	322,235.00	43,108.00
2013 Mar	462,258	Naive	365,343.00	96,915.00
2013 Apr	516,930	Naive	462,258.00	54,672.00
2013 May	608,081	Naive	516,930.00	91,151.00
2013 Jun	578,633	Naive	608,081.00	-29,448.00
2013 Jul	677,083	Naive	578,633.00	98,450.00
2013 Aug	775,941	Naive	677,083.00	98,858.00
2013 Sep	639,271	Naive	775,941.00	-136,670.00
2013 Oct	535,649	Naive	639,271.00	-103,622.00
2013 Nov	390,742	Naive	535,649.00	-144,907.00
2013 Dec	342,783	Naive	390,742.00	-47,959.00
2014 Jan	374,568	Naive	342,783.00	31,785.00
2014 Feb	401,859	Naive	374,568.00	27,291.00
2014 Mar	503,533	Naive	401,859.00	101,674.00
2014 Apr	557,275	Naive	503,533.00	53,742.00
2014 May	610,148	Naive	557,275.00	52,873.00
2014 Jun	595,332	Naive	610,148.00	-14,816.00
2014 Jul	687,207	Naive	595,332.00	91,875.00
2014 Aug	787,020	Naive	687,207.00	99,813.00
2014 Sep	652,671	Naive	787,020.00	-134,349.00
2014 Oct	554,671	Naive	652,671.00	-98,000.00
2014 Nov	415,750	Naive	554,671.00	-138,921.00
2014 Dec	366,832	Naive	415,750.00	-48,918.00
2015 Jan	399,040	Naive	366,832.00	32,208.00
2015 Feb	442,963	Naive	399,040.00	43,923.00
2015 Mar	545,523	Naive	442,963.00	102,560.00
2015 Apr	586,230	Naive	545,523.00	40,707.00
2015 May	628,998	Naive	586,230.00	42,768.00
2015 Jun	654,715	Naive	628,998.00	25,717.00
2015 Jul	766,557	Naive	654,715.00	111,842.00
2015 Aug	829,230	Naive	766,557.00	62,673.00
2015 Sep	696,849	Naive	829,230.00	-132,381.00
2015 Oct	597,629	Naive	696,849.00	-99,220.00
2015 Nov	475,257	Naive	597,629.00	-122,372.00
2015 Dec	407,035	Naive	475,257.00	-68,222.00
2016 Jan	448,784	Naive	407,035.00	41,749.00
2016 Feb	506,179	Naive	448,784.00	57,395.00
2016 Mar	611,987	Naive	506,179.00	105,808.00
2016 Apr	663,878	Naive	611,987.00	51,891.00
2016 May	726,980	Naive	663,878.00	63,102.00
2016 Jun	759,256	Naive	726,980.00	32,276.00
2016 Jul	849,148	Naive	759,256.00	89,892.00
2016 Aug	891,091	Naive	849,148.00	41,943.00
2016 Sep	768,042	Naive	891,091.00	-123,049.00
2016 Oct	702,530	Naive	768,042.00	-65,512.00
2016 Nov	545,468	Naive	702,530.00	-157,062.00
2016 Dec	457,565	Naive	545,468.00	-87,903.00
2017 Jan	503,654	Naive	457,565.00	46,089.00
2017 Feb	541,368	Naive	503,654.00	37,714.00
2017 Mar	647,679	Naive	541,368.00	106,311.00
2017 Apr	710,409	Naive	647,679.00	62,730.00
2017 May	745,096	Naive	710,409.00	34,687.00
2017 Jun	794,118	Naive	745,096.00	49,022.00
2017 Jul	864,476	Naive	794,118.00	70,358.00
2017 Aug	939,077	Naive	864,476.00	74,601.00
2017 Sep	818,705	Naive	939,077.00	-120,372.00
2017 Oct	734,287	Naive	818,705.00	-84,418.00
2017 Nov	582,743	Naive	734,287.00	-151,544.00
2017 Dec	478,377	Naive	582,743.00	-104,366.00
2018 Jan	534,281	Naive	478,377.00	55,904.00
2018 Feb	555,841	Naive	534,281.00	21,560.00
2018 Mar	652,082	Naive	555,841.00	96,241.00
2018 Apr	689,214	Naive	652,082.00	37,132.00
2018 May	755,491	Naive	689,214.00	66,277.00
2018 Jun	782,628	Naive	755,491.00	27,137.00
2018 Jul	837,740	Naive	782,628.00	55,112.00
2018 Aug	936,644	Naive	837,740.00	98,904.00
2018 Sep	806,267	Naive	936,644.00	-130,377.00
2018 Oct	721,989	Naive	806,267.00	-84,278.00
2018 Nov	575,096	Naive	721,989.00	-146,893.00
2018 Dec	496,993	Naive	575,096.00	-78,103.00
2019 Jan	486,306	Naive	496,993.00	-10,687.00
2019 Feb	498,081	Naive	486,306.00	11,775.00
2019 Mar	606,616	Naive	498,081.00	108,535.00
2019 Apr	608,322	Naive	606,616.00	1,706.00
2019 May	665,724	Naive	608,322.00	57,402.00
2019 Jun	714,041	Naive	665,724.00	48,317.00
2019 Jul	747,112	Naive	714,041.00	33,071.00
2019 Aug	828,426	Naive	747,112.00	81,314.00
2019 Sep	719,254	Naive	828,426.00	-109,172.00
2019 Oct	629,555	Naive	719,254.00	-89,699.00
2019 Nov	508,290	Naive	629,555.00	-121,265.00
2019 Dec	445,470	Naive	508,290.00	-62,820.00
2020 Jan	488,461	Naive	445,470.00	42,991.00
2020 Feb	540,254	Naive	488,461.00	51,793.00
2020 Mar	297,649	Naive	540,254.00	-242,605.00
2020 Apr	2,191	Naive	297,649.00	-295,458.00
2020 May	2,955	Naive	2,191.00	764.00
2020 Jun	14,932	Naive	2,955.00	11,977.00
2020 Jul	95,576	Naive	14,932.00	80,644.00
2020 Aug	240,322	Naive	95,576.00	144,746.00
2020 Sep	251,221	Naive	240,322.00	10,899.00
2020 Oct	253,895	Naive	251,221.00	2,674.00
2020 Nov	116,634	Naive	253,895.00	-137,261.00
2020 Dec	137,446	Naive	116,634.00	20,812.00
2021 Jan	93,013	Naive	137,446.00	-44,433.00
2021 Feb	40,883	Naive	93,013.00	-52,130.00
2021 Mar	60,163	Naive	40,883.00	19,280.00
2021 Apr	95,116	Naive	60,163.00	34,953.00
2021 May	179,599	Naive	95,116.00	84,483.00
2021 Jun	321,985	Naive	179,599.00	142,386.00
2021 Jul	552,399	Naive	321,985.00	230,414.00
2021 Aug	780,123	Naive	552,399.00	227,724.00
2021 Sep	697,572	Naive	780,123.00	-82,551.00
2021 Oct	655,682	Naive	697,572.00	-41,890.00
2021 Nov	521,638	Naive	655,682.00	-134,044.00
2021 Dec	397,592	Naive	521,638.00	-124,046.00
2022 Jan	341,744	Naive	397,592.00	-55,848.00
2022 Feb	391,699	Naive	341,744.00	49,955.00
2022 Mar	569,482	Naive	391,699.00	177,783.00
2022 Apr	727,326	Naive	569,482.00	157,844.00
2022 May	779,426	Naive	727,326.00	52,100.00
2022 Jun	833,955	Naive	779,426.00	54,529.00
2010 Jan	319,379	Naive_log	310,979.74	8,399.26
2010 Feb	329,697	Naive_log	322,361.76	7,335.24
2010 Mar	388,978	Naive_log	332,752.06	56,225.94
2010 Apr	427,950	Naive_log	392,596.41	35,353.59
2010 May	431,385	Naive_log	431,914.44	-529.44
2010 Jun	432,522	Naive_log	435,349.14	-2,827.14
2010 Jul	492,382	Naive_log	436,464.80	55,917.20
2010 Aug	624,383	Naive_log	496,867.69	127,515.31
2010 Sep	496,609	Naive_log	630,165.12	-133,556.12
2010 Oct	450,841	Naive_log	501,273.63	-50,432.63
2010 Nov	327,330	Naive_log	455,059.24	-127,729.24
2010 Dec	272,069	Naive_log	330,498.10	-58,429.10
2011 Jan	286,010	Naive_log	274,717.66	11,292.34
2011 Feb	319,015	Naive_log	288,775.99	30,239.01
2011 Mar	448,224	Naive_log	322,091.28	126,132.72
2011 Apr	517,979	Naive_log	452,707.40	65,271.60
2011 May	575,401	Naive_log	523,161.89	52,239.11
2011 Jun	519,950	Naive_log	581,139.50	-61,189.50
2011 Jul	589,288	Naive_log	525,117.12	64,170.88
2011 Aug	678,877	Naive_log	595,135.20	83,741.80
2011 Sep	577,108	Naive_log	685,613.60	-108,505.60
2011 Oct	471,268	Naive_log	582,848.19	-111,580.19
2011 Nov	319,900	Naive_log	475,990.81	-156,090.81
2011 Dec	262,266	Naive_log	323,252.37	-60,986.37
2012 Jan	289,312	Naive_log	265,031.36	24,280.64
2012 Feb	329,299	Naive_log	292,351.03	36,947.97
2012 Mar	399,988	Naive_log	332,753.24	67,234.76
2012 Apr	508,131	Naive_log	404,206.81	103,924.19
2012 May	521,638	Naive_log	513,552.95	8,085.05
2012 Jun	509,865	Naive_log	527,167.68	-17,302.68
2012 Jul	602,837	Naive_log	515,234.50	87,602.50
2012 Aug	681,135	Naive_log	609,199.66	71,935.34
2012 Sep	562,007	Naive_log	688,310.08	-126,303.08
2012 Oct	468,951	Naive_log	567,956.56	-99,005.56
2012 Nov	350,902	Naive_log	473,933.22	-123,031.22
2012 Dec	283,620	Naive_log	354,701.64	-71,081.64
2013 Jan	322,235	Naive_log	286,712.74	35,522.26
2013 Feb	365,343	Naive_log	325,743.13	39,599.87
2013 Mar	462,258	Naive_log	369,313.44	92,944.56
2013 Apr	516,930	Naive_log	467,330.88	49,599.12
2013 May	608,081	Naive_log	522,587.49	85,493.51
2013 Jun	578,633	Naive_log	614,744.60	-36,111.60
2013 Jul	677,083	Naive_log	584,938.94	92,144.06
2013 Aug	775,941	Naive_log	684,467.90	91,473.10
2013 Sep	639,271	Naive_log	784,396.42	-145,125.42
2013 Oct	535,649	Naive_log	646,267.81	-110,618.81
2013 Nov	390,742	Naive_log	541,526.91	-150,784.91
2013 Dec	342,783	Naive_log	395,121.05	-52,338.05
2014 Jan	374,568	Naive_log	346,619.17	27,948.83
2014 Feb	401,859	Naive_log	378,743.70	23,115.30
2014 Mar	503,533	Naive_log	406,318.31	97,214.69
2014 Apr	557,275	Naive_log	509,163.03	48,111.97
2014 May	610,148	Naive_log	563,486.24	46,661.76
2014 Jun	595,332	Naive_log	616,923.58	-21,591.58
2014 Jul	687,207	Naive_log	601,905.88	85,301.12
2014 Aug	787,020	Naive_log	694,792.46	92,227.54
2014 Sep	652,671	Naive_log	795,698.92	-143,027.92
2014 Oct	554,671	Naive_log	659,892.45	-105,221.45
2014 Nov	415,750	Naive_log	560,814.94	-145,064.94
2014 Dec	366,832	Naive_log	420,426.34	-53,594.34
2015 Jan	399,040	Naive_log	370,951.11	28,088.89
2015 Feb	442,963	Naive_log	403,503.73	39,459.27
2015 Mar	545,523	Naive_log	447,904.03	97,618.97
2015 Apr	586,230	Naive_log	551,639.60	34,590.40
2015 May	628,998	Naive_log	592,775.40	36,222.60
2015 Jun	654,715	Naive_log	635,991.22	18,723.78
2015 Jul	766,557	Naive_log	661,957.64	104,599.36
2015 Aug	829,230	Naive_log	775,042.53	54,187.47
2015 Sep	696,849	Naive_log	838,373.91	-141,524.91
2015 Oct	597,629	Naive_log	704,548.33	-106,919.33
2015 Nov	475,257	Naive_log	604,234.44	-128,977.44
2015 Dec	407,035	Naive_log	480,547.90	-73,512.90
2016 Jan	448,784	Naive_log	411,568.26	37,215.74
2016 Feb	506,179	Naive_log	453,767.34	52,411.66
2016 Mar	611,987	Naive_log	511,789.53	100,197.47
2016 Apr	663,878	Naive_log	618,792.19	45,085.81
2016 May	726,980	Naive_log	671,233.62	55,746.38
2016 Jun	759,256	Naive_log	735,008.97	24,247.03
2016 Jul	849,148	Naive_log	767,602.51	81,545.49
2016 Aug	891,091	Naive_log	858,462.39	32,628.61
2016 Sep	768,042	Naive_log	900,821.56	-132,779.56
2016 Oct	702,530	Naive_log	776,429.35	-73,899.35
2016 Nov	545,468	Naive_log	710,177.65	-164,709.65
2016 Dec	457,565	Naive_log	551,462.95	-93,897.95
2017 Jan	503,654	Naive_log	462,603.89	41,050.11
2017 Feb	541,368	Naive_log	509,184.62	32,183.38
2017 Mar	647,679	Naive_log	547,290.64	100,388.36
2017 Apr	710,409	Naive_log	654,780.84	55,628.16
2017 May	745,096	Naive_log	718,175.71	26,920.29
2017 Jun	794,118	Naive_log	753,206.84	40,911.16
2017 Jul	864,476	Naive_log	802,728.83	61,747.17
2017 Aug	939,077	Naive_log	873,819.94	65,257.06
2017 Sep	818,705	Naive_log	949,194.42	-130,489.42
2017 Oct	734,287	Naive_log	827,520.29	-93,233.29
2017 Nov	582,743	Naive_log	742,176.62	-159,433.62
2017 Dec	478,377	Naive_log	589,047.83	-110,670.83
2018 Jan	534,281	Naive_log	483,571.93	50,709.07
2018 Feb	555,841	Naive_log	540,071.26	15,769.74
2018 Mar	652,082	Naive_log	561,839.16	90,242.84
2018 Apr	689,214	Naive_log	659,124.57	30,089.43
2018 May	755,491	Naive_log	696,628.44	58,862.56
2018 Jun	782,628	Naive_log	763,595.97	19,032.03
2018 Jul	837,740	Naive_log	790,988.31	46,751.69
2018 Aug	936,644	Naive_log	846,657.46	89,986.54
2018 Sep	806,267	Naive_log	946,595.71	-140,328.71
2018 Oct	721,989	Naive_log	814,835.66	-92,846.66
2018 Nov	575,096	Naive_log	729,647.45	-154,551.45
2018 Dec	496,993	Naive_log	581,235.13	-84,242.13
2019 Jan	486,306	Naive_log	502,298.34	-15,992.34
2019 Feb	498,081	Naive_log	491,474.99	6,606.01
2019 Mar	606,616	Naive_log	503,352.65	103,263.35
2019 Apr	608,322	Naive_log	613,059.71	-4,737.71
2019 May	665,724	Naive_log	614,755.87	50,968.13
2019 Jun	714,041	Naive_log	672,746.29	41,294.71
2019 Jul	747,112	Naive_log	721,548.15	25,563.85
2019 Aug	828,426	Naive_log	754,936.55	73,489.45
2019 Sep	719,254	Naive_log	837,084.05	-117,830.05
2019 Oct	629,555	Naive_log	726,769.65	-97,214.65
2019 Nov	508,290	Naive_log	636,129.17	-127,839.17
2019 Dec	445,470	Naive_log	513,624.44	-68,154.44
2020 Jan	488,461	Naive_log	450,141.81	38,319.19
2020 Feb	540,254	Naive_log	493,570.96	46,683.04
2020 Mar	297,649	Naive_log	545,893.72	-248,244.72
2020 Apr	2,191	Naive_log	300,961.87	-298,770.87
2020 May	2,955	Naive_log	2,324.04	630.96
2020 Jun	14,932	Naive_log	3,134.24	11,797.76
2020 Jul	95,576	Naive_log	15,913.99	79,662.01
2020 Aug	240,322	Naive_log	102,505.37	137,816.63
2020 Sep	251,221	Naive_log	258,088.68	-6,867.68
2020 Oct	253,895	Naive_log	269,719.53	-15,824.53
2020 Nov	116,634	Naive_log	272,515.40	-155,881.40
2020 Dec	137,446	Naive_log	125,294.76	12,151.24
2021 Jan	93,013	Naive_log	147,618.89	-54,605.89
2021 Feb	40,883	Naive_log	99,898.06	-59,015.06
2021 Mar	60,163	Naive_log	43,951.90	16,211.10
2021 Apr	95,116	Naive_log	64,679.06	30,436.94
2021 May	179,599	Naive_log	102,266.89	77,332.11
2021 Jun	321,985	Naive_log	193,190.35	128,794.65
2021 Jul	552,399	Naive_log	346,470.25	205,928.75
2021 Aug	780,123	Naive_log	594,555.09	185,567.91
2021 Sep	697,572	Naive_log	839,607.33	-142,035.33
2021 Oct	655,682	Naive_log	750,574.02	-94,892.02
2021 Nov	521,638	Naive_log	705,315.13	-183,677.13
2021 Dec	397,592	Naive_log	561,025.77	-163,433.77
2022 Jan	341,744	Naive_log	427,554.91	-85,810.91
2022 Feb	391,699	Naive_log	367,415.42	24,283.58
2022 Mar	569,482	Naive_log	421,025.71	148,456.29
2022 Apr	727,326	Naive_log	612,109.04	115,216.96
2022 May	779,426	Naive_log	781,645.65	-2,219.65
2022 Jun	833,955	Naive_log	837,426.44	-3,471.44
2010 Jan	319,379	Prophet	385,717.17	-66,338.17
2010 Feb	329,697	Prophet	406,827.88	-77,130.88
2010 Mar	388,978	Prophet	489,594.74	-100,616.74
2010 Apr	427,950	Prophet	518,967.01	-91,017.01
2010 May	431,385	Prophet	457,125.38	-25,740.38
2010 Jun	432,522	Prophet	425,351.13	7,170.87
2010 Jul	492,382	Prophet	476,142.16	16,239.84
2010 Aug	624,383	Prophet	571,864.24	52,518.76
2010 Sep	496,609	Prophet	469,048.68	27,560.32
2010 Oct	450,841	Prophet	426,539.94	24,301.06
2010 Nov	327,330	Prophet	353,889.73	-26,559.73
2010 Dec	272,069	Prophet	304,433.62	-32,364.62
2011 Jan	286,010	Prophet	316,431.56	-30,421.56
2011 Feb	319,015	Prophet	347,709.43	-28,694.43
2011 Mar	448,224	Prophet	424,672.89	23,551.11
2011 Apr	517,979	Prophet	468,291.52	49,687.48
2011 May	575,401	Prophet	421,322.35	154,078.65
2011 Jun	519,950	Prophet	415,923.84	104,026.16
2011 Jul	589,288	Prophet	469,700.62	119,587.38
2011 Aug	678,877	Prophet	588,542.17	90,334.83
2011 Sep	577,108	Prophet	477,439.51	99,668.49
2011 Oct	471,268	Prophet	445,731.63	25,536.37
2011 Nov	319,900	Prophet	372,748.88	-52,848.88
2011 Dec	262,266	Prophet	323,993.61	-61,727.61
2012 Jan	289,312	Prophet	341,015.27	-51,703.27
2012 Feb	329,299	Prophet	375,216.81	-45,917.81
2012 Mar	399,988	Prophet	455,613.43	-55,625.43
2012 Apr	508,131	Prophet	495,829.97	12,301.03
2012 May	521,638	Prophet	460,935.24	60,702.76
2012 Jun	509,865	Prophet	438,045.04	71,819.96
2012 Jul	602,837	Prophet	488,294.94	114,542.06
2012 Aug	681,135	Prophet	582,123.42	99,011.58
2012 Sep	562,007	Prophet	484,884.77	77,122.23
2012 Oct	468,951	Prophet	452,302.81	16,648.19
2012 Nov	350,902	Prophet	373,940.44	-23,038.44
2012 Dec	283,620	Prophet	319,206.44	-35,586.44
2013 Jan	322,235	Prophet	336,604.35	-14,369.35
2013 Feb	365,343	Prophet	367,479.88	-2,136.88
2013 Mar	462,258	Prophet	458,181.60	4,076.40
2013 Apr	516,930	Prophet	508,555.29	8,374.71
2013 May	608,081	Prophet	477,848.53	130,232.47
2013 Jun	578,633	Prophet	458,359.50	120,273.50
2013 Jul	677,083	Prophet	513,417.83	163,665.17
2013 Aug	775,941	Prophet	618,762.03	157,178.97
2013 Sep	639,271	Prophet	527,546.71	111,724.29
2013 Oct	535,649	Prophet	487,862.41	47,786.59
2013 Nov	390,742	Prophet	403,804.25	-13,062.25
2013 Dec	342,783	Prophet	360,593.82	-17,810.82
2014 Jan	374,568	Prophet	375,791.65	-1,223.65
2014 Feb	401,859	Prophet	411,561.77	-9,702.77
2014 Mar	503,533	Prophet	501,729.17	1,803.83
2014 Apr	557,275	Prophet	547,246.98	10,028.02
2014 May	610,148	Prophet	527,380.65	82,767.35
2014 Jun	595,332	Prophet	508,856.16	86,475.84
2014 Jul	687,207	Prophet	574,676.57	112,530.43
2014 Aug	787,020	Prophet	684,958.52	102,061.48
2014 Sep	652,671	Prophet	585,484.73	67,186.27
2014 Oct	554,671	Prophet	538,566.39	16,104.61
2014 Nov	415,750	Prophet	448,297.06	-32,547.06
2014 Dec	366,832	Prophet	398,686.81	-31,854.81
2015 Jan	399,040	Prophet	419,264.50	-20,224.50
2015 Feb	442,963	Prophet	456,993.67	-14,030.67
2015 Mar	545,523	Prophet	543,975.83	1,547.17
2015 Apr	586,230	Prophet	594,087.40	-7,857.40
2015 May	628,998	Prophet	577,308.40	51,689.60
2015 Jun	654,715	Prophet	559,562.65	95,152.35
2015 Jul	766,557	Prophet	624,928.16	141,628.84
2015 Aug	829,230	Prophet	744,110.72	85,119.28
2015 Sep	696,849	Prophet	634,941.38	61,907.62
2015 Oct	597,629	Prophet	585,240.52	12,388.48
2015 Nov	475,257	Prophet	490,286.74	-15,029.74
2015 Dec	407,035	Prophet	447,851.54	-40,816.54
2016 Jan	448,784	Prophet	474,064.48	-25,280.48
2016 Feb	506,179	Prophet	511,991.22	-5,812.22
2016 Mar	611,987	Prophet	600,609.90	11,377.10
2016 Apr	663,878	Prophet	654,127.63	9,750.37
2016 May	726,980	Prophet	643,216.90	83,763.10
2016 Jun	759,256	Prophet	624,703.04	134,552.96
2016 Jul	849,148	Prophet	690,789.70	158,358.30
2016 Aug	891,091	Prophet	791,885.31	99,205.69
2016 Sep	768,042	Prophet	694,692.93	73,349.07
2016 Oct	702,530	Prophet	650,486.26	52,043.74
2016 Nov	545,468	Prophet	567,830.82	-22,362.82
2016 Dec	457,565	Prophet	516,732.22	-59,167.22
2017 Jan	503,654	Prophet	538,783.63	-35,129.63
2017 Feb	541,368	Prophet	568,476.38	-27,108.38
2017 Mar	647,679	Prophet	666,352.18	-18,673.18
2017 Apr	710,409	Prophet	716,567.37	-6,158.37
2017 May	745,096	Prophet	710,847.34	34,248.66
2017 Jun	794,118	Prophet	697,429.54	96,688.46
2017 Jul	864,476	Prophet	765,896.00	98,580.00
2017 Aug	939,077	Prophet	865,843.54	73,233.46
2017 Sep	818,705	Prophet	762,695.90	56,009.10
2017 Oct	734,287	Prophet	714,470.22	19,816.78
2017 Nov	582,743	Prophet	620,808.82	-38,065.82
2017 Dec	478,377	Prophet	564,139.17	-85,762.17
2018 Jan	534,281	Prophet	586,472.03	-52,191.03
2018 Feb	555,841	Prophet	620,830.68	-64,989.68
2018 Mar	652,082	Prophet	713,722.13	-61,640.13
2018 Apr	689,214	Prophet	762,918.43	-73,704.43
2018 May	755,491	Prophet	755,090.11	400.89
2018 Jun	782,628	Prophet	744,578.41	38,049.59
2018 Jul	837,740	Prophet	810,183.10	27,556.90
2018 Aug	936,644	Prophet	911,401.42	25,242.58
2018 Sep	806,267	Prophet	800,119.28	6,147.72
2018 Oct	721,989	Prophet	738,281.86	-16,292.86
2018 Nov	575,096	Prophet	640,614.38	-65,518.38
2018 Dec	496,993	Prophet	584,001.46	-87,008.46
2019 Jan	486,306	Prophet	609,426.04	-123,120.04
2019 Feb	498,081	Prophet	642,843.46	-144,762.46
2019 Mar	606,616	Prophet	729,110.87	-122,494.87
2019 Apr	608,322	Prophet	772,832.01	-164,510.01
2019 May	665,724	Prophet	769,822.40	-104,098.40
2019 Jun	714,041	Prophet	755,048.14	-41,007.14
2019 Jul	747,112	Prophet	818,061.21	-70,949.21
2019 Aug	828,426	Prophet	921,201.11	-92,775.11
2019 Sep	719,254	Prophet	799,137.05	-79,883.05
2019 Oct	629,555	Prophet	728,910.96	-99,355.96
2019 Nov	508,290	Prophet	620,718.22	-112,428.22
2019 Dec	445,470	Prophet	567,136.95	-121,666.95
2020 Jan	488,461	Prophet	589,856.34	-101,395.34
2020 Feb	540,254	Prophet	628,388.13	-88,134.13
2020 Mar	297,649	Prophet	711,290.28	-413,641.28
2020 Apr	2,191	Prophet	746,923.57	-744,732.57
2020 May	2,955	Prophet	730,827.40	-727,872.40
2020 Jun	14,932	Prophet	696,074.34	-681,142.34
2020 Jul	95,576	Prophet	735,399.77	-639,823.77
2020 Aug	240,322	Prophet	799,081.68	-558,759.68
2020 Sep	251,221	Prophet	668,766.09	-417,545.09
2020 Oct	253,895	Prophet	593,750.15	-339,855.15
2020 Nov	116,634	Prophet	483,068.58	-366,434.58
2020 Dec	137,446	Prophet	393,231.85	-255,785.85
2021 Jan	93,013	Prophet	401,354.85	-308,341.85
2021 Feb	40,883	Prophet	426,094.99	-385,211.99
2021 Mar	60,163	Prophet	489,353.86	-429,190.86
2021 Apr	95,116	Prophet	494,490.68	-399,374.68
2021 May	179,599	Prophet	466,790.77	-287,191.77
2021 Jun	321,985	Prophet	449,611.76	-127,626.76
2021 Jul	552,399	Prophet	487,861.95	64,537.05
2021 Aug	780,123	Prophet	584,726.62	195,396.38
2021 Sep	697,572	Prophet	469,079.75	228,492.25
2021 Oct	655,682	Prophet	456,607.54	199,074.46
2021 Nov	521,638	Prophet	354,990.22	166,647.78
2021 Dec	397,592	Prophet	289,068.75	108,523.25
2022 Jan	341,744	Prophet	323,046.99	18,697.01
2022 Feb	391,699	Prophet	350,704.90	40,994.10
2022 Mar	569,482	Prophet	431,659.97	137,822.03
2022 Apr	727,326	Prophet	453,192.80	274,133.20
2022 May	779,426	Prophet	482,962.89	296,463.11
2022 Jun	833,955	Prophet	491,752.80	342,202.20
2010 Jan	319,379	Prophet_log	353,575.01	-34,196.01
2010 Feb	329,697	Prophet_log	375,922.62	-46,225.62
2010 Mar	388,978	Prophet_log	448,925.92	-59,947.92
2010 Apr	427,950	Prophet_log	473,975.78	-46,025.78
2010 May	431,385	Prophet_log	414,647.20	16,737.80
2010 Jun	432,522	Prophet_log	391,492.78	41,029.22
2010 Jul	492,382	Prophet_log	429,359.09	63,022.91
2010 Aug	624,383	Prophet_log	519,119.96	105,263.04
2010 Sep	496,609	Prophet_log	432,561.43	64,047.57
2010 Oct	450,841	Prophet_log	401,479.71	49,361.29
2010 Nov	327,330	Prophet_log	342,636.62	-15,306.62
2010 Dec	272,069	Prophet_log	297,608.60	-25,539.60
2011 Jan	286,010	Prophet_log	310,927.53	-24,917.53
2011 Feb	319,015	Prophet_log	335,138.95	-16,123.95
2011 Mar	448,224	Prophet_log	394,929.17	53,294.83
2011 Apr	517,979	Prophet_log	433,143.82	84,835.18
2011 May	575,401	Prophet_log	391,740.48	183,660.52
2011 Jun	519,950	Prophet_log	393,342.80	126,607.20
2011 Jul	589,288	Prophet_log	441,425.29	147,862.71
2011 Aug	678,877	Prophet_log	560,624.85	118,252.15
2011 Sep	577,108	Prophet_log	469,639.14	107,468.86
2011 Oct	471,268	Prophet_log	439,912.81	31,355.19
2011 Nov	319,900	Prophet_log	369,833.11	-49,933.11
2011 Dec	262,266	Prophet_log	326,185.81	-63,919.81
2012 Jan	289,312	Prophet_log	343,796.69	-54,484.69
2012 Feb	329,299	Prophet_log	378,738.21	-49,439.21
2012 Mar	399,988	Prophet_log	446,761.66	-46,773.66
2012 Apr	508,131	Prophet_log	486,160.39	21,970.61
2012 May	521,638	Prophet_log	454,137.84	67,500.16
2012 Jun	509,865	Prophet_log	437,999.21	71,865.79
2012 Jul	602,837	Prophet_log	496,562.70	106,274.30
2012 Aug	681,135	Prophet_log	589,639.80	91,495.20
2012 Sep	562,007	Prophet_log	496,182.15	65,824.85
2012 Oct	468,951	Prophet_log	469,598.95	-647.95
2012 Nov	350,902	Prophet_log	402,123.36	-51,221.36
2012 Dec	283,620	Prophet_log	345,720.40	-62,100.40
2013 Jan	322,235	Prophet_log	361,881.31	-39,646.31
2013 Feb	365,343	Prophet_log	382,233.81	-16,890.81
2013 Mar	462,258	Prophet_log	473,428.12	-11,170.12
2013 Apr	516,930	Prophet_log	526,843.35	-9,913.35
2013 May	608,081	Prophet_log	493,514.87	114,566.13
2013 Jun	578,633	Prophet_log	478,447.22	100,185.78
2013 Jul	677,083	Prophet_log	545,061.96	132,021.04
2013 Aug	775,941	Prophet_log	661,284.36	114,656.64
2013 Sep	639,271	Prophet_log	559,431.63	79,839.37
2013 Oct	535,649	Prophet_log	519,943.50	15,705.50
2013 Nov	390,742	Prophet_log	429,462.60	-38,720.60
2013 Dec	342,783	Prophet_log	368,732.30	-25,949.30
2014 Jan	374,568	Prophet_log	393,264.73	-18,696.73
2014 Feb	401,859	Prophet_log	428,755.17	-26,896.17
2014 Mar	503,533	Prophet_log	531,412.59	-27,879.59
2014 Apr	557,275	Prophet_log	587,350.58	-30,075.58
2014 May	610,148	Prophet_log	558,840.81	51,307.19
2014 Jun	595,332	Prophet_log	537,456.01	57,875.99
2014 Jul	687,207	Prophet_log	605,168.50	82,038.50
2014 Aug	787,020	Prophet_log	735,904.23	51,115.77
2014 Sep	652,671	Prophet_log	614,318.26	38,352.74
2014 Oct	554,671	Prophet_log	562,545.62	-7,874.62
2014 Nov	415,750	Prophet_log	455,183.46	-39,433.46
2014 Dec	366,832	Prophet_log	395,733.82	-28,901.82
2015 Jan	399,040	Prophet_log	425,512.88	-26,472.88
2015 Feb	442,963	Prophet_log	469,037.15	-26,074.15
2015 Mar	545,523	Prophet_log	579,041.46	-33,518.46
2015 Apr	586,230	Prophet_log	635,703.39	-49,473.39
2015 May	628,998	Prophet_log	611,683.67	17,314.33
2015 Jun	654,715	Prophet_log	586,501.01	68,213.99
2015 Jul	766,557	Prophet_log	659,050.88	107,506.12
2015 Aug	829,230	Prophet_log	811,936.39	17,293.61
2015 Sep	696,849	Prophet_log	671,979.09	24,869.91
2015 Oct	597,629	Prophet_log	608,431.13	-10,802.13
2015 Nov	475,257	Prophet_log	483,667.68	-8,410.68
2015 Dec	407,035	Prophet_log	425,605.80	-18,570.80
2016 Jan	448,784	Prophet_log	459,096.40	-10,312.40
2016 Feb	506,179	Prophet_log	515,461.74	-9,282.74
2016 Mar	611,987	Prophet_log	625,726.51	-13,739.51
2016 Apr	663,878	Prophet_log	706,036.81	-42,158.81
2016 May	726,980	Prophet_log	679,258.40	47,721.60
2016 Jun	759,256	Prophet_log	649,624.18	109,631.82
2016 Jul	849,148	Prophet_log	740,422.09	108,725.91
2016 Aug	891,091	Prophet_log	874,425.81	16,665.19
2016 Sep	768,042	Prophet_log	728,118.01	39,923.99
2016 Oct	702,530	Prophet_log	667,560.58	34,969.42
2016 Nov	545,468	Prophet_log	552,293.68	-6,825.68
2016 Dec	457,565	Prophet_log	476,384.59	-18,819.59
2017 Jan	503,654	Prophet_log	513,805.53	-10,151.53
2017 Feb	541,368	Prophet_log	555,891.59	-14,523.59
2017 Mar	647,679	Prophet_log	697,175.70	-49,496.70
2017 Apr	710,409	Prophet_log	770,596.64	-60,187.64
2017 May	745,096	Prophet_log	751,592.44	-6,496.44
2017 Jun	794,118	Prophet_log	728,620.00	65,498.00
2017 Jul	864,476	Prophet_log	824,534.70	39,941.30
2017 Aug	939,077	Prophet_log	966,500.10	-27,423.10
2017 Sep	818,705	Prophet_log	808,454.19	10,250.81
2017 Oct	734,287	Prophet_log	732,902.49	1,384.51
2017 Nov	582,743	Prophet_log	593,902.23	-11,159.23
2017 Dec	478,377	Prophet_log	511,628.77	-33,251.77
2018 Jan	534,281	Prophet_log	551,251.98	-16,970.98
2018 Feb	555,841	Prophet_log	602,878.76	-47,037.76
2018 Mar	652,082	Prophet_log	746,496.79	-94,414.79
2018 Apr	689,214	Prophet_log	821,241.26	-132,027.26
2018 May	755,491	Prophet_log	801,556.28	-46,065.28
2018 Jun	782,628	Prophet_log	777,105.49	5,522.51
2018 Jul	837,740	Prophet_log	874,213.76	-36,473.76
2018 Aug	936,644	Prophet_log	1,030,807.75	-94,163.75
2018 Sep	806,267	Prophet_log	854,865.02	-48,598.02
2018 Oct	721,989	Prophet_log	764,065.37	-42,076.37
2018 Nov	575,096	Prophet_log	608,760.74	-33,664.74
2018 Dec	496,993	Prophet_log	525,613.35	-28,620.35
2019 Jan	486,306	Prophet_log	568,230.15	-81,924.15
2019 Feb	498,081	Prophet_log	618,409.46	-120,328.46
2019 Mar	606,616	Prophet_log	749,738.84	-143,122.84
2019 Apr	608,322	Prophet_log	808,746.81	-200,424.81
2019 May	665,724	Prophet_log	786,410.88	-120,686.88
2019 Jun	714,041	Prophet_log	758,776.01	-44,735.01
2019 Jul	747,112	Prophet_log	838,495.64	-91,383.64
2019 Aug	828,426	Prophet_log	985,665.77	-157,239.77
2019 Sep	719,254	Prophet_log	809,552.94	-90,298.94
2019 Oct	629,555	Prophet_log	710,715.58	-81,160.58
2019 Nov	508,290	Prophet_log	558,588.95	-50,298.95
2019 Dec	445,470	Prophet_log	479,845.74	-34,375.74
2020 Jan	488,461	Prophet_log	507,715.71	-19,254.71
2020 Feb	540,254	Prophet_log	563,705.78	-23,451.78
2020 Mar	297,649	Prophet_log	672,289.63	-374,640.63
2020 Apr	2,191	Prophet_log	723,922.44	-721,731.44
2020 May	2,955	Prophet_log	660,178.73	-657,223.73
2020 Jun	14,932	Prophet_log	569,082.42	-554,150.42
2020 Jul	95,576	Prophet_log	524,087.71	-428,511.71
2020 Aug	240,322	Prophet_log	503,176.80	-262,854.80
2020 Sep	251,221	Prophet_log	385,211.33	-133,990.33
2020 Oct	253,895	Prophet_log	310,671.02	-56,776.02
2020 Nov	116,634	Prophet_log	237,174.64	-120,540.64
2020 Dec	137,446	Prophet_log	192,574.58	-55,128.58
2021 Jan	93,013	Prophet_log	198,194.55	-105,181.55
2021 Feb	40,883	Prophet_log	219,286.52	-178,403.52
2021 Mar	60,163	Prophet_log	224,046.38	-163,883.38
2021 Apr	95,116	Prophet_log	162,712.18	-67,596.18
2021 May	179,599	Prophet_log	154,142.17	25,456.83
2021 Jun	321,985	Prophet_log	152,126.59	169,858.41
2021 Jul	552,399	Prophet_log	204,502.46	347,896.54
2021 Aug	780,123	Prophet_log	249,441.16	530,681.84
2021 Sep	697,572	Prophet_log	216,934.68	480,637.32
2021 Oct	655,682	Prophet_log	200,771.43	454,910.57
2021 Nov	521,638	Prophet_log	167,530.54	354,107.46
2021 Dec	397,592	Prophet_log	150,651.57	246,940.43
2022 Jan	341,744	Prophet_log	171,409.36	170,334.64
2022 Feb	391,699	Prophet_log	187,346.21	204,352.79
2022 Mar	569,482	Prophet_log	219,171.49	350,310.51
2022 Apr	727,326	Prophet_log	220,006.72	507,319.28
2022 May	779,426	Prophet_log	246,060.98	533,365.02
2022 Jun	833,955	Prophet_log	264,851.57	569,103.43
2010 Jan	319,379	SNaive	337,043.00	-17,664.00
2010 Feb	329,697	SNaive	371,317.00	-41,620.00
2010 Mar	388,978	SNaive	473,879.00	-84,901.00
2010 Apr	427,950	SNaive	525,648.00	-97,698.00
2010 May	431,385	SNaive	510,850.00	-79,465.00
2010 Jun	432,522	SNaive	501,923.00	-69,401.00
2010 Jul	492,382	SNaive	523,383.00	-31,001.00
2010 Aug	624,383	SNaive	623,297.00	1,086.00
2010 Sep	496,609	SNaive	517,222.00	-20,613.00
2010 Oct	450,841	SNaive	454,129.00	-3,288.00
2010 Nov	327,330	SNaive	350,155.00	-22,825.00
2010 Dec	272,069	SNaive	308,080.00	-36,011.00
2011 Jan	286,010	SNaive	319,379.00	-33,369.00
2011 Feb	319,015	SNaive	329,697.00	-10,682.00
2011 Mar	448,224	SNaive	388,978.00	59,246.00
2011 Apr	517,979	SNaive	427,950.00	90,029.00
2011 May	575,401	SNaive	431,385.00	144,016.00
2011 Jun	519,950	SNaive	432,522.00	87,428.00
2011 Jul	589,288	SNaive	492,382.00	96,906.00
2011 Aug	678,877	SNaive	624,383.00	54,494.00
2011 Sep	577,108	SNaive	496,609.00	80,499.00
2011 Oct	471,268	SNaive	450,841.00	20,427.00
2011 Nov	319,900	SNaive	327,330.00	-7,430.00
2011 Dec	262,266	SNaive	272,069.00	-9,803.00
2012 Jan	289,312	SNaive	286,010.00	3,302.00
2012 Feb	329,299	SNaive	319,015.00	10,284.00
2012 Mar	399,988	SNaive	448,224.00	-48,236.00
2012 Apr	508,131	SNaive	517,979.00	-9,848.00
2012 May	521,638	SNaive	575,401.00	-53,763.00
2012 Jun	509,865	SNaive	519,950.00	-10,085.00
2012 Jul	602,837	SNaive	589,288.00	13,549.00
2012 Aug	681,135	SNaive	678,877.00	2,258.00
2012 Sep	562,007	SNaive	577,108.00	-15,101.00
2012 Oct	468,951	SNaive	471,268.00	-2,317.00
2012 Nov	350,902	SNaive	319,900.00	31,002.00
2012 Dec	283,620	SNaive	262,266.00	21,354.00
2013 Jan	322,235	SNaive	289,312.00	32,923.00
2013 Feb	365,343	SNaive	329,299.00	36,044.00
2013 Mar	462,258	SNaive	399,988.00	62,270.00
2013 Apr	516,930	SNaive	508,131.00	8,799.00
2013 May	608,081	SNaive	521,638.00	86,443.00
2013 Jun	578,633	SNaive	509,865.00	68,768.00
2013 Jul	677,083	SNaive	602,837.00	74,246.00
2013 Aug	775,941	SNaive	681,135.00	94,806.00
2013 Sep	639,271	SNaive	562,007.00	77,264.00
2013 Oct	535,649	SNaive	468,951.00	66,698.00
2013 Nov	390,742	SNaive	350,902.00	39,840.00
2013 Dec	342,783	SNaive	283,620.00	59,163.00
2014 Jan	374,568	SNaive	322,235.00	52,333.00
2014 Feb	401,859	SNaive	365,343.00	36,516.00
2014 Mar	503,533	SNaive	462,258.00	41,275.00
2014 Apr	557,275	SNaive	516,930.00	40,345.00
2014 May	610,148	SNaive	608,081.00	2,067.00
2014 Jun	595,332	SNaive	578,633.00	16,699.00
2014 Jul	687,207	SNaive	677,083.00	10,124.00
2014 Aug	787,020	SNaive	775,941.00	11,079.00
2014 Sep	652,671	SNaive	639,271.00	13,400.00
2014 Oct	554,671	SNaive	535,649.00	19,022.00
2014 Nov	415,750	SNaive	390,742.00	25,008.00
2014 Dec	366,832	SNaive	342,783.00	24,049.00
2015 Jan	399,040	SNaive	374,568.00	24,472.00
2015 Feb	442,963	SNaive	401,859.00	41,104.00
2015 Mar	545,523	SNaive	503,533.00	41,990.00
2015 Apr	586,230	SNaive	557,275.00	28,955.00
2015 May	628,998	SNaive	610,148.00	18,850.00
2015 Jun	654,715	SNaive	595,332.00	59,383.00
2015 Jul	766,557	SNaive	687,207.00	79,350.00
2015 Aug	829,230	SNaive	787,020.00	42,210.00
2015 Sep	696,849	SNaive	652,671.00	44,178.00
2015 Oct	597,629	SNaive	554,671.00	42,958.00
2015 Nov	475,257	SNaive	415,750.00	59,507.00
2015 Dec	407,035	SNaive	366,832.00	40,203.00
2016 Jan	448,784	SNaive	399,040.00	49,744.00
2016 Feb	506,179	SNaive	442,963.00	63,216.00
2016 Mar	611,987	SNaive	545,523.00	66,464.00
2016 Apr	663,878	SNaive	586,230.00	77,648.00
2016 May	726,980	SNaive	628,998.00	97,982.00
2016 Jun	759,256	SNaive	654,715.00	104,541.00
2016 Jul	849,148	SNaive	766,557.00	82,591.00
2016 Aug	891,091	SNaive	829,230.00	61,861.00
2016 Sep	768,042	SNaive	696,849.00	71,193.00
2016 Oct	702,530	SNaive	597,629.00	104,901.00
2016 Nov	545,468	SNaive	475,257.00	70,211.00
2016 Dec	457,565	SNaive	407,035.00	50,530.00
2017 Jan	503,654	SNaive	448,784.00	54,870.00
2017 Feb	541,368	SNaive	506,179.00	35,189.00
2017 Mar	647,679	SNaive	611,987.00	35,692.00
2017 Apr	710,409	SNaive	663,878.00	46,531.00
2017 May	745,096	SNaive	726,980.00	18,116.00
2017 Jun	794,118	SNaive	759,256.00	34,862.00
2017 Jul	864,476	SNaive	849,148.00	15,328.00
2017 Aug	939,077	SNaive	891,091.00	47,986.00
2017 Sep	818,705	SNaive	768,042.00	50,663.00
2017 Oct	734,287	SNaive	702,530.00	31,757.00
2017 Nov	582,743	SNaive	545,468.00	37,275.00
2017 Dec	478,377	SNaive	457,565.00	20,812.00
2018 Jan	534,281	SNaive	503,654.00	30,627.00
2018 Feb	555,841	SNaive	541,368.00	14,473.00
2018 Mar	652,082	SNaive	647,679.00	4,403.00
2018 Apr	689,214	SNaive	710,409.00	-21,195.00
2018 May	755,491	SNaive	745,096.00	10,395.00
2018 Jun	782,628	SNaive	794,118.00	-11,490.00
2018 Jul	837,740	SNaive	864,476.00	-26,736.00
2018 Aug	936,644	SNaive	939,077.00	-2,433.00
2018 Sep	806,267	SNaive	818,705.00	-12,438.00
2018 Oct	721,989	SNaive	734,287.00	-12,298.00
2018 Nov	575,096	SNaive	582,743.00	-7,647.00
2018 Dec	496,993	SNaive	478,377.00	18,616.00
2019 Jan	486,306	SNaive	534,281.00	-47,975.00
2019 Feb	498,081	SNaive	555,841.00	-57,760.00
2019 Mar	606,616	SNaive	652,082.00	-45,466.00
2019 Apr	608,322	SNaive	689,214.00	-80,892.00
2019 May	665,724	SNaive	755,491.00	-89,767.00
2019 Jun	714,041	SNaive	782,628.00	-68,587.00
2019 Jul	747,112	SNaive	837,740.00	-90,628.00
2019 Aug	828,426	SNaive	936,644.00	-108,218.00
2019 Sep	719,254	SNaive	806,267.00	-87,013.00
2019 Oct	629,555	SNaive	721,989.00	-92,434.00
2019 Nov	508,290	SNaive	575,096.00	-66,806.00
2019 Dec	445,470	SNaive	496,993.00	-51,523.00
2020 Jan	488,461	SNaive	486,306.00	2,155.00
2020 Feb	540,254	SNaive	498,081.00	42,173.00
2020 Mar	297,649	SNaive	606,616.00	-308,967.00
2020 Apr	2,191	SNaive	608,322.00	-606,131.00
2020 May	2,955	SNaive	665,724.00	-662,769.00
2020 Jun	14,932	SNaive	714,041.00	-699,109.00
2020 Jul	95,576	SNaive	747,112.00	-651,536.00
2020 Aug	240,322	SNaive	828,426.00	-588,104.00
2020 Sep	251,221	SNaive	719,254.00	-468,033.00
2020 Oct	253,895	SNaive	629,555.00	-375,660.00
2020 Nov	116,634	SNaive	508,290.00	-391,656.00
2020 Dec	137,446	SNaive	445,470.00	-308,024.00
2021 Jan	93,013	SNaive	488,461.00	-395,448.00
2021 Feb	40,883	SNaive	540,254.00	-499,371.00
2021 Mar	60,163	SNaive	297,649.00	-237,486.00
2021 Apr	95,116	SNaive	2,191.00	92,925.00
2021 May	179,599	SNaive	2,955.00	176,644.00
2021 Jun	321,985	SNaive	14,932.00	307,053.00
2021 Jul	552,399	SNaive	95,576.00	456,823.00
2021 Aug	780,123	SNaive	240,322.00	539,801.00
2021 Sep	697,572	SNaive	251,221.00	446,351.00
2021 Oct	655,682	SNaive	253,895.00	401,787.00
2021 Nov	521,638	SNaive	116,634.00	405,004.00
2021 Dec	397,592	SNaive	137,446.00	260,146.00
2022 Jan	341,744	SNaive	93,013.00	248,731.00
2022 Feb	391,699	SNaive	40,883.00	350,816.00
2022 Mar	569,482	SNaive	60,163.00	509,319.00
2022 Apr	727,326	SNaive	95,116.00	632,210.00
2022 May	779,426	SNaive	179,599.00	599,827.00
2022 Jun	833,955	SNaive	321,985.00	511,970.00
2010 Jan	319,379	SNaive_log	338,055.14	-18,676.14
2010 Feb	329,697	SNaive_log	372,426.77	-42,729.77
2010 Mar	388,978	SNaive_log	475,312.87	-86,334.87
2010 Apr	427,950	SNaive_log	527,316.47	-99,366.47
2010 May	431,385	SNaive_log	512,553.45	-81,168.45
2010 Jun	432,522	SNaive_log	503,645.36	-71,123.36
2010 Jul	492,382	SNaive_log	525,214.08	-32,832.08
2010 Aug	624,383	SNaive_log	625,468.78	-1,085.78
2010 Sep	496,609	SNaive_log	519,008.65	-22,399.65
2010 Oct	450,841	SNaive_log	455,687.51	-4,846.51
2010 Nov	327,330	SNaive_log	351,346.58	-24,016.58
2010 Dec	272,069	SNaive_log	309,125.47	-37,056.47
2011 Jan	286,010	SNaive_log	320,474.34	-34,464.34
2011 Feb	319,015	SNaive_log	330,834.97	-11,819.97
2011 Mar	448,224	SNaive_log	390,311.31	57,912.69
2011 Apr	517,979	SNaive_log	429,439.93	88,539.07
2011 May	575,401	SNaive_log	432,938.19	142,462.81
2011 Jun	519,950	SNaive_log	434,210.39	85,739.61
2011 Jul	589,288	SNaive_log	494,355.03	94,932.97
2011 Aug	678,877	SNaive_log	626,944.62	51,932.38
2011 Sep	577,108	SNaive_log	498,644.07	78,463.93
2011 Oct	471,268	SNaive_log	452,713.63	18,554.37
2011 Nov	319,900	SNaive_log	328,681.63	-8,781.63
2011 Dec	262,266	SNaive_log	273,184.41	-10,918.41
2012 Jan	289,312	SNaive_log	287,175.14	2,136.86
2012 Feb	329,299	SNaive_log	320,304.98	8,994.02
2012 Mar	399,988	SNaive_log	450,024.62	-50,036.62
2012 Apr	508,131	SNaive_log	520,069.29	-11,938.29
2012 May	521,638	SNaive_log	577,706.73	-56,068.73
2012 Jun	509,865	SNaive_log	522,036.58	-12,171.58
2012 Jul	602,837	SNaive_log	591,636.51	11,200.49
2012 Aug	681,135	SNaive_log	681,564.35	-429.35
2012 Sep	562,007	SNaive_log	579,376.20	-17,369.20
2012 Oct	468,951	SNaive_log	473,108.26	-4,157.26
2012 Nov	350,902	SNaive_log	321,140.41	29,761.59
2012 Dec	283,620	SNaive_log	263,283.67	20,336.33
2013 Jan	322,235	SNaive_log	290,432.98	31,802.02
2013 Feb	365,343	SNaive_log	330,579.30	34,763.70
2013 Mar	462,258	SNaive_log	401,547.26	60,710.74
2013 Apr	516,930	SNaive_log	510,134.54	6,795.46
2013 May	608,081	SNaive_log	523,681.42	84,399.58
2013 Jun	578,633	SNaive_log	511,889.13	66,743.87
2013 Jul	677,083	SNaive_log	605,246.43	71,836.57
2013 Aug	775,941	SNaive_log	683,869.77	92,071.23
2013 Sep	639,271	SNaive_log	564,280.02	74,990.98
2013 Oct	535,649	SNaive_log	470,860.69	64,788.31
2013 Nov	390,742	SNaive_log	352,341.83	38,400.17
2013 Dec	342,783	SNaive_log	284,786.83	57,996.17
2014 Jan	374,568	SNaive_log	323,589.27	50,978.73
2014 Feb	401,859	SNaive_log	366,895.01	34,963.99
2014 Mar	503,533	SNaive_log	464,222.57	39,310.43
2014 Apr	557,275	SNaive_log	519,124.99	38,150.01
2014 May	610,148	SNaive_log	610,657.63	-509.63
2014 Jun	595,332	SNaive_log	581,069.64	14,262.36
2014 Jul	687,207	SNaive_log	679,918.31	7,288.69
2014 Aug	787,020	SNaive_log	779,170.87	7,849.13
2014 Sep	652,671	SNaive_log	641,916.15	10,754.85
2014 Oct	554,671	SNaive_log	537,852.65	16,818.35
2014 Nov	415,750	SNaive_log	392,341.26	23,408.74
2014 Dec	366,832	SNaive_log	344,181.51	22,650.49
2015 Jan	399,040	SNaive_log	376,092.22	22,947.78
2015 Feb	442,963	SNaive_log	403,489.36	39,473.64
2015 Mar	545,523	SNaive_log	505,577.89	39,945.11
2015 Apr	586,230	SNaive_log	559,535.36	26,694.64
2015 May	628,998	SNaive_log	612,612.98	16,385.02
2015 Jun	654,715	SNaive_log	597,724.81	56,990.19
2015 Jul	766,557	SNaive_log	689,971.06	76,585.94
2015 Aug	829,230	SNaive_log	790,194.29	39,035.71
2015 Sep	696,849	SNaive_log	655,293.52	41,555.48
2015 Oct	597,629	SNaive_log	556,893.87	40,735.13
2015 Nov	475,257	SNaive_log	417,413.28	57,843.72
2015 Dec	407,035	SNaive_log	368,309.71	38,725.29
2016 Jan	448,784	SNaive_log	400,650.51	48,133.49
2016 Feb	506,179	SNaive_log	444,757.80	61,421.20
2016 Mar	611,987	SNaive_log	547,747.88	64,239.12
2016 Apr	663,878	SNaive_log	588,629.00	75,249.00
2016 May	726,980	SNaive_log	631,584.47	95,395.53
2016 Jun	759,256	SNaive_log	657,429.76	101,826.24
2016 Jul	849,148	SNaive_log	769,763.64	79,384.36
2016 Aug	891,091	SNaive_log	832,703.48	58,387.52
2016 Sep	768,042	SNaive_log	699,762.03	68,279.97
2016 Oct	702,530	SNaive_log	600,129.00	102,401.00
2016 Nov	545,468	SNaive_log	477,267.34	68,200.66
2016 Dec	457,565	SNaive_log	408,767.98	48,797.02
2017 Jan	503,654	SNaive_log	450,700.78	52,953.22
2017 Feb	541,368	SNaive_log	508,347.16	33,020.84
2017 Mar	647,679	SNaive_log	614,601.99	33,077.01
2017 Apr	710,409	SNaive_log	666,705.64	43,703.36
2017 May	745,096	SNaive_log	730,069.12	15,026.88
2017 Jun	794,118	SNaive_log	762,467.06	31,650.94
2017 Jul	864,476	SNaive_log	852,725.42	11,750.58
2017 Aug	939,077	SNaive_log	894,826.97	44,250.03
2017 Sep	818,705	SNaive_log	771,251.26	47,453.74
2017 Oct	734,287	SNaive_log	705,458.04	28,828.96
2017 Nov	582,743	SNaive_log	547,732.82	35,010.18
2017 Dec	478,377	SNaive_log	459,460.40	18,916.60
2018 Jan	534,281	SNaive_log	505,732.54	28,548.46
2018 Feb	555,841	SNaive_log	543,595.88	12,245.12
2018 Mar	652,082	SNaive_log	650,332.54	1,749.46
2018 Apr	689,214	SNaive_log	713,305.56	-24,091.56
2018 May	755,491	SNaive_log	748,121.03	7,369.97
2018 Jun	782,628	SNaive_log	797,326.99	-14,698.99
2018 Jul	837,740	SNaive_log	867,953.11	-30,213.11
2018 Aug	936,644	SNaive_log	942,838.46	-6,194.46
2018 Sep	806,267	SNaive_log	821,968.86	-15,701.86
2018 Oct	721,989	SNaive_log	737,200.98	-15,211.98
2018 Nov	575,096	SNaive_log	585,045.17	-9,949.17
2018 Dec	496,993	SNaive_log	480,258.27	16,734.73
2019 Jan	486,306	SNaive_log	536,374.19	-50,068.19
2019 Feb	498,081	SNaive_log	558,019.96	-59,938.96
2019 Mar	606,616	SNaive_log	654,644.51	-48,028.51
2019 Apr	608,322	SNaive_log	691,918.28	-83,596.28
2019 May	665,724	SNaive_log	758,468.62	-92,744.62
2019 Jun	714,041	SNaive_log	785,726.95	-71,685.95
2019 Jul	747,112	SNaive_log	841,058.11	-93,946.11
2019 Aug	828,426	SNaive_log	940,364.74	-111,938.74
2019 Sep	719,254	SNaive_log	809,482.66	-90,228.66
2019 Oct	629,555	SNaive_log	724,876.66	-95,321.66
2019 Nov	508,290	SNaive_log	577,409.85	-69,119.85
2019 Dec	445,470	SNaive_log	499,000.49	-53,530.49
2020 Jan	488,461	SNaive_log	488,274.48	186.52
2020 Feb	540,254	SNaive_log	500,088.36	40,165.64
2020 Mar	297,649	SNaive_log	609,058.86	-311,409.86
2020 Apr	2,191	SNaive_log	611,428.59	-609,237.59
2020 May	2,955	SNaive_log	714,527.20	-711,572.20
2020 Jun	14,932	SNaive_log	811,130.80	-796,198.80
2020 Jul	95,576	SNaive_log	872,141.73	-776,565.73
2020 Aug	240,322	SNaive_log	973,926.65	-733,604.65
2020 Sep	251,221	SNaive_log	847,378.74	-596,157.74
2020 Oct	253,895	SNaive_log	742,697.53	-488,802.53
2020 Nov	116,634	SNaive_log	600,135.75	-483,501.75
2020 Dec	137,446	SNaive_log	527,647.01	-390,201.01
2021 Jan	93,013	SNaive_log	579,600.34	-486,587.34
2021 Feb	40,883	SNaive_log	643,721.98	-602,838.98
2021 Mar	60,163	SNaive_log	358,516.11	-298,353.11
2021 Apr	95,116	SNaive_log	2,648.72	92,467.28
2021 May	179,599	SNaive_log	3,655.90	175,943.10
2021 Jun	321,985	SNaive_log	18,973.35	303,011.65
2021 Jul	552,399	SNaive_log	123,170.61	429,228.39
2021 Aug	780,123	SNaive_log	310,923.88	469,199.12
2021 Sep	697,572	SNaive_log	325,429.42	372,142.58
2021 Oct	655,682	SNaive_log	329,123.84	326,558.16
2021 Nov	521,638	SNaive_log	151,264.28	370,373.72
2021 Dec	397,592	SNaive_log	178,707.42	218,884.58
2022 Jan	341,744	SNaive_log	121,033.00	220,711.00
2022 Feb	391,699	SNaive_log	53,287.08	338,411.92
2022 Mar	569,482	SNaive_log	78,949.63	490,532.37
2022 Apr	727,326	SNaive_log	125,642.86	601,683.14
2022 May	779,426	SNaive_log	238,466.59	540,959.41
2022 Jun	833,955	SNaive_log	428,461.80	405,493.20
2010 Jan	319,379	TSLM	406,210.22	-86,831.22
2010 Feb	329,697	TSLM	438,638.33	-108,941.33
2010 Mar	388,978	TSLM	527,259.15	-138,281.15
2010 Apr	427,950	TSLM	565,319.28	-137,369.28
2010 May	431,385	TSLM	514,736.65	-83,351.65
2010 Jun	432,522	TSLM	488,409.88	-55,887.88
2010 Jul	492,382	TSLM	533,043.12	-40,661.12
2010 Aug	624,383	TSLM	631,115.51	-6,732.51
2010 Sep	496,609	TSLM	526,701.00	-30,092.00
2010 Oct	450,841	TSLM	488,558.29	-37,717.29
2010 Nov	327,330	TSLM	415,953.35	-88,623.35
2010 Dec	272,069	TSLM	364,371.54	-92,302.54
2011 Jan	286,010	TSLM	381,110.32	-95,100.32
2011 Feb	319,015	TSLM	411,342.34	-92,327.34
2011 Mar	448,224	TSLM	497,703.89	-49,479.89
2011 Apr	517,979	TSLM	537,919.56	-19,940.56
2011 May	575,401	TSLM	494,916.46	80,484.54
2011 Jun	519,950	TSLM	474,723.09	45,226.91
2011 Jul	589,288	TSLM	522,933.47	66,354.53
2011 Aug	678,877	TSLM	626,361.72	52,515.28
2011 Sep	577,108	TSLM	521,056.79	56,051.21
2011 Oct	471,268	TSLM	483,972.69	-12,704.69
2011 Nov	319,900	TSLM	407,231.23	-87,331.23
2011 Dec	262,266	TSLM	355,316.77	-93,050.77
2012 Jan	289,312	TSLM	372,192.36	-82,880.36
2012 Feb	329,299	TSLM	402,939.91	-73,640.91
2012 Mar	399,988	TSLM	493,286.27	-93,298.27
2012 Apr	508,131	TSLM	535,033.29	-26,902.29
2012 May	521,638	TSLM	500,253.90	21,384.10
2012 Jun	509,865	TSLM	475,919.31	33,945.69
2012 Jul	602,837	TSLM	525,667.98	77,169.02
2012 Aug	681,135	TSLM	628,161.93	52,973.07
2012 Sep	562,007	TSLM	523,167.48	38,839.52
2012 Oct	468,951	TSLM	480,037.96	-11,086.96
2012 Nov	350,902	TSLM	397,105.23	-46,203.23
2012 Dec	283,620	TSLM	345,443.76	-61,823.76
2013 Jan	322,235	TSLM	363,945.45	-41,710.45
2013 Feb	365,343	TSLM	396,252.60	-30,909.60
2013 Mar	462,258	TSLM	485,946.41	-23,688.41
2013 Apr	516,930	TSLM	534,168.70	-17,238.70
2013 May	608,081	TSLM	503,289.49	104,791.51
2013 Jun	578,633	TSLM	481,495.54	97,137.46
2013 Jul	677,083	TSLM	535,741.23	141,341.77
2013 Aug	775,941	TSLM	637,547.08	138,393.92
2013 Sep	639,271	TSLM	532,996.40	106,274.60
2013 Oct	535,649	TSLM	487,214.40	48,434.60
2013 Nov	390,742	TSLM	402,605.02	-11,863.02
2013 Dec	342,783	TSLM	350,316.34	-7,533.34
2014 Jan	374,568	TSLM	372,125.38	2,442.62
2014 Feb	401,859	TSLM	406,040.54	-4,181.54
2014 Mar	503,533	TSLM	496,746.74	6,786.26
2014 Apr	557,275	TSLM	545,984.42	11,290.58
2014 May	610,148	TSLM	524,331.11	85,816.89
2014 Jun	595,332	TSLM	501,660.02	93,671.98
2014 Jul	687,207	TSLM	559,007.84	128,199.16
2014 Aug	787,020	TSLM	660,389.71	126,630.29
2014 Sep	652,671	TSLM	553,360.50	99,310.50
2014 Oct	554,671	TSLM	503,343.83	51,327.17
2014 Nov	415,750	TSLM	414,479.90	1,270.10
2014 Dec	366,832	TSLM	362,707.34	4,124.66
2015 Jan	399,040	TSLM	386,080.90	12,959.10
2015 Feb	442,963	TSLM	419,738.79	23,224.21
2015 Mar	545,523	TSLM	511,648.87	33,874.13
2015 Apr	586,230	TSLM	561,645.81	24,584.19
2015 May	628,998	TSLM	545,182.48	83,815.52
2015 Jun	654,715	TSLM	523,003.90	131,711.10
2015 Jul	766,557	TSLM	583,270.54	183,286.46
2015 Aug	829,230	TSLM	685,429.12	143,800.88
2015 Sep	696,849	TSLM	576,855.68	119,993.32
2015 Oct	597,629	TSLM	523,966.66	73,662.34
2015 Nov	475,257	TSLM	432,109.02	43,147.98
2015 Dec	407,035	TSLM	381,151.96	25,883.04
2016 Jan	448,784	TSLM	406,271.78	42,512.22
2016 Feb	506,179	TSLM	441,055.01	65,123.99
2016 Mar	611,987	TSLM	534,305.71	77,681.29
2016 Apr	663,878	TSLM	584,416.81	79,461.19
2016 May	726,980	TSLM	572,512.89	154,467.11
2016 Jun	759,256	TSLM	554,416.06	204,839.94
2016 Jul	849,148	TSLM	619,018.19	230,129.81
2016 Aug	891,091	TSLM	719,416.21	171,674.79
2016 Sep	768,042	TSLM	609,772.97	158,269.03
2016 Oct	702,530	TSLM	554,551.35	147,978.65
2016 Nov	545,468	TSLM	461,854.20	83,613.80
2016 Dec	457,565	TSLM	410,391.99	47,173.01
2017 Jan	503,654	TSLM	437,981.52	65,672.48
2017 Feb	541,368	TSLM	474,449.28	66,918.72
2017 Mar	647,679	TSLM	568,463.97	79,215.03
2017 Apr	710,409	TSLM	618,701.57	91,707.43
2017 May	745,096	TSLM	611,389.86	133,706.14
2017 Jun	794,118	TSLM	595,957.28	198,160.72
2017 Jul	864,476	TSLM	661,956.85	202,519.15
2017 Aug	939,077	TSLM	758,536.00	180,541.00
2017 Sep	818,705	TSLM	648,235.57	170,469.43
2017 Oct	734,287	TSLM	592,585.00	141,702.00
2017 Nov	582,743	TSLM	496,026.95	86,716.05
2017 Dec	478,377	TSLM	442,468.99	35,908.01
2018 Jan	534,281	TSLM	471,930.31	62,350.69
2018 Feb	555,841	TSLM	508,416.72	47,424.28
2018 Mar	652,082	TSLM	602,834.43	49,247.57
2018 Apr	689,214	TSLM	653,343.06	35,870.94
2018 May	755,491	TSLM	647,589.10	107,901.90
2018 Jun	782,628	TSLM	635,385.32	147,242.68
2018 Jul	837,740	TSLM	700,943.20	136,796.80
2018 Aug	936,644	TSLM	795,431.38	141,212.62
2018 Sep	806,267	TSLM	684,061.27	122,205.73
2018 Oct	721,989	TSLM	626,194.14	95,794.86
2018 Nov	575,096	TSLM	526,000.94	49,095.06
2018 Dec	496,993	TSLM	469,149.79	27,843.21
2019 Jan	486,306	TSLM	500,521.10	-14,215.10
2019 Feb	498,081	TSLM	535,171.11	-37,090.11
2019 Mar	606,616	TSLM	628,541.73	-21,925.73
2019 Apr	608,322	TSLM	677,396.87	-69,074.87
2019 May	665,724	TSLM	674,053.14	-8,329.14
2019 Jun	714,041	TSLM	662,411.45	51,629.55
2019 Jul	747,112	TSLM	726,196.42	20,915.58
2019 Aug	828,426	TSLM	819,453.80	8,972.20
2019 Sep	719,254	TSLM	705,435.22	13,818.78
2019 Oct	629,555	TSLM	644,845.08	-15,290.08
2019 Nov	508,290	TSLM	540,844.04	-32,554.04
2019 Dec	445,470	TSLM	481,893.40	-36,423.40
2020 Jan	488,461	TSLM	510,234.78	-21,773.78
2020 Feb	540,254	TSLM	543,643.26	-3,389.26
2020 Mar	297,649	TSLM	638,204.80	-340,555.80
2020 Apr	2,191	TSLM	680,669.37	-678,478.37
2020 May	2,955	TSLM	672,745.39	-669,790.39
2020 Jun	14,932	TSLM	655,935.37	-641,003.37
2020 Jul	95,576	TSLM	709,738.71	-614,162.71
2020 Aug	240,322	TSLM	794,747.86	-554,425.86
2020 Sep	251,221	TSLM	674,264.75	-423,043.75
2020 Oct	253,895	TSLM	607,080.12	-353,185.12
2020 Nov	116,634	TSLM	498,286.21	-381,652.21
2020 Dec	137,446	TSLM	435,127.90	-297,681.90
2021 Jan	93,013	TSLM	458,422.92	-365,409.92
2021 Feb	40,883	TSLM	488,464.92	-447,581.92
2021 Mar	60,163	TSLM	561,553.98	-501,390.98
2021 Apr	95,116	TSLM	585,991.70	-490,875.70
2021 May	179,599	TSLM	580,714.80	-401,115.80
2021 Jun	321,985	TSLM	568,431.84	-246,446.84
2021 Jul	552,399	TSLM	628,092.51	-75,693.51
2021 Aug	780,123	TSLM	722,123.42	57,999.58
2021 Sep	697,572	TSLM	614,841.70	82,730.30
2021 Oct	655,682	TSLM	556,653.21	99,028.79
2021 Nov	521,638	TSLM	451,515.29	70,122.71
2021 Dec	397,592	TSLM	397,304.06	287.94
2022 Jan	341,744	TSLM	420,169.37	-78,425.37
2022 Feb	391,699	TSLM	449,859.81	-58,160.81
2022 Mar	569,482	TSLM	525,036.93	44,445.07
2022 Apr	727,326	TSLM	556,229.75	171,096.25
2022 May	779,426	TSLM	562,555.25	216,870.75
2022 Jun	833,955	TSLM	564,243.95	269,711.05
2010 Jan	319,379	TSLM_log	397,141.32	-77,762.32
2010 Feb	329,697	TSLM_log	432,134.62	-102,437.62
2010 Mar	388,978	TSLM_log	525,934.25	-136,956.25
2010 Apr	427,950	TSLM_log	566,403.93	-138,453.93
2010 May	431,385	TSLM_log	511,918.76	-80,533.76
2010 Jun	432,522	TSLM_log	484,215.85	-51,693.85
2010 Jul	492,382	TSLM_log	530,963.46	-38,581.46
2010 Aug	624,383	TSLM_log	632,760.14	-8,377.14
2010 Sep	496,609	TSLM_log	524,802.10	-28,193.10
2010 Oct	450,841	TSLM_log	486,217.08	-35,376.08
2010 Nov	327,330	TSLM_log	411,410.07	-84,080.07
2010 Dec	272,069	TSLM_log	358,376.28	-86,307.28
2011 Jan	286,010	TSLM_log	374,580.08	-88,570.08
2011 Feb	319,015	TSLM_log	405,192.24	-86,177.24
2011 Mar	448,224	TSLM_log	492,112.63	-43,888.63
2011 Apr	517,979	TSLM_log	533,429.84	-15,450.84
2011 May	575,401	TSLM_log	489,564.96	85,836.04
2011 Jun	519,950	TSLM_log	468,986.51	50,963.49
2011 Jul	589,288	TSLM_log	518,447.37	70,840.63
2011 Aug	678,877	TSLM_log	624,070.81	54,806.19
2011 Sep	577,108	TSLM_log	516,697.12	60,410.88
2011 Oct	471,268	TSLM_log	479,463.97	-8,195.97
2011 Nov	319,900	TSLM_log	400,545.93	-80,645.93
2011 Dec	262,266	TSLM_log	347,433.86	-85,167.86
2012 Jan	289,312	TSLM_log	363,653.36	-74,341.36
2012 Feb	329,299	TSLM_log	394,726.68	-65,427.68
2012 Mar	399,988	TSLM_log	485,840.27	-85,852.27
2012 Apr	508,131	TSLM_log	528,372.37	-20,241.37
2012 May	521,638	TSLM_log	492,607.75	29,030.25
2012 Jun	509,865	TSLM_log	468,578.91	41,286.09
2012 Jul	602,837	TSLM_log	518,880.68	83,956.32
2012 Aug	681,135	TSLM_log	622,606.59	58,528.41
2012 Sep	562,007	TSLM_log	516,688.49	45,318.51
2012 Oct	468,951	TSLM_log	474,142.47	-5,191.47
2012 Nov	350,902	TSLM_log	389,354.00	-38,452.00
2012 Dec	283,620	TSLM_log	336,822.93	-53,202.93
2013 Jan	322,235	TSLM_log	354,973.96	-32,738.96
2013 Feb	365,343	TSLM_log	387,712.10	-22,369.10
2013 Mar	462,258	TSLM_log	477,844.46	-15,586.46
2013 Apr	516,930	TSLM_log	527,531.31	-10,601.31
2013 May	608,081	TSLM_log	495,657.98	112,423.02
2013 Jun	578,633	TSLM_log	473,844.87	104,788.13
2013 Jul	677,083	TSLM_log	528,554.17	148,528.83
2013 Aug	775,941	TSLM_log	632,502.06	143,438.94
2013 Sep	639,271	TSLM_log	525,809.32	113,461.68
2013 Oct	535,649	TSLM_log	479,990.66	55,658.34
2013 Nov	390,742	TSLM_log	392,181.58	-1,439.58
2013 Dec	342,783	TSLM_log	338,060.48	4,722.52
2014 Jan	374,568	TSLM_log	360,062.98	14,505.02
2014 Feb	401,859	TSLM_log	395,332.72	6,526.28
2014 Mar	503,533	TSLM_log	488,837.17	14,695.83
2014 Apr	557,275	TSLM_log	540,783.58	16,491.42
2014 May	610,148	TSLM_log	516,799.64	93,348.36
2014 Jun	595,332	TSLM_log	493,542.28	101,789.72
2014 Jul	687,207	TSLM_log	552,292.87	134,914.13
2014 Aug	787,020	TSLM_log	658,530.62	128,489.38
2014 Sep	652,671	TSLM_log	546,850.89	105,820.11
2014 Oct	554,671	TSLM_log	496,003.20	58,667.80
2014 Nov	415,750	TSLM_log	402,016.02	13,733.98
2014 Dec	366,832	TSLM_log	347,180.08	19,651.92
2015 Jan	399,040	TSLM_log	371,167.23	27,872.77
2015 Feb	442,963	TSLM_log	407,136.68	35,826.32
2015 Mar	545,523	TSLM_log	504,480.66	41,042.34
2015 Apr	586,230	TSLM_log	558,575.47	27,654.53
2015 May	628,998	TSLM_log	538,832.73	90,165.27
2015 Jun	654,715	TSLM_log	515,222.51	139,492.49
2015 Jul	766,557	TSLM_log	578,277.54	188,279.46
2015 Aug	829,230	TSLM_log	688,428.32	140,801.68
2015 Sep	696,849	TSLM_log	571,711.36	125,137.64
2015 Oct	597,629	TSLM_log	516,495.22	81,133.78
2015 Nov	475,257	TSLM_log	416,680.76	58,576.24
2015 Dec	407,035	TSLM_log	360,907.60	46,127.40
2016 Jan	448,784	TSLM_log	387,248.03	61,535.97
2016 Feb	506,179	TSLM_log	425,637.20	80,541.80
2016 Mar	611,987	TSLM_log	527,996.21	83,990.79
2016 Apr	663,878	TSLM_log	584,193.98	79,684.02
2016 May	726,980	TSLM_log	568,038.41	158,941.59
2016 Jun	759,256	TSLM_log	546,872.36	212,383.64
2016 Jul	849,148	TSLM_log	616,344.63	232,803.37
2016 Aug	891,091	TSLM_log	729,850.19	161,240.81
2016 Sep	768,042	TSLM_log	606,701.37	161,340.63
2016 Oct	702,530	TSLM_log	546,663.84	155,866.16
2016 Nov	545,468	TSLM_log	441,344.14	104,123.86
2016 Dec	457,565	TSLM_log	382,470.61	75,094.39
2017 Jan	503,654	TSLM_log	412,178.97	91,475.03
2017 Feb	541,368	TSLM_log	454,123.58	87,244.42
2017 Mar	647,679	TSLM_log	562,509.27	85,169.73
2017 Apr	710,409	TSLM_log	621,599.51	88,809.49
2017 May	745,096	TSLM_log	608,710.52	136,385.48
2017 Jun	794,118	TSLM_log	588,440.75	205,677.25
2017 Jul	864,476	TSLM_log	662,607.91	201,868.09
2017 Aug	939,077	TSLM_log	778,432.96	160,644.04
2017 Sep	818,705	TSLM_log	648,362.94	170,342.06
2017 Oct	734,287	TSLM_log	584,711.67	149,575.33
2017 Nov	582,743	TSLM_log	470,831.52	111,911.48
2017 Dec	478,377	TSLM_log	407,262.71	71,114.29
2018 Jan	534,281	TSLM_log	439,920.63	94,360.37
2018 Feb	555,841	TSLM_log	483,978.51	71,862.49
2018 Mar	652,082	TSLM_log	597,999.85	54,082.15
2018 Apr	689,214	TSLM_log	660,022.31	29,191.69
2018 May	755,491	TSLM_log	647,970.48	107,520.52
2018 Jun	782,628	TSLM_log	629,357.83	153,270.17
2018 Jul	837,740	TSLM_log	706,506.75	131,233.25
2018 Aug	936,644	TSLM_log	825,276.44	111,367.56
2018 Sep	806,267	TSLM_log	688,547.69	117,719.31
2018 Oct	721,989	TSLM_log	620,119.21	101,869.79
2018 Nov	575,096	TSLM_log	498,429.54	76,666.46
2018 Dec	496,993	TSLM_log	429,483.16	67,509.84
2019 Jan	486,306	TSLM_log	465,025.65	21,280.35
2019 Feb	498,081	TSLM_log	509,003.97	-10,922.97
2019 Mar	606,616	TSLM_log	625,819.05	-19,203.05
2019 Apr	608,322	TSLM_log	688,059.75	-79,737.75
2019 May	665,724	TSLM_log	677,956.77	-12,232.77
2019 Jun	714,041	TSLM_log	659,210.26	54,830.74
2019 Jul	747,112	TSLM_log	736,793.42	10,318.58
2019 Aug	828,426	TSLM_log	856,917.34	-28,491.34
2019 Sep	719,254	TSLM_log	714,663.17	4,590.83
2019 Oct	629,555	TSLM_log	642,207.80	-12,652.80
2019 Nov	508,290	TSLM_log	514,831.30	-6,541.30
2019 Dec	445,470	TSLM_log	442,832.24	2,637.76
2020 Jan	488,461	TSLM_log	476,046.02	12,414.98
2020 Feb	540,254	TSLM_log	519,205.90	21,048.10
2020 Mar	297,649	TSLM_log	638,563.70	-340,914.70
2020 Apr	2,191	TSLM_log	693,251.14	-691,060.14
2020 May	2,955	TSLM_log	685,286.86	-682,331.86
2020 Jun	14,932	TSLM_log	662,574.71	-647,642.71
2020 Jul	95,576	TSLM_log	722,494.94	-626,918.94
2020 Aug	240,322	TSLM_log	824,140.87	-583,818.87
2020 Sep	251,221	TSLM_log	681,184.96	-429,963.96
2020 Oct	253,895	TSLM_log	605,627.91	-351,732.91
2020 Nov	116,634	TSLM_log	481,908.64	-365,274.64
2020 Dec	137,446	TSLM_log	409,877.10	-272,431.10
2021 Jan	93,013	TSLM_log	431,085.58	-338,072.58
2021 Feb	40,883	TSLM_log	463,647.94	-422,764.94
2021 Mar	60,163	TSLM_log	538,034.43	-477,871.43
2021 Apr	95,116	TSLM_log	455,910.12	-360,794.12
2021 May	179,599	TSLM_log	452,557.53	-272,958.53
2021 Jun	321,985	TSLM_log	474,236.65	-152,251.65
2021 Jul	552,399	TSLM_log	571,894.73	-19,495.73
2021 Aug	780,123	TSLM_log	689,032.08	91,090.92
2021 Sep	697,572	TSLM_log	583,902.55	113,669.45
2021 Oct	655,682	TSLM_log	528,822.18	126,859.82
2021 Nov	521,638	TSLM_log	414,712.00	106,926.00
2021 Dec	397,592	TSLM_log	363,961.75	33,630.25
2022 Jan	341,744	TSLM_log	379,046.79	-37,302.79
2022 Feb	391,699	TSLM_log	396,894.38	-5,195.38
2022 Mar	569,482	TSLM_log	474,877.81	94,604.19
2022 Apr	727,326	TSLM_log	422,698.64	304,627.36
2022 May	779,426	TSLM_log	441,513.11	337,912.89
2022 Jun	833,955	TSLM_log	482,109.88	351,845.12

# Show Point Forecasts in Plot: 2000-2022
error_fc_madeira_stretch %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_until2022, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2000-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2010-2022
tourism_madeira_from2010 <- tourism_madeira_until2022 %>%
  filter(year(Month) >= 2010)

error_fc_madeira_stretch %>%
  filter(year(Month) >= 2010) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_from2010, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2010-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2019-2022
tourism_madeira_from2019 <- tourism_madeira_until2022 %>%
  filter(year(Month) >= 2019)

error_fc_madeira_stretch %>%
  filter(year(Month) >= 2019) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_from2019, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2019-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2020-2022
tourism_madeira_from2020 <- tourism_madeira_until2022 %>%
  filter(year(Month) >= 2020)

error_fc_madeira_stretch %>%
  filter(year(Month) >= 2020) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_from2020, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2020-2022") +
  ylab("Overnight_Stays")

2.1.1.4 Change of RMSE: 2010-2019 vs. 2010-2022

All Models

Note: In the following, “All Models” means that all 20 models are shown. Each model appears twice: With the original & with the log-transformed variable.

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_stretch, tourism_madeira_until2019) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_stretch, tourism_madeira_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
ARIMA_d0D1	1	24,386.04	1	59,729.41
Drift_STL	7	26,899.35	2	60,088.61
ARIMA_d1D1	2	24,724.45	3	60,178.35
ARIMA_auto	3	24,913.02	4	60,451.53
HWA_log	9	30,719.70	5	65,805.38
ARIMA_d0D1_log	4	25,369.19	6	66,049.77
ETS_auto_log	12	34,099.55	7	66,826.92
ETS_auto	10	32,949.29	8	66,975.51
HWA	11	33,635.74	9	69,030.40
Drift_STL_log	8	29,861.82	10	75,104.73
ARIMA_auto_log	5	26,327.99	11	75,949.29
ARIMA_d1D1_log	6	26,769.65	12	83,733.94
Naive	17	82,367.68	13	91,659.07
Naive_log	18	82,974.60	14	92,047.44
Prophet_log	15	67,718.90	15	171,910.50
Prophet	16	73,226.04	16	178,006.40
TSLM	19	90,460.21	17	180,367.90
TSLM_log	20	93,011.49	18	180,891.97
SNaive	14	53,807.75	19	204,508.35
SNaive_log	13	53,238.30	20	215,248.72

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

Note: In the following, “Each Model once” means that each model appears only once: Either with the original or with the log-transformed variable (depending on the lowest RMSE for the 2010-2022 Forecasts).

# Save best models according to the RMSE of Forecasts from 2010-2022
best_models_fc_madeira_stretch <- c("ARIMA_d0D1", "Drift_STL", "ARIMA_d1D1", "ARIMA_auto", "HWA_log", "ETS_auto_log", "Naive", "Prophet_log", "TSLM", "SNaive")

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_stretch, tourism_madeira_until2019) %>%
  filter(.model %in% best_models_fc_madeira_stretch) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_stretch, tourism_madeira_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
ARIMA_d0D1	1	24,386.04	1	59,729.41
Drift_STL	4	26,899.35	2	60,088.61
ARIMA_d1D1	2	24,724.45	3	60,178.35
ARIMA_auto	3	24,913.02	4	60,451.53
HWA_log	5	30,719.70	5	65,805.38
ETS_auto_log	6	34,099.55	7	66,826.92
Naive	9	82,367.68	13	91,659.07
Prophet_log	8	67,718.90	15	171,910.50
TSLM	10	90,460.21	17	180,367.90
SNaive	7	53,807.75	19	204,508.35

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.1.1.5 RMSE Development by including more Years in Time Series

# Compute RMSE and RMSSE for 2010 and create tibble
tourism_until_i <- tourism_madeira_until2022 %>%
    filter(year(Month) <= 2010)

accuracy_madeira_stretch <- accuracy(fc_madeira_stretch, tourism_until_i) %>%
  select(c(.model, RMSE, RMSSE)) %>%
  mutate(Until_Year = 2010)

# Create tsibble of summarized RMSE and RMSSE, beginning in 2010 and including more years
for (i in 2011:2022){
  tourism_until_i <- tourism_madeira_until2022 %>%
    filter(year(Month) <= i)

  accuracy_next_year <- accuracy(fc_madeira_stretch, tourism_until_i) %>%
    select(c(.model, RMSE, RMSSE)) %>%
    mutate(Until_Year = i)

  accuracy_madeira_stretch <- rbind(accuracy_madeira_stretch, accuracy_next_year)
}

rm(accuracy_next_year, tourism_until_i) # remove variables from R environment

accuracy_madeira_stretch <- accuracy_madeira_stretch %>%
  rename(Model = .model) %>%
  select(c(Until_Year, Model, RMSE, RMSSE)) %>%
  as_tsibble(key = Model, index = Until_Year)

# Show table
accuracy_madeira_stretch %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	25,746.67	0.67
2011	ARIMA_auto	31,990.62	0.75
2012	ARIMA_auto	29,360.78	0.71
2013	ARIMA_auto	29,129.77	0.67
2014	ARIMA_auto	26,714.44	0.63
2015	ARIMA_auto	25,927.53	0.60
2016	ARIMA_auto	25,891.07	0.57
2017	ARIMA_auto	24,924.56	0.55
2018	ARIMA_auto	24,332.97	0.55
2019	ARIMA_auto	24,913.02	0.54
2020	ARIMA_auto	56,055.39	0.48
2021	ARIMA_auto	58,575.79	0.42
2022	ARIMA_auto	60,451.53	0.39
2010	ARIMA_auto_log	25,063.92	0.65
2011	ARIMA_auto_log	32,912.62	0.77
2012	ARIMA_auto_log	30,052.29	0.73
2013	ARIMA_auto_log	29,624.53	0.68
2014	ARIMA_auto_log	27,411.29	0.64
2015	ARIMA_auto_log	26,933.86	0.63
2016	ARIMA_auto_log	27,194.60	0.59
2017	ARIMA_auto_log	26,461.56	0.58
2018	ARIMA_auto_log	26,146.95	0.59
2019	ARIMA_auto_log	26,327.99	0.57
2020	ARIMA_auto_log	56,045.50	0.48
2021	ARIMA_auto_log	58,643.29	0.42
2022	ARIMA_auto_log	75,949.29	0.49
2010	ARIMA_d0D1	27,273.37	0.71
2011	ARIMA_d0D1	30,431.93	0.71
2012	ARIMA_d0D1	28,234.56	0.68
2013	ARIMA_d0D1	28,282.41	0.65
2014	ARIMA_d0D1	25,975.80	0.61
2015	ARIMA_d0D1	25,294.35	0.59
2016	ARIMA_d0D1	25,329.17	0.55
2017	ARIMA_d0D1	24,569.42	0.54
2018	ARIMA_d0D1	23,850.53	0.54
2019	ARIMA_d0D1	24,386.04	0.52
2020	ARIMA_d0D1	55,580.87	0.48
2021	ARIMA_d0D1	57,798.98	0.41
2022	ARIMA_d0D1	59,729.41	0.39
2010	ARIMA_d0D1_log	25,142.28	0.65
2011	ARIMA_d0D1_log	30,072.52	0.71
2012	ARIMA_d0D1_log	27,997.93	0.68
2013	ARIMA_d0D1_log	28,074.38	0.65
2014	ARIMA_d0D1_log	26,073.46	0.61
2015	ARIMA_d0D1_log	25,803.19	0.60
2016	ARIMA_d0D1_log	26,273.08	0.57
2017	ARIMA_d0D1_log	25,675.24	0.57
2018	ARIMA_d0D1_log	25,071.66	0.57
2019	ARIMA_d0D1_log	25,369.19	0.55
2020	ARIMA_d0D1_log	55,802.04	0.48
2021	ARIMA_d0D1_log	56,565.56	0.40
2022	ARIMA_d0D1_log	66,049.77	0.43
2010	ARIMA_d1D1	25,332.85	0.66
2011	ARIMA_d1D1	31,938.76	0.75
2012	ARIMA_d1D1	29,778.51	0.72
2013	ARIMA_d1D1	29,655.63	0.68
2014	ARIMA_d1D1	26,966.21	0.63
2015	ARIMA_d1D1	25,828.01	0.60
2016	ARIMA_d1D1	25,372.67	0.55
2017	ARIMA_d1D1	24,453.63	0.54
2018	ARIMA_d1D1	23,904.47	0.54
2019	ARIMA_d1D1	24,724.45	0.53
2020	ARIMA_d1D1	55,087.27	0.47
2021	ARIMA_d1D1	57,892.88	0.41
2022	ARIMA_d1D1	60,178.35	0.39
2010	ARIMA_d1D1_log	25,063.92	0.65
2011	ARIMA_d1D1_log	32,823.63	0.77
2012	ARIMA_d1D1_log	30,345.75	0.73
2013	ARIMA_d1D1_log	29,763.90	0.68
2014	ARIMA_d1D1_log	27,627.18	0.65
2015	ARIMA_d1D1_log	27,302.19	0.64
2016	ARIMA_d1D1_log	27,402.02	0.60
2017	ARIMA_d1D1_log	26,648.13	0.59
2018	ARIMA_d1D1_log	26,298.32	0.59
2019	ARIMA_d1D1_log	26,769.65	0.58
2020	ARIMA_d1D1_log	54,519.59	0.47
2021	ARIMA_d1D1_log	64,247.68	0.46
2022	ARIMA_d1D1_log	83,733.94	0.54
2010	Drift_STL	24,851.11	0.64
2011	Drift_STL	32,432.81	0.76
2012	Drift_STL	31,138.22	0.75
2013	Drift_STL	31,731.73	0.73
2014	Drift_STL	29,354.90	0.69
2015	Drift_STL	28,438.31	0.66
2016	Drift_STL	28,172.00	0.62
2017	Drift_STL	27,490.44	0.61
2018	Drift_STL	26,517.72	0.60
2019	Drift_STL	26,899.35	0.58
2020	Drift_STL	56,113.79	0.48
2021	Drift_STL	58,370.71	0.42
2022	Drift_STL	60,088.61	0.39
2010	Drift_STL_log	24,303.39	0.63
2011	Drift_STL_log	33,270.32	0.78
2012	Drift_STL_log	32,020.08	0.77
2013	Drift_STL_log	31,612.49	0.73
2014	Drift_STL_log	29,066.84	0.68
2015	Drift_STL_log	28,786.23	0.67
2016	Drift_STL_log	29,602.33	0.65
2017	Drift_STL_log	29,732.41	0.66
2018	Drift_STL_log	29,504.13	0.67
2019	Drift_STL_log	29,861.82	0.64
2020	Drift_STL_log	54,780.68	0.47
2021	Drift_STL_log	54,837.58	0.39
2022	Drift_STL_log	75,104.73	0.49
2010	ETS_auto	28,769.91	0.75
2011	ETS_auto	38,100.00	0.89
2012	ETS_auto	36,593.46	0.88
2013	ETS_auto	39,048.98	0.90
2014	ETS_auto	37,274.25	0.88
2015	ETS_auto	36,240.57	0.85
2016	ETS_auto	36,463.02	0.80
2017	ETS_auto	34,701.08	0.77
2018	ETS_auto	33,386.22	0.75
2019	ETS_auto	32,949.29	0.71
2020	ETS_auto	63,731.87	0.55
2021	ETS_auto	66,348.25	0.47
2022	ETS_auto	66,975.51	0.43
2010	ETS_auto_log	28,093.89	0.73
2011	ETS_auto_log	38,850.50	0.91
2012	ETS_auto_log	37,696.62	0.91
2013	ETS_auto_log	39,263.46	0.90
2014	ETS_auto_log	37,420.76	0.88
2015	ETS_auto_log	36,492.30	0.85
2016	ETS_auto_log	37,030.17	0.81
2017	ETS_auto_log	35,797.04	0.79
2018	ETS_auto_log	34,456.45	0.78
2019	ETS_auto_log	34,099.55	0.73
2020	ETS_auto_log	63,815.00	0.55
2021	ETS_auto_log	65,435.21	0.47
2022	ETS_auto_log	66,826.92	0.43
2010	HWA	29,105.48	0.75
2011	HWA	37,739.95	0.89
2012	HWA	36,399.46	0.88
2013	HWA	38,721.25	0.89
2014	HWA	37,435.15	0.88
2015	HWA	36,886.44	0.86
2016	HWA	36,144.75	0.79
2017	HWA	34,153.01	0.75
2018	HWA	32,865.52	0.74
2019	HWA	33,635.74	0.72
2020	HWA	66,238.47	0.57
2021	HWA	68,559.18	0.49
2022	HWA	69,030.40	0.45
2010	HWA_log	30,453.80	0.79
2011	HWA_log	38,973.59	0.92
2012	HWA_log	35,985.05	0.87
2013	HWA_log	34,936.14	0.80
2014	HWA_log	33,738.24	0.79
2015	HWA_log	32,936.68	0.77
2016	HWA_log	32,752.38	0.72
2017	HWA_log	31,302.00	0.69
2018	HWA_log	30,663.33	0.69
2019	HWA_log	30,719.70	0.66
2020	HWA_log	62,139.90	0.53
2021	HWA_log	63,851.00	0.46
2022	HWA_log	65,805.38	0.43
2010	Naive	72,466.89	1.88
2011	Naive	79,807.28	1.87
2012	Naive	79,633.17	1.92
2013	Naive	82,332.93	1.89
2014	Naive	82,777.15	1.94
2015	Naive	82,680.03	1.93
2016	Naive	82,937.73	1.81
2017	Naive	83,303.36	1.84
2018	Naive	83,341.41	1.88
2019	Naive	82,367.68	1.77
2020	Naive	87,551.46	0.75
2021	Naive	90,996.94	0.65
2022	Naive	91,659.07	0.59
2010	Naive_log	73,052.58	1.89
2011	Naive_log	80,405.97	1.89
2012	Naive_log	80,207.34	1.94
2013	Naive_log	82,886.58	1.91
2014	Naive_log	83,338.69	1.96
2015	Naive_log	83,235.99	1.94
2016	Naive_log	83,486.83	1.82
2017	Naive_log	83,867.09	1.85
2018	Naive_log	83,915.15	1.90
2019	Naive_log	82,974.60	1.78
2020	Naive_log	88,374.83	0.76
2021	Naive_log	92,331.87	0.66
2022	Naive_log	92,047.44	0.59
2010	Prophet	54,464.58	1.41
2011	Prophet	69,095.78	1.62
2012	Prophet	67,164.16	1.62
2013	Prophet	73,720.50	1.69
2014	Prophet	71,335.02	1.67
2015	Prophet	69,811.14	1.63
2016	Prophet	71,040.37	1.55
2017	Prophet	69,538.50	1.53
2018	Prophet	67,728.23	1.53
2019	Prophet	73,226.04	1.57
2020	Prophet	164,963.42	1.41
2021	Prophet	175,826.92	1.25
2022	Prophet	178,006.40	1.15
2010	Prophet_log	52,804.07	1.37
2011	Prophet_log	78,818.55	1.85
2012	Prophet_log	74,045.78	1.79
2013	Prophet_log	73,879.42	1.70
2014	Prophet_log	68,798.66	1.62
2015	Prophet_log	65,288.62	1.52
2016	Prophet_log	63,497.21	1.39
2017	Prophet_log	60,646.04	1.34
2018	Prophet_log	60,885.64	1.38
2019	Prophet_log	67,718.90	1.46
2020	Prophet_log	130,353.87	1.12
2021	Prophet_log	153,065.03	1.09
2022	Prophet_log	171,910.50	1.11
2010	SNaive	52,554.91	1.36
2011	SNaive	62,510.14	1.47
2012	SNaive	53,007.37	1.28
2013	SNaive	55,845.42	1.28
2014	SNaive	51,535.61	1.21
2015	SNaive	50,711.51	1.18
2016	SNaive	55,292.47	1.21
2017	SNaive	53,422.12	1.18
2018	SNaive	50,668.17	1.15
2019	SNaive	53,807.75	1.16
2020	SNaive	153,714.16	1.32
2021	SNaive	182,718.86	1.30
2022	SNaive	204,508.35	1.32
2010	SNaive_log	53,776.72	1.39
2011	SNaive_log	62,342.18	1.46
2012	SNaive_log	52,979.17	1.28
2013	SNaive_log	55,315.64	1.27
2014	SNaive_log	50,903.72	1.19
2015	SNaive_log	49,861.14	1.16
2016	SNaive_log	54,142.73	1.18
2017	SNaive_log	52,154.55	1.15
2018	SNaive_log	49,512.09	1.12
2019	SNaive_log	53,238.30	1.14
2020	SNaive_log	175,631.72	1.51
2021	SNaive_log	199,423.81	1.42
2022	SNaive_log	215,248.72	1.39
2010	TSLM	85,572.32	2.22
2011	TSLM	77,340.72	1.82
2012	TSLM	71,343.78	1.72
2013	TSLM	73,622.94	1.69
2014	TSLM	73,200.42	1.72
2015	TSLM	76,825.82	1.79
2016	TSLM	87,815.46	1.92
2017	TSLM	94,645.68	2.09
2018	TSLM	94,725.33	2.14
2019	TSLM	90,460.21	1.95
2020	TSLM	166,078.42	1.42
2021	TSLM	181,033.44	1.29
2022	TSLM	180,367.90	1.17
2010	TSLM_log	82,537.02	2.14
2011	TSLM_log	74,901.50	1.76
2012	TSLM_log	69,050.05	1.67
2013	TSLM_log	73,004.44	1.68
2014	TSLM_log	73,661.96	1.73
2015	TSLM_log	78,239.12	1.83
2016	TSLM_log	90,091.68	1.97
2017	TSLM_log	97,325.65	2.15
2018	TSLM_log	97,493.22	2.20
2019	TSLM_log	93,011.49	2.00
2020	TSLM_log	168,945.92	1.45
2021	TSLM_log	178,090.55	1.27
2022	TSLM_log	180,891.97	1.17

All Models

# Plot development of RMSE for period 2010-2022
accuracy_madeira_stretch %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_madeira_stretch %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_madeira_stretch %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

#  Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_madeira_stretch %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_madeira_stretch %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	82,367.68	87,551.46	5,183.78	0.0629
Naive_log	82,974.60	88,374.83	5,400.23	0.0651
TSLM_log	93,011.49	168,945.92	75,934.43	0.8164
Drift_STL_log	29,861.82	54,780.68	24,918.86	0.8345
TSLM	90,460.21	166,078.42	75,618.22	0.8359
ETS_auto_log	34,099.55	63,815.00	29,715.45	0.8714
Prophet_log	67,718.90	130,353.87	62,634.97	0.9249
ETS_auto	32,949.29	63,731.87	30,782.58	0.9342
HWA	33,635.74	66,238.47	32,602.73	0.9693
HWA_log	30,719.70	62,139.90	31,420.20	1.0228
ARIMA_d1D1_log	26,769.65	54,519.59	27,749.95	1.0366
Drift_STL	26,899.35	56,113.79	29,214.44	1.0861
ARIMA_auto_log	26,327.99	56,045.50	29,717.51	1.1287
ARIMA_d0D1_log	25,369.19	55,802.04	30,432.85	1.1996
ARIMA_d1D1	24,724.45	55,087.27	30,362.82	1.2280
ARIMA_auto	24,913.02	56,055.39	31,142.36	1.2500
Prophet	73,226.04	164,963.42	91,737.38	1.2528
ARIMA_d0D1	24,386.04	55,580.87	31,194.83	1.2792
SNaive	53,807.75	153,714.16	99,906.41	1.8567
SNaive_log	53,238.30	175,631.72	122,393.42	2.2990

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

Each Model once

# Plot development of RMSE for period 2010-2022
accuracy_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_madeira_stretch %>%
  filter(Until_Year <= 2019) %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_madeira_stretch %>%
  filter(Until_Year > 2019) %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	82,367.68	87,551.46	5,183.78	0.0629
TSLM	90,460.21	166,078.42	75,618.22	0.8359
ETS_auto_log	34,099.55	63,815.00	29,715.45	0.8714
Prophet_log	67,718.90	130,353.87	62,634.97	0.9249
HWA_log	30,719.70	62,139.90	31,420.20	1.0228
Drift_STL	26,899.35	56,113.79	29,214.44	1.0861
ARIMA_d1D1	24,724.45	55,087.27	30,362.82	1.2280
ARIMA_auto	24,913.02	56,055.39	31,142.36	1.2500
ARIMA_d0D1	24,386.04	55,580.87	31,194.83	1.2792
SNaive	53,807.75	153,714.16	99,906.41	1.8567

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

2.1.1.6 RMSE per Year

All Models

# Calculate RMSE per year and save as tsibble
rmse_pyear_madeira_stretch <- error_fc_madeira_stretch %>%
  mutate(Year = year(Month)) %>%
  index_by(Year) %>%
  group_by(Model) %>%
  summarise(RMSE = (mean(Forecast_Error**2))**0.5)

# Create Plot for 2010-2022
rmse_pyear_madeira_stretch %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Create Plot for 2020-2022
rmse_pyear_madeira_stretch %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_madeira_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	128,349.1	55,326.97	0.7577
Naive_log	130,626.8	56,653.38	0.7659
Prophet_log	375,572.8	263,792.08	2.3599
Prophet	495,703.2	384,633.37	3.4630
Drift_STL_log	155,218.8	122,312.17	3.7169
HWA	192,221.9	152,317.64	3.8171
ARIMA_d1D1_log	159,781.4	129,093.91	4.2067
ARIMA_d1D1	165,129.4	133,981.78	4.3015
Drift_STL	165,531.2	135,414.08	4.4962
ARIMA_auto	168,397.4	138,770.58	4.6840
HWA_log	181,763.7	150,541.18	4.8216
ARIMA_d0D1	167,435.9	138,675.51	4.8218
ETS_auto_log	182,121.1	151,419.79	4.9320
ARIMA_auto_log	166,194.0	138,289.46	4.9558
ARIMA_d0D1_log	166,783.0	138,878.50	4.9769
SNaive	480,578.5	404,110.50	5.2847
ETS_auto	183,909.5	155,190.23	5.4037
SNaive_log	557,645.4	478,398.04	6.0368
TSLM	470,714.3	437,934.84	13.3600
TSLM_log	476,926.2	445,829.26	14.3368

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_madeira_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Drift_STL_log	55,459.58	-99,759.19	-0.6427
ARIMA_d0D1_log	64,369.33	-102,413.71	-0.6141
HWA_log	80,301.68	-101,462.01	-0.5582
ETS_auto_log	81,149.87	-100,971.25	-0.5544
ARIMA_d0D1	78,148.00	-89,287.88	-0.5333
HWA	90,229.93	-101,991.96	-0.5306
Drift_STL	79,052.77	-86,478.44	-0.5224
ARIMA_auto	81,297.07	-87,100.33	-0.5172
ETS_auto	90,254.17	-93,655.34	-0.5092
ARIMA_auto_log	81,953.35	-84,240.67	-0.5069
ARIMA_d1D1	82,694.29	-82,435.06	-0.4992
Prophet	267,654.71	-228,048.53	-0.4601
TSLM_log	258,118.13	-218,808.06	-0.4588
TSLM	299,791.25	-170,923.08	-0.3631
SNaive_log	371,384.93	-186,260.43	-0.3340
SNaive	375,134.24	-105,444.30	-0.2194
ARIMA_d1D1_log	129,757.17	-30,024.26	-0.1879
Prophet_log	306,974.57	-68,598.26	-0.1826
Naive	122,668.21	-5,680.89	-0.0443
Naive_log	128,026.89	-2,599.94	-0.0199

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_madeira_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
TSLM	163,584.58	-136,206.67	-0.4543
Naive_log	84,935.66	-43,091.23	-0.3366
Prophet	224,041.19	-43,613.52	-0.1629
Naive	106,320.15	-16,348.06	-0.1333
HWA	79,506.28	-10,723.65	-0.1188
ETS_auto	80,578.10	-9,676.07	-0.1072
TSLM_log	238,448.59	-19,669.54	-0.0762
ETS_auto_log	94,252.54	13,102.67	0.1615
Drift_STL	92,166.67	13,113.90	0.1659
ARIMA_auto	94,935.39	13,638.32	0.1678
ARIMA_d0D1	94,935.39	16,787.39	0.2148
ARIMA_d1D1	100,487.70	17,793.41	0.2152
SNaive_log	451,468.42	80,083.49	0.2156
HWA_log	102,038.70	21,737.01	0.2707
SNaive	494,290.74	119,156.50	0.3176
Prophet_log	420,162.91	113,188.34	0.3687
ARIMA_d1D1_log	276,076.00	146,318.83	1.1276
ARIMA_d0D1_log	179,645.19	115,275.85	1.7909
ARIMA_auto_log	248,335.48	166,382.13	2.0302
Drift_STL_log	262,385.57	206,925.99	3.7311

Each Model once

# Create Plot for 2010-2022
rmse_pyear_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022")

# Create Plot for 2020-2022
rmse_pyear_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022")

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	128,349.1	55,326.97	0.7577
Prophet_log	375,572.8	263,792.08	2.3599
ARIMA_d1D1	165,129.4	133,981.78	4.3015
Drift_STL	165,531.2	135,414.08	4.4962
ARIMA_auto	168,397.4	138,770.58	4.6840
HWA_log	181,763.7	150,541.18	4.8216
ARIMA_d0D1	167,435.9	138,675.51	4.8218
ETS_auto_log	182,121.1	151,419.79	4.9320
SNaive	480,578.5	404,110.50	5.2847
TSLM	470,714.3	437,934.84	13.3600

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
HWA_log	80,301.68	-101,462.01	-0.5582
ETS_auto_log	81,149.87	-100,971.25	-0.5544
ARIMA_d0D1	78,148.00	-89,287.88	-0.5333
Drift_STL	79,052.77	-86,478.44	-0.5224
ARIMA_auto	81,297.07	-87,100.33	-0.5172
ARIMA_d1D1	82,694.29	-82,435.06	-0.4992
TSLM	299,791.25	-170,923.08	-0.3631
SNaive	375,134.24	-105,444.30	-0.2194
Prophet_log	306,974.57	-68,598.26	-0.1826
Naive	122,668.21	-5,680.89	-0.0443

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
TSLM	163,584.58	-136,206.67	-0.4543
Naive	106,320.15	-16,348.06	-0.1333
ETS_auto_log	94,252.54	13,102.67	0.1615
Drift_STL	92,166.67	13,113.90	0.1659
ARIMA_auto	94,935.39	13,638.32	0.1678
ARIMA_d0D1	94,935.39	16,787.39	0.2148
ARIMA_d1D1	100,487.70	17,793.41	0.2152
HWA_log	102,038.70	21,737.01	0.2707
SNaive	494,290.74	119,156.50	0.3176
Prophet_log	420,162.91	113,188.34	0.3687

2.1.1.7 Change of RMSSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_stretch, tourism_madeira_until2019) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_stretch, tourism_madeira_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
ARIMA_d0D1	1	0.5245	1	0.3859
Drift_STL	7	0.5785	2	0.3882
ARIMA_d1D1	2	0.5317	3	0.3888
ARIMA_auto	3	0.5358	4	0.3906
HWA_log	9	0.6607	5	0.4252
ARIMA_d0D1_log	4	0.5456	6	0.4267
ETS_auto_log	12	0.7334	7	0.4318
ETS_auto	10	0.7086	8	0.4327
HWA	11	0.7234	9	0.4460
Drift_STL_log	8	0.6422	10	0.4852
ARIMA_auto_log	5	0.5662	11	0.4907
ARIMA_d1D1_log	6	0.5757	12	0.5410
Naive	17	1.7715	13	0.5922
Naive_log	18	1.7845	14	0.5947
Prophet_log	15	1.4564	15	1.1107
Prophet	16	1.5749	16	1.1501
TSLM	19	1.9455	17	1.1653
TSLM_log	20	2.0004	18	1.1687
SNaive	14	1.1572	19	1.3213
SNaive_log	13	1.1450	20	1.3907

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_stretch, tourism_madeira_until2019) %>%
  filter(.model %in% best_models_fc_madeira_stretch) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_stretch, tourism_madeira_until2022) %>%
  filter(.model %in% best_models_fc_madeira_stretch) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
ARIMA_d0D1	1	0.5245	1	0.3859
Drift_STL	4	0.5785	2	0.3882
ARIMA_d1D1	2	0.5317	3	0.3888
ARIMA_auto	3	0.5358	4	0.3906
HWA_log	5	0.6607	5	0.4252
ETS_auto_log	6	0.7334	6	0.4318
Naive	9	1.7715	7	0.5922
Prophet_log	8	1.4564	8	1.1107
TSLM	10	1.9455	9	1.1653
SNaive	7	1.1572	10	1.3213

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.1.1.8 RMSSE Development by including more Years in Time Series

All Models

# Plot development of RMSSE for period 2010-2022
accuracy_madeira_stretch %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_madeira_stretch %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_madeira_stretch %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

Each Model once

# Plot development of RMSSE for period 2010-2022
accuracy_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_madeira_stretch %>%
  filter(Model %in% best_models_fc_madeira_stretch) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSSE")

2.1.2 Rolling Window Cross-Validation

2.1.2.1 Time series Cross-Validation & Seasonal Strength Test

# Cross-Validation with sliding Window to create Training sets
data_slide_madeira <- tourism_madeira_until2022 %>%
  slide_tsibble (.size = 120, .step = 1) %>%
  filter (.id != max(.id))

# Testing for Seasonal Strength
data_slide_madeira %>%
  features(Overnight_Stays, unitroot_nsdiffs) %>%
  group_by(Region) %>%
  summarise(Mean_nsdiffs = (mean(nsdiffs))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Strength Test</span>", align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Strength Test

Region	Mean_nsdiffs
Madeira	1

2.1.2.2 Fitting Models and one-step ahead Forecasts

# Fit models
fit_madeira_slide <- data_slide_madeira %>%
  model(
    SNaive = SNAIVE(Overnight_Stays),
    Drift_STL = decomposition_model(STL(Overnight_Stays),RW(season_adjust ~ drift())),
    Naive = NAIVE(Overnight_Stays),
    TSLM = TSLM(Overnight_Stays ~ trend() + season()),
    ETS_auto = ETS(Overnight_Stays),
    HWA = ETS(Overnight_Stays ~ error("A") + trend("A") + season("A")),
    ARIMA_auto = ARIMA(Overnight_Stays),
    ARIMA_d1D1 = ARIMA(Overnight_Stays ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)),
    Prophet = fable.prophet::prophet(Overnight_Stays ~ season(period = 12)),
    SNaive_log = SNAIVE(log(Overnight_Stays)),
    Drift_STL_log = decomposition_model(STL(log(Overnight_Stays)),RW(season_adjust ~ drift())),
    Naive_log = NAIVE(log(Overnight_Stays)),
    TSLM_log = TSLM(log(Overnight_Stays) ~ trend() + season()),
    ETS_auto_log = ETS(log(Overnight_Stays)),
    HWA_log = ETS(log(Overnight_Stays) ~ error("A") + trend("A") + season("A")),
    ARIMA_auto_log = ARIMA(log(Overnight_Stays)),
    ARIMA_d1D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)),
    Prophet_log = fable.prophet::prophet(log(Overnight_Stays) ~ season(period = 12))
    )

# Perform a one-step ahead Forecast
fc_madeira_slide <- fit_madeira_slide %>% forecast(h=1)

2.1.2.3 Forecast Errors

# Calculate forecast error per observation and model
error_fc_madeira_slide <- merge(tourism_madeira_until2022, fc_madeira_slide, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# Show table
error_fc_madeira_slide %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Forecast Error per Observation and Model</span>", digits = 2, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Forecast Error per Observation and Model

Month	Overnight_Stays	Model	Point_Forecast	Forecast_Error
2010 Jan	319,379	ARIMA_auto	336,040.22	-16,661.22
2010 Feb	329,697	ARIMA_auto	366,012.50	-36,315.50
2010 Mar	388,978	ARIMA_auto	446,178.64	-57,200.64
2010 Apr	427,950	ARIMA_auto	453,649.89	-25,699.89
2010 May	431,385	ARIMA_auto	426,965.63	4,419.37
2010 Jun	432,522	ARIMA_auto	418,265.75	14,256.25
2010 Jul	492,382	ARIMA_auto	470,234.36	22,147.64
2010 Aug	624,383	ARIMA_auto	584,285.92	40,097.08
2010 Sep	496,609	ARIMA_auto	502,306.78	-5,697.78
2010 Oct	450,841	ARIMA_auto	431,403.34	19,437.66
2010 Nov	327,330	ARIMA_auto	348,662.55	-21,332.55
2010 Dec	272,069	ARIMA_auto	280,069.98	-8,000.98
2011 Jan	286,010	ARIMA_auto	285,496.71	513.29
2011 Feb	319,015	ARIMA_auto	312,917.75	6,097.25
2011 Mar	448,224	ARIMA_auto	407,026.81	41,197.19
2011 Apr	517,979	ARIMA_auto	469,083.01	48,895.99
2011 May	575,401	ARIMA_auto	503,435.36	71,965.64
2011 Jun	519,950	ARIMA_auto	549,249.87	-29,299.87
2011 Jul	589,288	ARIMA_auto	560,223.30	29,064.70
2011 Aug	678,877	ARIMA_auto	691,409.73	-12,532.73
2011 Sep	577,108	ARIMA_auto	553,587.72	23,520.28
2011 Oct	471,268	ARIMA_auto	514,162.47	-42,894.47
2011 Nov	319,900	ARIMA_auto	361,991.72	-42,091.72
2011 Dec	262,266	ARIMA_auto	275,103.80	-12,837.80
2012 Jan	289,312	ARIMA_auto	281,552.90	7,759.10
2012 Feb	329,299	ARIMA_auto	322,495.03	6,803.97
2012 Mar	399,988	ARIMA_auto	437,334.59	-37,346.59
2012 Apr	508,131	ARIMA_auto	464,892.35	43,238.65
2012 May	521,638	ARIMA_auto	522,261.38	-623.38
2012 Jun	509,865	ARIMA_auto	498,484.20	11,380.80
2012 Jul	602,837	ARIMA_auto	564,501.31	38,335.69
2012 Aug	681,135	ARIMA_auto	697,345.21	-16,210.21
2012 Sep	562,007	ARIMA_auto	570,937.98	-8,930.98
2012 Oct	468,951	ARIMA_auto	478,620.48	-9,669.48
2012 Nov	350,902	ARIMA_auto	339,138.35	11,763.65
2012 Dec	283,620	ARIMA_auto	293,434.62	-9,814.62
2013 Jan	322,235	ARIMA_auto	304,438.41	17,796.59
2013 Feb	365,343	ARIMA_auto	350,771.85	14,571.15
2013 Mar	462,258	ARIMA_auto	452,313.87	9,944.13
2013 Apr	516,930	ARIMA_auto	535,354.93	-18,424.93
2013 May	608,081	ARIMA_auto	530,965.46	77,115.54
2013 Jun	578,633	ARIMA_auto	571,328.06	7,304.94
2013 Jul	677,083	ARIMA_auto	640,532.30	36,550.70
2013 Aug	775,941	ARIMA_auto	752,023.47	23,917.53
2013 Sep	639,271	ARIMA_auto	645,900.97	-6,629.97
2013 Oct	535,649	ARIMA_auto	540,806.03	-5,157.03
2013 Nov	390,742	ARIMA_auto	400,876.53	-10,134.53
2013 Dec	342,783	ARIMA_auto	322,633.84	20,149.16
2014 Jan	374,568	ARIMA_auto	362,829.06	11,738.94
2014 Feb	401,859	ARIMA_auto	404,459.35	-2,600.35
2014 Mar	503,533	ARIMA_auto	487,306.23	16,226.77
2014 Apr	557,275	ARIMA_auto	563,553.45	-6,278.45
2014 May	610,148	ARIMA_auto	606,721.15	3,426.85
2014 Jun	595,332	ARIMA_auto	578,925.36	16,406.64
2014 Jul	687,207	ARIMA_auto	676,524.67	10,682.33
2014 Aug	787,020	ARIMA_auto	774,625.64	12,394.36
2014 Sep	652,671	ARIMA_auto	652,909.37	-238.37
2014 Oct	554,671	ARIMA_auto	550,381.89	4,289.11
2014 Nov	415,750	ARIMA_auto	413,041.13	2,708.87
2014 Dec	366,832	ARIMA_auto	355,360.04	11,471.96
2015 Jan	399,040	ARIMA_auto	390,987.42	8,052.58
2015 Feb	442,963	ARIMA_auto	425,428.56	17,534.44
2015 Mar	545,523	ARIMA_auto	532,754.33	12,768.67
2015 Apr	586,230	ARIMA_auto	599,555.95	-13,325.95
2015 May	628,998	ARIMA_auto	636,389.47	-7,391.47
2015 Jun	654,715	ARIMA_auto	604,920.00	49,795.00
2015 Jul	766,557	ARIMA_auto	736,869.90	29,687.10
2015 Aug	829,230	ARIMA_auto	860,617.29	-31,387.29
2015 Sep	696,849	ARIMA_auto	703,976.75	-7,127.75
2015 Oct	597,629	ARIMA_auto	599,447.46	-1,818.46
2015 Nov	475,257	ARIMA_auto	460,110.46	15,146.54
2015 Dec	407,035	ARIMA_auto	421,408.92	-14,373.92
2016 Jan	448,784	ARIMA_auto	441,754.67	7,029.33
2016 Feb	506,179	ARIMA_auto	485,942.87	20,236.13
2016 Mar	611,987	ARIMA_auto	603,392.53	8,594.47
2016 Apr	663,878	ARIMA_auto	658,540.05	5,337.95
2016 May	726,980	ARIMA_auto	717,595.83	9,384.17
2016 Jun	759,256	ARIMA_auto	727,130.25	32,125.75
2016 Jul	849,148	ARIMA_auto	857,828.31	-8,680.31
2016 Aug	891,091	ARIMA_auto	932,725.64	-41,634.64
2016 Sep	768,042	ARIMA_auto	759,641.38	8,400.62
2016 Oct	702,530	ARIMA_auto	669,972.48	32,557.52
2016 Nov	545,468	ARIMA_auto	573,002.39	-27,534.39
2016 Dec	457,565	ARIMA_auto	490,227.87	-32,662.87
2017 Jan	503,654	ARIMA_auto	494,434.28	9,219.72
2017 Feb	541,368	ARIMA_auto	554,088.59	-12,720.59
2017 Mar	647,679	ARIMA_auto	646,511.35	1,167.65
2017 Apr	710,409	ARIMA_auto	698,502.29	11,906.71
2017 May	745,096	ARIMA_auto	766,696.47	-21,600.47
2017 Jun	794,118	ARIMA_auto	763,661.61	30,456.39
2017 Jul	864,476	ARIMA_auto	889,532.03	-25,056.03
2017 Aug	939,077	ARIMA_auto	925,069.17	14,007.83
2017 Sep	818,705	ARIMA_auto	809,397.53	9,307.47
2017 Oct	734,287	ARIMA_auto	737,892.55	-3,605.55
2017 Nov	582,743	ARIMA_auto	590,352.22	-7,609.22
2017 Dec	478,377	ARIMA_auto	508,146.32	-29,769.32
2018 Jan	534,281	ARIMA_auto	525,642.81	8,638.19
2018 Feb	555,841	ARIMA_auto	577,340.77	-21,499.77
2018 Mar	652,082	ARIMA_auto	667,046.69	-14,964.69
2018 Apr	689,214	ARIMA_auto	711,055.27	-21,841.27
2018 May	755,491	ARIMA_auto	737,006.92	18,484.08
2018 Jun	782,628	ARIMA_auto	788,093.39	-5,465.39
2018 Jul	837,740	ARIMA_auto	865,585.56	-27,845.56
2018 Aug	936,644	ARIMA_auto	902,600.82	34,043.18
2018 Sep	806,267	ARIMA_auto	808,060.07	-1,793.07
2018 Oct	721,989	ARIMA_auto	731,307.06	-9,318.06
2018 Nov	575,096	ARIMA_auto	569,626.57	5,469.43
2018 Dec	496,993	ARIMA_auto	475,614.90	21,378.10
2019 Jan	486,306	ARIMA_auto	547,572.51	-61,266.51
2019 Feb	498,081	ARIMA_auto	526,453.16	-28,372.16
2019 Mar	606,616	ARIMA_auto	600,568.35	6,047.65
2019 Apr	608,322	ARIMA_auto	662,638.14	-54,316.14
2019 May	665,724	ARIMA_auto	678,589.15	-12,865.15
2019 Jun	714,041	ARIMA_auto	700,619.38	13,421.62
2019 Jul	747,112	ARIMA_auto	796,725.45	-49,613.45
2019 Aug	828,426	ARIMA_auto	842,675.29	-14,249.29
2019 Sep	719,254	ARIMA_auto	706,231.48	13,022.52
2019 Oct	629,555	ARIMA_auto	636,464.67	-6,909.67
2019 Nov	508,290	ARIMA_auto	483,223.40	25,066.60
2019 Dec	445,470	ARIMA_auto	419,329.92	26,140.08
2020 Jan	488,461	ARIMA_auto	459,915.54	28,545.46
2020 Feb	540,254	ARIMA_auto	505,640.06	34,613.94
2020 Mar	297,649	ARIMA_auto	636,407.37	-338,758.37
2020 Apr	2,191	ARIMA_auto	484,608.72	-482,417.72
2020 May	2,955	ARIMA_auto	-93,905.41	96,860.41
2020 Jun	14,932	ARIMA_auto	50,377.98	-35,445.98
2020 Jul	95,576	ARIMA_auto	44,330.62	51,245.38
2020 Aug	240,322	ARIMA_auto	202,473.20	37,848.80
2020 Sep	251,221	ARIMA_auto	141,490.24	109,730.76
2020 Oct	253,895	ARIMA_auto	216,979.56	36,915.44
2020 Nov	116,634	ARIMA_auto	139,282.13	-22,648.13
2020 Dec	137,446	ARIMA_auto	33,635.89	103,810.11
2021 Jan	93,013	ARIMA_auto	219,864.56	-126,851.56
2021 Feb	40,883	ARIMA_auto	79,924.26	-39,041.26
2021 Mar	60,163	ARIMA_auto	-89,913.26	150,076.26
2021 Apr	95,116	ARIMA_auto	-27,301.20	122,417.20
2021 May	179,599	ARIMA_auto	181,569.00	-1,970.00
2021 Jun	321,985	ARIMA_auto	204,524.86	117,460.14
2021 Jul	552,399	ARIMA_auto	451,309.93	101,089.07
2021 Aug	780,123	ARIMA_auto	708,749.82	71,373.18
2021 Sep	697,572	ARIMA_auto	746,838.54	-49,266.54
2021 Oct	655,682	ARIMA_auto	608,794.95	46,887.05
2021 Nov	521,638	ARIMA_auto	533,915.33	-12,277.33
2021 Dec	397,592	ARIMA_auto	462,197.19	-64,605.19
2022 Jan	341,744	ARIMA_auto	361,702.72	-19,958.72
2022 Feb	391,699	ARIMA_auto	334,913.22	56,785.78
2022 Mar	569,482	ARIMA_auto	415,038.44	154,443.56
2022 Apr	727,326	ARIMA_auto	632,772.64	94,553.36
2022 May	779,426	ARIMA_auto	825,119.48	-45,693.48
2022 Jun	833,955	ARIMA_auto	805,990.27	27,964.73
2010 Jan	319,379	ARIMA_auto_log	323,544.30	-4,165.30
2010 Feb	329,697	ARIMA_auto_log	356,896.34	-27,199.34
2010 Mar	388,978	ARIMA_auto_log	430,957.47	-41,979.47
2010 Apr	427,950	ARIMA_auto_log	442,578.22	-14,628.22
2010 May	431,385	ARIMA_auto_log	417,793.35	13,591.65
2010 Jun	432,522	ARIMA_auto_log	411,987.15	20,534.85
2010 Jul	492,382	ARIMA_auto_log	461,682.38	30,699.62
2010 Aug	624,383	ARIMA_auto_log	569,383.49	54,999.51
2010 Sep	496,609	ARIMA_auto_log	502,047.98	-5,438.98
2010 Oct	450,841	ARIMA_auto_log	434,562.72	16,278.28
2010 Nov	327,330	ARIMA_auto_log	354,542.86	-27,212.86
2010 Dec	272,069	ARIMA_auto_log	289,667.16	-17,598.16
2011 Jan	286,010	ARIMA_auto_log	287,052.52	-1,042.52
2011 Feb	319,015	ARIMA_auto_log	310,166.05	8,848.95
2011 Mar	448,224	ARIMA_auto_log	393,307.84	54,916.16
2011 Apr	517,979	ARIMA_auto_log	476,554.77	41,424.23
2011 May	575,401	ARIMA_auto_log	495,202.73	80,198.27
2011 Jun	519,950	ARIMA_auto_log	548,038.67	-28,088.67
2011 Jul	589,288	ARIMA_auto_log	564,949.99	24,338.01
2011 Aug	678,877	ARIMA_auto_log	705,040.44	-26,163.44
2011 Sep	577,108	ARIMA_auto_log	546,484.52	30,623.48
2011 Oct	471,268	ARIMA_auto_log	509,032.96	-37,764.96
2011 Nov	319,900	ARIMA_auto_log	358,992.42	-39,092.42
2011 Dec	262,266	ARIMA_auto_log	277,417.15	-15,151.15
2012 Jan	289,312	ARIMA_auto_log	279,322.81	9,989.19
2012 Feb	329,299	ARIMA_auto_log	320,049.68	9,249.32
2012 Mar	399,988	ARIMA_auto_log	435,740.21	-35,752.21
2012 Apr	508,131	ARIMA_auto_log	458,935.17	49,195.83
2012 May	521,638	ARIMA_auto_log	532,267.05	-10,629.05
2012 Jun	509,865	ARIMA_auto_log	492,675.86	17,189.14
2012 Jul	602,837	ARIMA_auto_log	568,215.12	34,621.88
2012 Aug	681,135	ARIMA_auto_log	705,394.29	-24,259.29
2012 Sep	562,007	ARIMA_auto_log	563,227.84	-1,220.84
2012 Oct	468,951	ARIMA_auto_log	478,969.32	-10,018.32
2012 Nov	350,902	ARIMA_auto_log	336,295.24	14,606.76
2012 Dec	283,620	ARIMA_auto_log	291,755.16	-8,135.16
2013 Jan	322,235	ARIMA_auto_log	304,811.26	17,423.74
2013 Feb	365,343	ARIMA_auto_log	352,820.63	12,522.37
2013 Mar	462,258	ARIMA_auto_log	457,609.54	4,648.46
2013 Apr	516,930	ARIMA_auto_log	544,535.01	-27,605.01
2013 May	608,081	ARIMA_auto_log	531,309.73	76,771.27
2013 Jun	578,633	ARIMA_auto_log	569,064.71	9,568.29
2013 Jul	677,083	ARIMA_auto_log	650,861.21	26,221.79
2013 Aug	775,941	ARIMA_auto_log	764,008.08	11,932.92
2013 Sep	639,271	ARIMA_auto_log	628,154.53	11,116.47
2013 Oct	535,649	ARIMA_auto_log	528,166.71	7,482.29
2013 Nov	390,742	ARIMA_auto_log	384,344.65	6,397.35
2013 Dec	342,783	ARIMA_auto_log	314,854.74	27,928.26
2014 Jan	374,568	ARIMA_auto_log	368,291.84	6,276.16
2014 Feb	401,859	ARIMA_auto_log	411,623.72	-9,764.72
2014 Mar	503,533	ARIMA_auto_log	498,924.86	4,608.14
2014 Apr	557,275	ARIMA_auto_log	572,788.80	-15,513.80
2014 May	610,148	ARIMA_auto_log	610,579.78	-431.78
2014 Jun	595,332	ARIMA_auto_log	578,290.13	17,041.87
2014 Jul	687,207	ARIMA_auto_log	683,942.92	3,264.08
2014 Aug	787,020	ARIMA_auto_log	782,824.46	4,195.54
2014 Sep	652,671	ARIMA_auto_log	643,684.42	8,986.58
2014 Oct	554,671	ARIMA_auto_log	543,242.88	11,428.12
2014 Nov	415,750	ARIMA_auto_log	400,671.17	15,078.83
2014 Dec	366,832	ARIMA_auto_log	348,093.44	18,738.56
2015 Jan	399,040	ARIMA_auto_log	396,001.72	3,038.28
2015 Feb	442,963	ARIMA_auto_log	431,073.21	11,889.79
2015 Mar	545,523	ARIMA_auto_log	548,309.84	-2,786.84
2015 Apr	586,230	ARIMA_auto_log	609,152.85	-22,922.85
2015 May	628,998	ARIMA_auto_log	640,073.84	-11,075.84
2015 Jun	654,715	ARIMA_auto_log	603,969.36	50,745.64
2015 Jul	766,557	ARIMA_auto_log	758,828.45	7,728.55
2015 Aug	829,230	ARIMA_auto_log	881,421.96	-52,191.96
2015 Sep	696,849	ARIMA_auto_log	687,197.24	9,651.76
2015 Oct	597,629	ARIMA_auto_log	589,990.15	7,638.85
2015 Nov	475,257	ARIMA_auto_log	442,875.44	32,381.56
2015 Dec	407,035	ARIMA_auto_log	411,866.56	-4,831.56
2016 Jan	448,784	ARIMA_auto_log	445,347.31	3,436.69
2016 Feb	506,179	ARIMA_auto_log	496,174.63	10,004.37
2016 Mar	611,987	ARIMA_auto_log	631,108.77	-19,121.77
2016 Apr	663,878	ARIMA_auto_log	675,720.54	-11,842.54
2016 May	726,980	ARIMA_auto_log	721,787.19	5,192.81
2016 Jun	759,256	ARIMA_auto_log	727,574.92	31,681.08
2016 Jul	849,148	ARIMA_auto_log	884,458.05	-35,310.05
2016 Aug	891,091	ARIMA_auto_log	948,967.68	-57,876.68
2016 Sep	768,042	ARIMA_auto_log	744,065.53	23,976.47
2016 Oct	702,530	ARIMA_auto_log	654,803.43	47,726.57
2016 Nov	545,468	ARIMA_auto_log	540,051.47	5,416.53
2016 Dec	457,565	ARIMA_auto_log	470,290.84	-12,725.84
2017 Jan	503,654	ARIMA_auto_log	502,944.23	709.77
2017 Feb	541,368	ARIMA_auto_log	563,018.19	-21,650.19
2017 Mar	647,679	ARIMA_auto_log	664,483.62	-16,804.62
2017 Apr	710,409	ARIMA_auto_log	707,390.96	3,018.04
2017 May	745,096	ARIMA_auto_log	776,030.30	-30,934.30
2017 Jun	794,118	ARIMA_auto_log	765,106.67	29,011.33
2017 Jul	864,476	ARIMA_auto_log	905,808.55	-41,332.55
2017 Aug	939,077	ARIMA_auto_log	931,389.57	7,687.43
2017 Sep	818,705	ARIMA_auto_log	798,796.98	19,908.02
2017 Oct	734,287	ARIMA_auto_log	726,380.34	7,906.66
2017 Nov	582,743	ARIMA_auto_log	567,437.14	15,305.86
2017 Dec	478,377	ARIMA_auto_log	495,642.33	-17,265.33
2018 Jan	534,281	ARIMA_auto_log	526,587.10	7,693.90
2018 Feb	555,841	ARIMA_auto_log	585,080.45	-29,239.45
2018 Mar	652,082	ARIMA_auto_log	672,644.64	-20,562.64
2018 Apr	689,214	ARIMA_auto_log	714,486.39	-25,272.39
2018 May	755,491	ARIMA_auto_log	736,918.02	18,572.98
2018 Jun	782,628	ARIMA_auto_log	792,278.74	-9,650.74
2018 Jul	837,740	ARIMA_auto_log	870,876.33	-33,136.33
2018 Aug	936,644	ARIMA_auto_log	907,019.42	29,624.58
2018 Sep	806,267	ARIMA_auto_log	808,351.74	-2,084.74
2018 Oct	721,989	ARIMA_auto_log	720,232.32	1,756.68
2018 Nov	575,096	ARIMA_auto_log	566,946.72	8,149.28
2018 Dec	496,993	ARIMA_auto_log	476,044.72	20,948.28
2019 Jan	486,306	ARIMA_auto_log	551,046.34	-64,740.34
2019 Feb	498,081	ARIMA_auto_log	526,750.98	-28,669.98
2019 Mar	606,616	ARIMA_auto_log	595,505.69	11,110.31
2019 Apr	608,322	ARIMA_auto_log	665,080.22	-56,758.22
2019 May	665,724	ARIMA_auto_log	679,445.31	-13,721.31
2019 Jun	714,041	ARIMA_auto_log	712,609.03	1,431.97
2019 Jul	747,112	ARIMA_auto_log	800,125.16	-53,013.16
2019 Aug	828,426	ARIMA_auto_log	847,558.57	-19,132.57
2019 Sep	719,254	ARIMA_auto_log	732,696.38	-13,442.38
2019 Oct	629,555	ARIMA_auto_log	658,817.38	-29,262.38
2019 Nov	508,290	ARIMA_auto_log	501,176.52	7,113.48
2019 Dec	445,470	ARIMA_auto_log	428,195.22	17,274.78
2020 Jan	488,461	ARIMA_auto_log	461,604.00	26,857.00
2020 Feb	540,254	ARIMA_auto_log	498,710.30	41,543.70
2020 Mar	297,649	ARIMA_auto_log	634,645.40	-336,996.40
2020 Apr	2,191	ARIMA_auto_log	500,713.51	-498,522.51
2020 May	2,955	ARIMA_auto_log	237.62	2,717.38
2020 Jun	14,932	ARIMA_auto_log	51,712.68	-36,780.68
2020 Jul	95,576	ARIMA_auto_log	43,919.57	51,656.43
2020 Aug	240,322	ARIMA_auto_log	245,292.64	-4,970.64
2020 Sep	251,221	ARIMA_auto_log	397,226.09	-146,005.09
2020 Oct	253,895	ARIMA_auto_log	312,453.96	-58,558.96
2020 Nov	116,634	ARIMA_auto_log	308,507.87	-191,873.87
2020 Dec	137,446	ARIMA_auto_log	136,388.47	1,057.53
2021 Jan	93,013	ARIMA_auto_log	230,206.84	-137,193.84
2021 Feb	40,883	ARIMA_auto_log	143,749.94	-102,866.94
2021 Mar	60,163	ARIMA_auto_log	61,286.35	-1,123.35
2021 Apr	95,116	ARIMA_auto_log	19,821.88	75,294.12
2021 May	179,599	ARIMA_auto_log	134,341.66	45,257.34
2021 Jun	321,985	ARIMA_auto_log	221,527.35	100,457.65
2021 Jul	552,399	ARIMA_auto_log	328,025.27	224,373.73
2021 Aug	780,123	ARIMA_auto_log	528,529.17	251,593.83
2021 Sep	697,572	ARIMA_auto_log	616,665.06	80,906.94
2021 Oct	655,682	ARIMA_auto_log	501,869.35	153,812.65
2021 Nov	521,638	ARIMA_auto_log	526,741.71	-5,103.71
2021 Dec	397,592	ARIMA_auto_log	466,963.29	-69,371.29
2022 Jan	341,744	ARIMA_auto_log	367,039.30	-25,295.30
2022 Feb	391,699	ARIMA_auto_log	351,849.78	39,849.22
2022 Mar	569,482	ARIMA_auto_log	435,097.74	134,384.26
2022 Apr	727,326	ARIMA_auto_log	629,488.93	97,837.07
2022 May	779,426	ARIMA_auto_log	721,296.91	58,129.09
2022 Jun	833,955	ARIMA_auto_log	769,892.48	64,062.52
2010 Jan	319,379	ARIMA_d0D1	336,040.22	-16,661.22
2010 Feb	329,697	ARIMA_d0D1	366,012.50	-36,315.50
2010 Mar	388,978	ARIMA_d0D1	452,188.25	-63,210.25
2010 Apr	427,950	ARIMA_d0D1	456,904.24	-28,954.24
2010 May	431,385	ARIMA_d0D1	425,569.42	5,815.58
2010 Jun	432,522	ARIMA_d0D1	427,946.26	4,575.74
2010 Jul	492,382	ARIMA_d0D1	486,568.44	5,813.56
2010 Aug	624,383	ARIMA_d0D1	600,229.76	24,153.24
2010 Sep	496,609	ARIMA_d0D1	519,014.33	-22,405.33
2010 Oct	450,841	ARIMA_d0D1	447,892.67	2,948.33
2010 Nov	327,330	ARIMA_d0D1	363,907.69	-36,577.69
2010 Dec	272,069	ARIMA_d0D1	290,667.38	-18,598.38
2011 Jan	286,010	ARIMA_d0D1	296,405.14	-10,395.14
2011 Feb	319,015	ARIMA_d0D1	324,427.44	-5,412.44
2011 Mar	448,224	ARIMA_d0D1	416,727.10	31,496.90
2011 Apr	517,979	ARIMA_d0D1	484,737.73	33,241.27
2011 May	575,401	ARIMA_d0D1	503,435.36	71,965.64
2011 Jun	519,950	ARIMA_d0D1	549,249.87	-29,299.87
2011 Jul	589,288	ARIMA_d0D1	560,223.30	29,064.70
2011 Aug	678,877	ARIMA_d0D1	691,409.73	-12,532.73
2011 Sep	577,108	ARIMA_d0D1	553,587.72	23,520.28
2011 Oct	471,268	ARIMA_d0D1	514,162.47	-42,894.47
2011 Nov	319,900	ARIMA_d0D1	361,991.72	-42,091.72
2011 Dec	262,266	ARIMA_d0D1	275,103.80	-12,837.80
2012 Jan	289,312	ARIMA_d0D1	281,552.90	7,759.10
2012 Feb	329,299	ARIMA_d0D1	322,495.03	6,803.97
2012 Mar	399,988	ARIMA_d0D1	437,334.59	-37,346.59
2012 Apr	508,131	ARIMA_d0D1	464,892.35	43,238.65
2012 May	521,638	ARIMA_d0D1	522,261.38	-623.38
2012 Jun	509,865	ARIMA_d0D1	498,484.20	11,380.80
2012 Jul	602,837	ARIMA_d0D1	564,501.31	38,335.69
2012 Aug	681,135	ARIMA_d0D1	697,345.21	-16,210.21
2012 Sep	562,007	ARIMA_d0D1	570,937.98	-8,930.98
2012 Oct	468,951	ARIMA_d0D1	478,620.48	-9,669.48
2012 Nov	350,902	ARIMA_d0D1	339,138.35	11,763.65
2012 Dec	283,620	ARIMA_d0D1	293,434.62	-9,814.62
2013 Jan	322,235	ARIMA_d0D1	304,438.41	17,796.59
2013 Feb	365,343	ARIMA_d0D1	350,771.85	14,571.15
2013 Mar	462,258	ARIMA_d0D1	452,313.87	9,944.13
2013 Apr	516,930	ARIMA_d0D1	535,354.93	-18,424.93
2013 May	608,081	ARIMA_d0D1	530,965.46	77,115.54
2013 Jun	578,633	ARIMA_d0D1	571,328.06	7,304.94
2013 Jul	677,083	ARIMA_d0D1	640,532.30	36,550.70
2013 Aug	775,941	ARIMA_d0D1	752,023.47	23,917.53
2013 Sep	639,271	ARIMA_d0D1	645,900.97	-6,629.97
2013 Oct	535,649	ARIMA_d0D1	540,806.03	-5,157.03
2013 Nov	390,742	ARIMA_d0D1	400,876.53	-10,134.53
2013 Dec	342,783	ARIMA_d0D1	322,633.84	20,149.16
2014 Jan	374,568	ARIMA_d0D1	362,829.06	11,738.94
2014 Feb	401,859	ARIMA_d0D1	404,459.35	-2,600.35
2014 Mar	503,533	ARIMA_d0D1	487,306.23	16,226.77
2014 Apr	557,275	ARIMA_d0D1	563,553.45	-6,278.45
2014 May	610,148	ARIMA_d0D1	606,721.15	3,426.85
2014 Jun	595,332	ARIMA_d0D1	578,925.36	16,406.64
2014 Jul	687,207	ARIMA_d0D1	676,524.67	10,682.33
2014 Aug	787,020	ARIMA_d0D1	774,625.64	12,394.36
2014 Sep	652,671	ARIMA_d0D1	652,909.37	-238.37
2014 Oct	554,671	ARIMA_d0D1	550,381.89	4,289.11
2014 Nov	415,750	ARIMA_d0D1	413,041.13	2,708.87
2014 Dec	366,832	ARIMA_d0D1	355,360.04	11,471.96
2015 Jan	399,040	ARIMA_d0D1	390,987.42	8,052.58
2015 Feb	442,963	ARIMA_d0D1	425,428.56	17,534.44
2015 Mar	545,523	ARIMA_d0D1	532,754.33	12,768.67
2015 Apr	586,230	ARIMA_d0D1	599,555.95	-13,325.95
2015 May	628,998	ARIMA_d0D1	636,389.47	-7,391.47
2015 Jun	654,715	ARIMA_d0D1	604,920.00	49,795.00
2015 Jul	766,557	ARIMA_d0D1	736,869.90	29,687.10
2015 Aug	829,230	ARIMA_d0D1	853,818.97	-24,588.97
2015 Sep	696,849	ARIMA_d0D1	690,471.17	6,377.83
2015 Oct	597,629	ARIMA_d0D1	591,639.08	5,989.92
2015 Nov	475,257	ARIMA_d0D1	454,854.16	20,402.84
2015 Dec	407,035	ARIMA_d0D1	415,319.30	-8,284.30
2016 Jan	448,784	ARIMA_d0D1	432,231.03	16,552.97
2016 Feb	506,179	ARIMA_d0D1	480,991.72	25,187.28
2016 Mar	611,987	ARIMA_d0D1	599,690.21	12,296.79
2016 Apr	663,878	ARIMA_d0D1	652,490.56	11,387.44
2016 May	726,980	ARIMA_d0D1	704,733.46	22,246.54
2016 Jun	759,256	ARIMA_d0D1	719,846.76	39,409.24
2016 Jul	849,148	ARIMA_d0D1	852,642.30	-3,494.30
2016 Aug	891,091	ARIMA_d0D1	924,743.43	-33,652.43
2016 Sep	768,042	ARIMA_d0D1	752,815.22	15,226.78
2016 Oct	702,530	ARIMA_d0D1	662,091.26	40,438.74
2016 Nov	545,468	ARIMA_d0D1	562,985.89	-17,517.89
2016 Dec	457,565	ARIMA_d0D1	480,861.47	-23,296.47
2017 Jan	503,654	ARIMA_d0D1	489,305.94	14,348.06
2017 Feb	541,368	ARIMA_d0D1	546,204.14	-4,836.14
2017 Mar	647,679	ARIMA_d0D1	640,485.55	7,193.45
2017 Apr	710,409	ARIMA_d0D1	691,661.43	18,747.57
2017 May	745,096	ARIMA_d0D1	760,242.39	-15,146.39
2017 Jun	794,118	ARIMA_d0D1	762,090.90	32,027.10
2017 Jul	864,476	ARIMA_d0D1	884,949.68	-20,473.68
2017 Aug	939,077	ARIMA_d0D1	915,501.88	23,575.12
2017 Sep	818,705	ARIMA_d0D1	805,998.53	12,706.47
2017 Oct	734,287	ARIMA_d0D1	733,949.45	337.55
2017 Nov	582,743	ARIMA_d0D1	586,363.74	-3,620.74
2017 Dec	478,377	ARIMA_d0D1	497,599.02	-19,222.02
2018 Jan	534,281	ARIMA_d0D1	522,521.66	11,759.34
2018 Feb	555,841	ARIMA_d0D1	574,906.46	-19,065.46
2018 Mar	652,082	ARIMA_d0D1	665,149.64	-13,067.64
2018 Apr	689,214	ARIMA_d0D1	709,200.91	-19,986.91
2018 May	755,491	ARIMA_d0D1	735,609.88	19,881.12
2018 Jun	782,628	ARIMA_d0D1	787,076.31	-4,448.31
2018 Jul	837,740	ARIMA_d0D1	863,761.97	-26,021.97
2018 Aug	936,644	ARIMA_d0D1	903,399.52	33,244.48
2018 Sep	806,267	ARIMA_d0D1	808,143.36	-1,876.36
2018 Oct	721,989	ARIMA_d0D1	730,325.37	-8,336.37
2018 Nov	575,096	ARIMA_d0D1	569,395.90	5,700.10
2018 Dec	496,993	ARIMA_d0D1	475,614.90	21,378.10
2019 Jan	486,306	ARIMA_d0D1	547,572.51	-61,266.51
2019 Feb	498,081	ARIMA_d0D1	526,453.16	-28,372.16
2019 Mar	606,616	ARIMA_d0D1	600,568.35	6,047.65
2019 Apr	608,322	ARIMA_d0D1	662,638.14	-54,316.14
2019 May	665,724	ARIMA_d0D1	678,589.15	-12,865.15
2019 Jun	714,041	ARIMA_d0D1	700,619.38	13,421.62
2019 Jul	747,112	ARIMA_d0D1	796,725.45	-49,613.45
2019 Aug	828,426	ARIMA_d0D1	842,675.29	-14,249.29
2019 Sep	719,254	ARIMA_d0D1	706,231.48	13,022.52
2019 Oct	629,555	ARIMA_d0D1	636,464.67	-6,909.67
2019 Nov	508,290	ARIMA_d0D1	486,723.86	21,566.14
2019 Dec	445,470	ARIMA_d0D1	422,388.01	23,081.99
2020 Jan	488,461	ARIMA_d0D1	461,204.70	27,256.30
2020 Feb	540,254	ARIMA_d0D1	506,218.35	34,035.65
2020 Mar	297,649	ARIMA_d0D1	652,630.48	-354,981.48
2020 Apr	2,191	ARIMA_d0D1	489,378.47	-487,187.47
2020 May	2,955	ARIMA_d0D1	7,614.52	-4,659.52
2020 Jun	14,932	ARIMA_d0D1	69,249.33	-54,317.33
2020 Jul	95,576	ARIMA_d0D1	703,828.69	-608,252.69
2020 Aug	240,322	ARIMA_d0D1	217,964.58	22,357.42
2020 Sep	251,221	ARIMA_d0D1	157,338.62	93,882.38
2020 Oct	253,895	ARIMA_d0D1	246,460.30	7,434.70
2020 Nov	116,634	ARIMA_d0D1	193,498.27	-76,864.27
2020 Dec	137,446	ARIMA_d0D1	50,614.39	86,831.61
2021 Jan	93,013	ARIMA_d0D1	239,447.15	-146,434.15
2021 Feb	40,883	ARIMA_d0D1	94,886.13	-54,003.13
2021 Mar	60,163	ARIMA_d0D1	-66,467.46	126,630.46
2021 Apr	95,116	ARIMA_d0D1	-13,603.02	108,719.02
2021 May	179,599	ARIMA_d0D1	196,348.40	-16,749.40
2021 Jun	321,985	ARIMA_d0D1	214,923.58	107,061.42
2021 Jul	552,399	ARIMA_d0D1	457,960.91	94,438.09
2021 Aug	780,123	ARIMA_d0D1	705,964.17	74,158.83
2021 Sep	697,572	ARIMA_d0D1	738,029.97	-40,457.97
2021 Oct	655,682	ARIMA_d0D1	608,794.95	46,887.05
2021 Nov	521,638	ARIMA_d0D1	533,915.33	-12,277.33
2021 Dec	397,592	ARIMA_d0D1	462,197.19	-64,605.19
2022 Jan	341,744	ARIMA_d0D1	361,702.72	-19,958.72
2022 Feb	391,699	ARIMA_d0D1	334,913.22	56,785.78
2022 Mar	569,482	ARIMA_d0D1	415,038.44	154,443.56
2022 Apr	727,326	ARIMA_d0D1	632,772.64	94,553.36
2022 May	779,426	ARIMA_d0D1	825,119.48	-45,693.48
2022 Jun	833,955	ARIMA_d0D1	805,990.27	27,964.73
2010 Jan	319,379	ARIMA_d0D1_log	328,145.67	-8,766.67
2010 Feb	329,697	ARIMA_d0D1_log	360,029.72	-30,332.72
2010 Mar	388,978	ARIMA_d0D1_log	437,198.34	-48,220.34
2010 Apr	427,950	ARIMA_d0D1_log	447,811.11	-19,861.11
2010 May	431,385	ARIMA_d0D1_log	426,494.52	4,890.48
2010 Jun	432,522	ARIMA_d0D1_log	420,364.16	12,157.84
2010 Jul	492,382	ARIMA_d0D1_log	470,019.79	22,362.21
2010 Aug	624,383	ARIMA_d0D1_log	583,158.66	41,224.34
2010 Sep	496,609	ARIMA_d0D1_log	522,432.79	-25,823.79
2010 Oct	450,841	ARIMA_d0D1_log	450,474.18	366.82
2010 Nov	327,330	ARIMA_d0D1_log	367,463.07	-40,133.07
2010 Dec	272,069	ARIMA_d0D1_log	298,249.33	-26,180.33
2011 Jan	286,010	ARIMA_d0D1_log	292,026.54	-6,016.54
2011 Feb	319,015	ARIMA_d0D1_log	317,381.70	1,633.30
2011 Mar	448,224	ARIMA_d0D1_log	402,267.09	45,956.91
2011 Apr	517,979	ARIMA_d0D1_log	490,729.93	27,249.07
2011 May	575,401	ARIMA_d0D1_log	504,793.33	70,607.67
2011 Jun	519,950	ARIMA_d0D1_log	548,038.67	-28,088.67
2011 Jul	589,288	ARIMA_d0D1_log	564,949.99	24,338.01
2011 Aug	678,877	ARIMA_d0D1_log	705,040.44	-26,163.44
2011 Sep	577,108	ARIMA_d0D1_log	546,484.52	30,623.48
2011 Oct	471,268	ARIMA_d0D1_log	509,032.96	-37,764.96
2011 Nov	319,900	ARIMA_d0D1_log	358,992.42	-39,092.42
2011 Dec	262,266	ARIMA_d0D1_log	277,417.15	-15,151.15
2012 Jan	289,312	ARIMA_d0D1_log	279,322.81	9,989.19
2012 Feb	329,299	ARIMA_d0D1_log	320,049.68	9,249.32
2012 Mar	399,988	ARIMA_d0D1_log	435,740.21	-35,752.21
2012 Apr	508,131	ARIMA_d0D1_log	458,935.17	49,195.83
2012 May	521,638	ARIMA_d0D1_log	532,267.05	-10,629.05
2012 Jun	509,865	ARIMA_d0D1_log	492,675.86	17,189.14
2012 Jul	602,837	ARIMA_d0D1_log	568,215.12	34,621.88
2012 Aug	681,135	ARIMA_d0D1_log	705,394.29	-24,259.29
2012 Sep	562,007	ARIMA_d0D1_log	563,227.84	-1,220.84
2012 Oct	468,951	ARIMA_d0D1_log	478,969.32	-10,018.32
2012 Nov	350,902	ARIMA_d0D1_log	336,295.24	14,606.76
2012 Dec	283,620	ARIMA_d0D1_log	291,755.16	-8,135.16
2013 Jan	322,235	ARIMA_d0D1_log	304,811.26	17,423.74
2013 Feb	365,343	ARIMA_d0D1_log	352,820.63	12,522.37
2013 Mar	462,258	ARIMA_d0D1_log	457,609.54	4,648.46
2013 Apr	516,930	ARIMA_d0D1_log	544,535.01	-27,605.01
2013 May	608,081	ARIMA_d0D1_log	531,309.73	76,771.27
2013 Jun	578,633	ARIMA_d0D1_log	569,064.71	9,568.29
2013 Jul	677,083	ARIMA_d0D1_log	650,861.21	26,221.79
2013 Aug	775,941	ARIMA_d0D1_log	764,008.08	11,932.92
2013 Sep	639,271	ARIMA_d0D1_log	628,154.53	11,116.47
2013 Oct	535,649	ARIMA_d0D1_log	528,166.71	7,482.29
2013 Nov	390,742	ARIMA_d0D1_log	384,344.65	6,397.35
2013 Dec	342,783	ARIMA_d0D1_log	314,854.74	27,928.26
2014 Jan	374,568	ARIMA_d0D1_log	368,291.84	6,276.16
2014 Feb	401,859	ARIMA_d0D1_log	411,623.72	-9,764.72
2014 Mar	503,533	ARIMA_d0D1_log	498,924.86	4,608.14
2014 Apr	557,275	ARIMA_d0D1_log	572,788.80	-15,513.80
2014 May	610,148	ARIMA_d0D1_log	610,579.78	-431.78
2014 Jun	595,332	ARIMA_d0D1_log	578,290.13	17,041.87
2014 Jul	687,207	ARIMA_d0D1_log	683,942.92	3,264.08
2014 Aug	787,020	ARIMA_d0D1_log	782,824.46	4,195.54
2014 Sep	652,671	ARIMA_d0D1_log	643,684.42	8,986.58
2014 Oct	554,671	ARIMA_d0D1_log	543,242.88	11,428.12
2014 Nov	415,750	ARIMA_d0D1_log	400,671.17	15,078.83
2014 Dec	366,832	ARIMA_d0D1_log	348,093.44	18,738.56
2015 Jan	399,040	ARIMA_d0D1_log	396,001.72	3,038.28
2015 Feb	442,963	ARIMA_d0D1_log	431,073.21	11,889.79
2015 Mar	545,523	ARIMA_d0D1_log	548,309.84	-2,786.84
2015 Apr	586,230	ARIMA_d0D1_log	609,152.85	-22,922.85
2015 May	628,998	ARIMA_d0D1_log	640,073.84	-11,075.84
2015 Jun	654,715	ARIMA_d0D1_log	603,969.36	50,745.64
2015 Jul	766,557	ARIMA_d0D1_log	747,812.00	18,745.00
2015 Aug	829,230	ARIMA_d0D1_log	866,921.25	-37,691.25
2015 Sep	696,849	ARIMA_d0D1_log	680,292.06	16,556.94
2015 Oct	597,629	ARIMA_d0D1_log	583,023.92	14,605.08
2015 Nov	475,257	ARIMA_d0D1_log	437,371.03	37,885.97
2015 Dec	407,035	ARIMA_d0D1_log	404,875.53	2,159.47
2016 Jan	448,784	ARIMA_d0D1_log	437,751.18	11,032.82
2016 Feb	506,179	ARIMA_d0D1_log	487,495.82	18,683.18
2016 Mar	611,987	ARIMA_d0D1_log	619,065.03	-7,078.03
2016 Apr	663,878	ARIMA_d0D1_log	663,567.18	310.82
2016 May	726,980	ARIMA_d0D1_log	711,981.56	14,998.44
2016 Jun	759,256	ARIMA_d0D1_log	718,842.21	40,413.79
2016 Jul	849,148	ARIMA_d0D1_log	871,110.77	-21,962.77
2016 Aug	891,091	ARIMA_d0D1_log	933,848.81	-42,757.81
2016 Sep	768,042	ARIMA_d0D1_log	737,218.44	30,823.56
2016 Oct	702,530	ARIMA_d0D1_log	647,180.53	55,349.47
2016 Nov	545,468	ARIMA_d0D1_log	532,644.82	12,823.18
2016 Dec	457,565	ARIMA_d0D1_log	463,065.87	-5,500.87
2017 Jan	503,654	ARIMA_d0D1_log	495,968.80	7,685.20
2017 Feb	541,368	ARIMA_d0D1_log	555,554.88	-14,186.88
2017 Mar	647,679	ARIMA_d0D1_log	655,627.85	-7,948.85
2017 Apr	710,409	ARIMA_d0D1_log	699,384.67	11,024.33
2017 May	745,096	ARIMA_d0D1_log	768,362.81	-23,266.81
2017 Jun	794,118	ARIMA_d0D1_log	761,713.68	32,404.32
2017 Jul	864,476	ARIMA_d0D1_log	895,819.53	-31,343.53
2017 Aug	939,077	ARIMA_d0D1_log	922,384.47	16,692.53
2017 Sep	818,705	ARIMA_d0D1_log	794,001.50	24,703.50
2017 Oct	734,287	ARIMA_d0D1_log	721,993.86	12,293.14
2017 Nov	582,743	ARIMA_d0D1_log	563,780.41	18,962.59
2017 Dec	478,377	ARIMA_d0D1_log	490,344.26	-11,967.26
2018 Jan	534,281	ARIMA_d0D1_log	522,673.66	11,607.34
2018 Feb	555,841	ARIMA_d0D1_log	580,059.55	-24,218.55
2018 Mar	652,082	ARIMA_d0D1_log	668,246.49	-16,164.49
2018 Apr	689,214	ARIMA_d0D1_log	711,102.14	-21,888.14
2018 May	755,491	ARIMA_d0D1_log	734,678.52	20,812.48
2018 Jun	782,628	ARIMA_d0D1_log	790,947.86	-8,319.86
2018 Jul	837,740	ARIMA_d0D1_log	866,749.79	-29,009.79
2018 Aug	936,644	ARIMA_d0D1_log	900,929.21	35,714.79
2018 Sep	806,267	ARIMA_d0D1_log	812,640.93	-6,373.93
2018 Oct	721,989	ARIMA_d0D1_log	728,786.95	-6,797.95
2018 Nov	575,096	ARIMA_d0D1_log	568,707.78	6,388.22
2018 Dec	496,993	ARIMA_d0D1_log	476,044.72	20,948.28
2019 Jan	486,306	ARIMA_d0D1_log	551,046.34	-64,740.34
2019 Feb	498,081	ARIMA_d0D1_log	526,750.98	-28,669.98
2019 Mar	606,616	ARIMA_d0D1_log	595,505.69	11,110.31
2019 Apr	608,322	ARIMA_d0D1_log	665,080.22	-56,758.22
2019 May	665,724	ARIMA_d0D1_log	679,445.31	-13,721.31
2019 Jun	714,041	ARIMA_d0D1_log	712,609.03	1,431.97
2019 Jul	747,112	ARIMA_d0D1_log	800,125.16	-53,013.16
2019 Aug	828,426	ARIMA_d0D1_log	847,558.57	-19,132.57
2019 Sep	719,254	ARIMA_d0D1_log	732,696.38	-13,442.38
2019 Oct	629,555	ARIMA_d0D1_log	658,817.38	-29,262.38
2019 Nov	508,290	ARIMA_d0D1_log	507,161.27	1,128.73
2019 Dec	445,470	ARIMA_d0D1_log	434,154.66	11,315.34
2020 Jan	488,461	ARIMA_d0D1_log	466,151.18	22,309.82
2020 Feb	540,254	ARIMA_d0D1_log	506,272.87	33,981.13
2020 Mar	297,649	ARIMA_d0D1_log	642,222.30	-344,573.30
2020 Apr	2,191	ARIMA_d0D1_log	508,103.18	-505,912.18
2020 May	2,955	ARIMA_d0D1_log	242.19	2,712.81
2020 Jun	14,932	ARIMA_d0D1_log	115,668.85	-100,736.85
2020 Jul	95,576	ARIMA_d0D1_log	45,548.14	50,027.86
2020 Aug	240,322	ARIMA_d0D1_log	285,696.63	-45,374.63
2020 Sep	251,221	ARIMA_d0D1_log	391,982.95	-140,761.95
2020 Oct	253,895	ARIMA_d0D1_log	317,684.34	-63,789.34
2020 Nov	116,634	ARIMA_d0D1_log	295,390.43	-178,756.43
2020 Dec	137,446	ARIMA_d0D1_log	130,480.82	6,965.18
2021 Jan	93,013	ARIMA_d0D1_log	252,409.07	-159,396.07
2021 Feb	40,883	ARIMA_d0D1_log	147,123.38	-106,240.38
2021 Mar	60,163	ARIMA_d0D1_log	33,128.88	27,034.12
2021 Apr	95,116	ARIMA_d0D1_log	1,022.96	94,093.04
2021 May	179,599	ARIMA_d0D1_log	205,251.48	-25,652.48
2021 Jun	321,985	ARIMA_d0D1_log	317,234.32	4,750.68
2021 Jul	552,399	ARIMA_d0D1_log	588,119.72	-35,720.72
2021 Aug	780,123	ARIMA_d0D1_log	821,389.72	-41,266.72
2021 Sep	697,572	ARIMA_d0D1_log	797,469.49	-99,897.49
2021 Oct	655,682	ARIMA_d0D1_log	700,092.99	-44,410.99
2021 Nov	521,638	ARIMA_d0D1_log	537,037.96	-15,399.96
2021 Dec	397,592	ARIMA_d0D1_log	526,848.38	-129,256.38
2022 Jan	341,744	ARIMA_d0D1_log	415,630.49	-73,886.49
2022 Feb	391,699	ARIMA_d0D1_log	360,470.87	31,228.13
2022 Mar	569,482	ARIMA_d0D1_log	398,677.39	170,804.61
2022 Apr	727,326	ARIMA_d0D1_log	87,051.74	640,274.26
2022 May	779,426	ARIMA_d0D1_log	970,844.69	-191,418.69
2022 Jun	833,955	ARIMA_d0D1_log	882,372.92	-48,417.92
2010 Jan	319,379	ARIMA_d1D1	324,272.23	-4,893.23
2010 Feb	329,697	ARIMA_d1D1	360,058.50	-30,361.50
2010 Mar	388,978	ARIMA_d1D1	446,178.64	-57,200.64
2010 Apr	427,950	ARIMA_d1D1	453,649.89	-25,699.89
2010 May	431,385	ARIMA_d1D1	426,965.63	4,419.37
2010 Jun	432,522	ARIMA_d1D1	418,265.75	14,256.25
2010 Jul	492,382	ARIMA_d1D1	470,234.36	22,147.64
2010 Aug	624,383	ARIMA_d1D1	584,285.92	40,097.08
2010 Sep	496,609	ARIMA_d1D1	502,306.78	-5,697.78
2010 Oct	450,841	ARIMA_d1D1	431,403.34	19,437.66
2010 Nov	327,330	ARIMA_d1D1	348,662.55	-21,332.55
2010 Dec	272,069	ARIMA_d1D1	280,069.98	-8,000.98
2011 Jan	286,010	ARIMA_d1D1	285,496.71	513.29
2011 Feb	319,015	ARIMA_d1D1	312,917.75	6,097.25
2011 Mar	448,224	ARIMA_d1D1	407,026.81	41,197.19
2011 Apr	517,979	ARIMA_d1D1	469,083.01	48,895.99
2011 May	575,401	ARIMA_d1D1	495,284.50	80,116.50
2011 Jun	519,950	ARIMA_d1D1	565,091.18	-45,141.18
2011 Jul	589,288	ARIMA_d1D1	568,734.05	20,553.95
2011 Aug	678,877	ARIMA_d1D1	702,536.45	-23,659.45
2011 Sep	577,108	ARIMA_d1D1	561,332.57	15,775.43
2011 Oct	471,268	ARIMA_d1D1	522,131.36	-50,863.36
2011 Nov	319,900	ARIMA_d1D1	369,587.71	-49,687.71
2011 Dec	262,266	ARIMA_d1D1	268,591.23	-6,325.23
2012 Jan	289,312	ARIMA_d1D1	274,119.67	15,192.33
2012 Feb	329,299	ARIMA_d1D1	317,697.19	11,601.81
2012 Mar	399,988	ARIMA_d1D1	434,333.73	-34,345.73
2012 Apr	508,131	ARIMA_d1D1	454,063.20	54,067.80
2012 May	521,638	ARIMA_d1D1	527,940.39	-6,302.39
2012 Jun	509,865	ARIMA_d1D1	491,159.84	18,705.16
2012 Jul	602,837	ARIMA_d1D1	567,424.68	35,412.32
2012 Aug	681,135	ARIMA_d1D1	705,641.25	-24,506.25
2012 Sep	562,007	ARIMA_d1D1	570,527.26	-8,520.26
2012 Oct	468,951	ARIMA_d1D1	485,749.53	-16,798.53
2012 Nov	350,902	ARIMA_d1D1	341,002.19	9,899.81
2012 Dec	283,620	ARIMA_d1D1	296,883.73	-13,263.73
2013 Jan	322,235	ARIMA_d1D1	302,124.61	20,110.39
2013 Feb	365,343	ARIMA_d1D1	355,757.77	9,585.23
2013 Mar	462,258	ARIMA_d1D1	454,790.44	7,467.56
2013 Apr	516,930	ARIMA_d1D1	540,963.29	-24,033.29
2013 May	608,081	ARIMA_d1D1	532,956.26	75,124.74
2013 Jun	578,633	ARIMA_d1D1	581,049.61	-2,416.61
2013 Jul	677,083	ARIMA_d1D1	649,219.37	27,863.63
2013 Aug	775,941	ARIMA_d1D1	763,145.39	12,795.61
2013 Sep	639,271	ARIMA_d1D1	658,131.21	-18,860.21
2013 Oct	535,649	ARIMA_d1D1	555,612.94	-19,963.94
2013 Nov	390,742	ARIMA_d1D1	413,047.05	-22,305.05
2013 Dec	342,783	ARIMA_d1D1	330,060.29	12,722.71
2014 Jan	374,568	ARIMA_d1D1	371,686.88	2,881.12
2014 Feb	401,859	ARIMA_d1D1	413,295.30	-11,436.30
2014 Mar	503,533	ARIMA_d1D1	513,038.06	-9,505.06
2014 Apr	557,275	ARIMA_d1D1	584,539.58	-27,264.58
2014 May	610,148	ARIMA_d1D1	612,324.16	-2,176.16
2014 Jun	595,332	ARIMA_d1D1	584,453.93	10,878.07
2014 Jul	687,207	ARIMA_d1D1	682,633.94	4,573.06
2014 Aug	787,020	ARIMA_d1D1	781,716.49	5,303.51
2014 Sep	652,671	ARIMA_d1D1	661,145.05	-8,474.05
2014 Oct	554,671	ARIMA_d1D1	557,843.10	-3,172.10
2014 Nov	415,750	ARIMA_d1D1	419,910.31	-4,160.31
2014 Dec	366,832	ARIMA_d1D1	361,288.11	5,543.89
2015 Jan	399,040	ARIMA_d1D1	397,120.70	1,919.30
2015 Feb	442,963	ARIMA_d1D1	432,026.20	10,936.80
2015 Mar	545,523	ARIMA_d1D1	538,501.35	7,021.65
2015 Apr	586,230	ARIMA_d1D1	605,250.54	-19,020.54
2015 May	628,998	ARIMA_d1D1	657,256.61	-28,258.61
2015 Jun	654,715	ARIMA_d1D1	611,519.14	43,195.86
2015 Jul	766,557	ARIMA_d1D1	737,498.89	29,058.11
2015 Aug	829,230	ARIMA_d1D1	860,617.29	-31,387.29
2015 Sep	696,849	ARIMA_d1D1	703,976.75	-7,127.75
2015 Oct	597,629	ARIMA_d1D1	599,447.46	-1,818.46
2015 Nov	475,257	ARIMA_d1D1	460,110.46	15,146.54
2015 Dec	407,035	ARIMA_d1D1	421,408.92	-14,373.92
2016 Jan	448,784	ARIMA_d1D1	441,754.67	7,029.33
2016 Feb	506,179	ARIMA_d1D1	485,942.87	20,236.13
2016 Mar	611,987	ARIMA_d1D1	603,392.53	8,594.47
2016 Apr	663,878	ARIMA_d1D1	658,540.05	5,337.95
2016 May	726,980	ARIMA_d1D1	717,595.83	9,384.17
2016 Jun	759,256	ARIMA_d1D1	727,130.25	32,125.75
2016 Jul	849,148	ARIMA_d1D1	857,828.31	-8,680.31
2016 Aug	891,091	ARIMA_d1D1	932,725.64	-41,634.64
2016 Sep	768,042	ARIMA_d1D1	759,641.38	8,400.62
2016 Oct	702,530	ARIMA_d1D1	669,972.48	32,557.52
2016 Nov	545,468	ARIMA_d1D1	573,002.39	-27,534.39
2016 Dec	457,565	ARIMA_d1D1	490,227.87	-32,662.87
2017 Jan	503,654	ARIMA_d1D1	494,434.28	9,219.72
2017 Feb	541,368	ARIMA_d1D1	554,088.59	-12,720.59
2017 Mar	647,679	ARIMA_d1D1	646,511.35	1,167.65
2017 Apr	710,409	ARIMA_d1D1	698,502.29	11,906.71
2017 May	745,096	ARIMA_d1D1	766,696.47	-21,600.47
2017 Jun	794,118	ARIMA_d1D1	763,661.61	30,456.39
2017 Jul	864,476	ARIMA_d1D1	889,532.03	-25,056.03
2017 Aug	939,077	ARIMA_d1D1	925,069.17	14,007.83
2017 Sep	818,705	ARIMA_d1D1	809,397.53	9,307.47
2017 Oct	734,287	ARIMA_d1D1	737,892.55	-3,605.55
2017 Nov	582,743	ARIMA_d1D1	590,352.22	-7,609.22
2017 Dec	478,377	ARIMA_d1D1	508,146.32	-29,769.32
2018 Jan	534,281	ARIMA_d1D1	525,642.81	8,638.19
2018 Feb	555,841	ARIMA_d1D1	577,340.77	-21,499.77
2018 Mar	652,082	ARIMA_d1D1	667,046.69	-14,964.69
2018 Apr	689,214	ARIMA_d1D1	711,055.27	-21,841.27
2018 May	755,491	ARIMA_d1D1	737,006.92	18,484.08
2018 Jun	782,628	ARIMA_d1D1	788,093.39	-5,465.39
2018 Jul	837,740	ARIMA_d1D1	865,585.56	-27,845.56
2018 Aug	936,644	ARIMA_d1D1	902,600.82	34,043.18
2018 Sep	806,267	ARIMA_d1D1	808,060.07	-1,793.07
2018 Oct	721,989	ARIMA_d1D1	731,307.06	-9,318.06
2018 Nov	575,096	ARIMA_d1D1	569,626.57	5,469.43
2018 Dec	496,993	ARIMA_d1D1	476,078.34	20,914.66
2019 Jan	486,306	ARIMA_d1D1	544,430.31	-58,124.31
2019 Feb	498,081	ARIMA_d1D1	528,895.95	-30,814.95
2019 Mar	606,616	ARIMA_d1D1	601,142.62	5,473.38
2019 Apr	608,322	ARIMA_d1D1	651,076.12	-42,754.12
2019 May	665,724	ARIMA_d1D1	672,349.13	-6,625.13
2019 Jun	714,041	ARIMA_d1D1	696,690.66	17,350.34
2019 Jul	747,112	ARIMA_d1D1	778,849.34	-31,737.34
2019 Aug	828,426	ARIMA_d1D1	838,447.13	-10,021.13
2019 Sep	719,254	ARIMA_d1D1	701,824.92	17,429.08
2019 Oct	629,555	ARIMA_d1D1	632,412.82	-2,857.82
2019 Nov	508,290	ARIMA_d1D1	483,223.40	25,066.60
2019 Dec	445,470	ARIMA_d1D1	419,329.92	26,140.08
2020 Jan	488,461	ARIMA_d1D1	459,915.54	28,545.46
2020 Feb	540,254	ARIMA_d1D1	505,640.06	34,613.94
2020 Mar	297,649	ARIMA_d1D1	636,407.37	-338,758.37
2020 Apr	2,191	ARIMA_d1D1	484,608.72	-482,417.72
2020 May	2,955	ARIMA_d1D1	-93,905.41	96,860.41
2020 Jun	14,932	ARIMA_d1D1	50,377.98	-35,445.98
2020 Jul	95,576	ARIMA_d1D1	44,330.62	51,245.38
2020 Aug	240,322	ARIMA_d1D1	202,473.20	37,848.80
2020 Sep	251,221	ARIMA_d1D1	141,490.24	109,730.76
2020 Oct	253,895	ARIMA_d1D1	216,979.56	36,915.44
2020 Nov	116,634	ARIMA_d1D1	139,282.13	-22,648.13
2020 Dec	137,446	ARIMA_d1D1	33,635.89	103,810.11
2021 Jan	93,013	ARIMA_d1D1	219,864.56	-126,851.56
2021 Feb	40,883	ARIMA_d1D1	79,924.26	-39,041.26
2021 Mar	60,163	ARIMA_d1D1	-89,913.26	150,076.26
2021 Apr	95,116	ARIMA_d1D1	-27,301.20	122,417.20
2021 May	179,599	ARIMA_d1D1	181,569.00	-1,970.00
2021 Jun	321,985	ARIMA_d1D1	204,524.86	117,460.14
2021 Jul	552,399	ARIMA_d1D1	451,309.93	101,089.07
2021 Aug	780,123	ARIMA_d1D1	708,749.82	71,373.18
2021 Sep	697,572	ARIMA_d1D1	746,838.54	-49,266.54
2021 Oct	655,682	ARIMA_d1D1	615,289.40	40,392.60
2021 Nov	521,638	ARIMA_d1D1	541,033.13	-19,395.13
2021 Dec	397,592	ARIMA_d1D1	470,427.70	-72,835.70
2022 Jan	341,744	ARIMA_d1D1	363,677.49	-21,933.49
2022 Feb	391,699	ARIMA_d1D1	334,431.84	57,267.16
2022 Mar	569,482	ARIMA_d1D1	419,246.59	150,235.41
2022 Apr	727,326	ARIMA_d1D1	619,406.29	107,919.71
2022 May	779,426	ARIMA_d1D1	847,577.52	-68,151.52
2022 Jun	833,955	ARIMA_d1D1	793,015.75	40,939.25
2010 Jan	319,379	ARIMA_d1D1_log	323,544.30	-4,165.30
2010 Feb	329,697	ARIMA_d1D1_log	356,896.34	-27,199.34
2010 Mar	388,978	ARIMA_d1D1_log	430,957.47	-41,979.47
2010 Apr	427,950	ARIMA_d1D1_log	442,578.22	-14,628.22
2010 May	431,385	ARIMA_d1D1_log	417,793.35	13,591.65
2010 Jun	432,522	ARIMA_d1D1_log	411,987.15	20,534.85
2010 Jul	492,382	ARIMA_d1D1_log	461,682.38	30,699.62
2010 Aug	624,383	ARIMA_d1D1_log	569,383.49	54,999.51
2010 Sep	496,609	ARIMA_d1D1_log	502,047.98	-5,438.98
2010 Oct	450,841	ARIMA_d1D1_log	434,562.72	16,278.28
2010 Nov	327,330	ARIMA_d1D1_log	354,542.86	-27,212.86
2010 Dec	272,069	ARIMA_d1D1_log	289,667.16	-17,598.16
2011 Jan	286,010	ARIMA_d1D1_log	287,052.52	-1,042.52
2011 Feb	319,015	ARIMA_d1D1_log	310,166.05	8,848.95
2011 Mar	448,224	ARIMA_d1D1_log	393,307.84	54,916.16
2011 Apr	517,979	ARIMA_d1D1_log	476,554.77	41,424.23
2011 May	575,401	ARIMA_d1D1_log	495,202.73	80,198.27
2011 Jun	519,950	ARIMA_d1D1_log	565,548.14	-45,598.14
2011 Jul	589,288	ARIMA_d1D1_log	575,168.08	14,119.92
2011 Aug	678,877	ARIMA_d1D1_log	720,094.23	-41,217.23
2011 Sep	577,108	ARIMA_d1D1_log	553,484.76	23,623.24
2011 Oct	471,268	ARIMA_d1D1_log	519,042.93	-47,774.93
2011 Nov	319,900	ARIMA_d1D1_log	360,607.29	-40,707.29
2011 Dec	262,266	ARIMA_d1D1_log	273,176.59	-10,910.59
2012 Jan	289,312	ARIMA_d1D1_log	277,631.87	11,680.13
2012 Feb	329,299	ARIMA_d1D1_log	316,008.35	13,290.65
2012 Mar	399,988	ARIMA_d1D1_log	432,765.69	-32,777.69
2012 Apr	508,131	ARIMA_d1D1_log	449,903.23	58,227.77
2012 May	521,638	ARIMA_d1D1_log	531,779.34	-10,141.34
2012 Jun	509,865	ARIMA_d1D1_log	492,783.80	17,081.20
2012 Jul	602,837	ARIMA_d1D1_log	571,097.16	31,739.84
2012 Aug	681,135	ARIMA_d1D1_log	716,907.08	-35,772.08
2012 Sep	562,007	ARIMA_d1D1_log	566,782.74	-4,775.74
2012 Oct	468,951	ARIMA_d1D1_log	482,615.26	-13,664.26
2012 Nov	350,902	ARIMA_d1D1_log	337,682.35	13,219.65
2012 Dec	283,620	ARIMA_d1D1_log	294,369.27	-10,749.27
2013 Jan	322,235	ARIMA_d1D1_log	303,666.65	18,568.35
2013 Feb	365,343	ARIMA_d1D1_log	359,299.90	6,043.10
2013 Mar	462,258	ARIMA_d1D1_log	461,800.16	457.84
2013 Apr	516,930	ARIMA_d1D1_log	553,266.02	-36,336.02
2013 May	608,081	ARIMA_d1D1_log	535,554.77	72,526.23
2013 Jun	578,633	ARIMA_d1D1_log	584,397.83	-5,764.83
2013 Jul	677,083	ARIMA_d1D1_log	666,344.60	10,738.40
2013 Aug	775,941	ARIMA_d1D1_log	785,553.58	-9,612.58
2013 Sep	639,271	ARIMA_d1D1_log	643,595.82	-4,324.82
2013 Oct	535,649	ARIMA_d1D1_log	541,051.47	-5,402.47
2013 Nov	390,742	ARIMA_d1D1_log	392,888.56	-2,146.56
2013 Dec	342,783	ARIMA_d1D1_log	321,611.51	21,171.49
2014 Jan	374,568	ARIMA_d1D1_log	378,829.12	-4,261.12
2014 Feb	401,859	ARIMA_d1D1_log	421,991.47	-20,132.47
2014 Mar	503,533	ARIMA_d1D1_log	508,583.99	-5,050.99
2014 Apr	557,275	ARIMA_d1D1_log	583,023.26	-25,748.26
2014 May	610,148	ARIMA_d1D1_log	616,956.39	-6,808.39
2014 Jun	595,332	ARIMA_d1D1_log	583,941.98	11,390.02
2014 Jul	687,207	ARIMA_d1D1_log	691,910.40	-4,703.40
2014 Aug	787,020	ARIMA_d1D1_log	792,511.24	-5,491.24
2014 Sep	652,671	ARIMA_d1D1_log	650,923.29	1,747.71
2014 Oct	554,671	ARIMA_d1D1_log	550,037.32	4,633.68
2014 Nov	415,750	ARIMA_d1D1_log	406,031.87	9,718.13
2014 Dec	366,832	ARIMA_d1D1_log	353,425.86	13,406.14
2015 Jan	399,040	ARIMA_d1D1_log	403,119.57	-4,079.57
2015 Feb	442,963	ARIMA_d1D1_log	438,945.93	4,017.07
2015 Mar	545,523	ARIMA_d1D1_log	558,393.89	-12,870.89
2015 Apr	586,230	ARIMA_d1D1_log	618,157.57	-31,927.57
2015 May	628,998	ARIMA_d1D1_log	645,718.94	-16,720.94
2015 Jun	654,715	ARIMA_d1D1_log	608,186.92	46,528.08
2015 Jul	766,557	ARIMA_d1D1_log	758,828.45	7,728.55
2015 Aug	829,230	ARIMA_d1D1_log	881,421.96	-52,191.96
2015 Sep	696,849	ARIMA_d1D1_log	687,197.24	9,651.76
2015 Oct	597,629	ARIMA_d1D1_log	589,990.15	7,638.85
2015 Nov	475,257	ARIMA_d1D1_log	442,875.44	32,381.56
2015 Dec	407,035	ARIMA_d1D1_log	411,866.56	-4,831.56
2016 Jan	448,784	ARIMA_d1D1_log	445,347.31	3,436.69
2016 Feb	506,179	ARIMA_d1D1_log	496,174.63	10,004.37
2016 Mar	611,987	ARIMA_d1D1_log	631,108.77	-19,121.77
2016 Apr	663,878	ARIMA_d1D1_log	675,720.54	-11,842.54
2016 May	726,980	ARIMA_d1D1_log	721,787.19	5,192.81
2016 Jun	759,256	ARIMA_d1D1_log	727,574.92	31,681.08
2016 Jul	849,148	ARIMA_d1D1_log	884,458.05	-35,310.05
2016 Aug	891,091	ARIMA_d1D1_log	948,967.68	-57,876.68
2016 Sep	768,042	ARIMA_d1D1_log	744,065.53	23,976.47
2016 Oct	702,530	ARIMA_d1D1_log	654,803.43	47,726.57
2016 Nov	545,468	ARIMA_d1D1_log	540,051.47	5,416.53
2016 Dec	457,565	ARIMA_d1D1_log	470,290.84	-12,725.84
2017 Jan	503,654	ARIMA_d1D1_log	502,944.23	709.77
2017 Feb	541,368	ARIMA_d1D1_log	563,018.19	-21,650.19
2017 Mar	647,679	ARIMA_d1D1_log	664,483.62	-16,804.62
2017 Apr	710,409	ARIMA_d1D1_log	707,390.96	3,018.04
2017 May	745,096	ARIMA_d1D1_log	776,030.30	-30,934.30
2017 Jun	794,118	ARIMA_d1D1_log	765,106.67	29,011.33
2017 Jul	864,476	ARIMA_d1D1_log	905,808.55	-41,332.55
2017 Aug	939,077	ARIMA_d1D1_log	931,389.57	7,687.43
2017 Sep	818,705	ARIMA_d1D1_log	798,796.98	19,908.02
2017 Oct	734,287	ARIMA_d1D1_log	726,380.34	7,906.66
2017 Nov	582,743	ARIMA_d1D1_log	567,437.14	15,305.86
2017 Dec	478,377	ARIMA_d1D1_log	495,642.33	-17,265.33
2018 Jan	534,281	ARIMA_d1D1_log	526,587.10	7,693.90
2018 Feb	555,841	ARIMA_d1D1_log	585,080.45	-29,239.45
2018 Mar	652,082	ARIMA_d1D1_log	672,644.64	-20,562.64
2018 Apr	689,214	ARIMA_d1D1_log	714,486.39	-25,272.39
2018 May	755,491	ARIMA_d1D1_log	736,918.02	18,572.98
2018 Jun	782,628	ARIMA_d1D1_log	792,278.74	-9,650.74
2018 Jul	837,740	ARIMA_d1D1_log	870,876.33	-33,136.33
2018 Aug	936,644	ARIMA_d1D1_log	907,019.42	29,624.58
2018 Sep	806,267	ARIMA_d1D1_log	808,351.74	-2,084.74
2018 Oct	721,989	ARIMA_d1D1_log	720,232.32	1,756.68
2018 Nov	575,096	ARIMA_d1D1_log	566,946.72	8,149.28
2018 Dec	496,993	ARIMA_d1D1_log	479,879.91	17,113.09
2019 Jan	486,306	ARIMA_d1D1_log	551,482.18	-65,176.18
2019 Feb	498,081	ARIMA_d1D1_log	518,968.91	-20,887.91
2019 Mar	606,616	ARIMA_d1D1_log	593,181.79	13,434.21
2019 Apr	608,322	ARIMA_d1D1_log	652,558.80	-44,236.80
2019 May	665,724	ARIMA_d1D1_log	659,581.24	6,142.76
2019 Jun	714,041	ARIMA_d1D1_log	693,536.64	20,504.36
2019 Jul	747,112	ARIMA_d1D1_log	780,358.48	-33,246.48
2019 Aug	828,426	ARIMA_d1D1_log	823,708.02	4,717.98
2019 Sep	719,254	ARIMA_d1D1_log	714,017.74	5,236.26
2019 Oct	629,555	ARIMA_d1D1_log	643,333.06	-13,778.06
2019 Nov	508,290	ARIMA_d1D1_log	501,176.52	7,113.48
2019 Dec	445,470	ARIMA_d1D1_log	428,195.22	17,274.78
2020 Jan	488,461	ARIMA_d1D1_log	461,604.00	26,857.00
2020 Feb	540,254	ARIMA_d1D1_log	498,710.30	41,543.70
2020 Mar	297,649	ARIMA_d1D1_log	634,645.40	-336,996.40
2020 Apr	2,191	ARIMA_d1D1_log	500,713.51	-498,522.51
2020 May	2,955	ARIMA_d1D1_log	2,678.14	276.86
2020 Jun	14,932	ARIMA_d1D1_log	3,540.60	11,391.40
2020 Jul	95,576	ARIMA_d1D1_log	13,834.40	81,741.60
2020 Aug	240,322	ARIMA_d1D1_log	91,331.27	148,990.73
2020 Sep	251,221	ARIMA_d1D1_log	220,244.96	30,976.04
2020 Oct	253,895	ARIMA_d1D1_log	242,954.70	10,940.30
2020 Nov	116,634	ARIMA_d1D1_log	205,029.28	-88,395.28
2020 Dec	137,446	ARIMA_d1D1_log	90,271.49	47,174.51
2021 Jan	93,013	ARIMA_d1D1_log	171,009.88	-77,996.88
2021 Feb	40,883	ARIMA_d1D1_log	108,293.64	-67,410.64
2021 Mar	60,163	ARIMA_d1D1_log	22,923.96	37,239.04
2021 Apr	95,116	ARIMA_d1D1_log	796.72	94,319.28
2021 May	179,599	ARIMA_d1D1_log	148,647.29	30,951.71
2021 Jun	321,985	ARIMA_d1D1_log	217,194.91	104,790.09
2021 Jul	552,399	ARIMA_d1D1_log	366,061.10	186,337.90
2021 Aug	780,123	ARIMA_d1D1_log	597,175.25	182,947.75
2021 Sep	697,572	ARIMA_d1D1_log	554,736.18	142,835.82
2021 Oct	655,682	ARIMA_d1D1_log	506,616.59	149,065.41
2021 Nov	521,638	ARIMA_d1D1_log	424,094.18	97,543.82
2021 Dec	397,592	ARIMA_d1D1_log	429,435.41	-31,843.41
2022 Jan	341,744	ARIMA_d1D1_log	360,892.88	-19,148.88
2022 Feb	391,699	ARIMA_d1D1_log	321,979.42	69,719.58
2022 Mar	569,482	ARIMA_d1D1_log	399,785.24	169,696.76
2022 Apr	727,326	ARIMA_d1D1_log	79,187.27	648,138.73
2022 May	779,426	ARIMA_d1D1_log	976,315.92	-196,889.92
2022 Jun	833,955	ARIMA_d1D1_log	815,844.73	18,110.27
2010 Jan	319,379	Drift_STL	330,843.27	-11,464.27
2010 Feb	329,697	Drift_STL	357,207.11	-27,510.11
2010 Mar	388,978	Drift_STL	437,917.81	-48,939.81
2010 Apr	427,950	Drift_STL	442,459.42	-14,509.42
2010 May	431,385	Drift_STL	402,693.72	28,691.28
2010 Jun	432,522	Drift_STL	401,869.43	30,652.57
2010 Jul	492,382	Drift_STL	470,861.83	21,520.17
2010 Aug	624,383	Drift_STL	587,697.98	36,685.02
2010 Sep	496,609	Drift_STL	503,611.07	-7,002.07
2010 Oct	450,841	Drift_STL	443,002.01	7,838.99
2010 Nov	327,330	Drift_STL	358,425.44	-31,095.44
2010 Dec	272,069	Drift_STL	284,168.96	-12,099.96
2011 Jan	286,010	Drift_STL	293,996.37	-7,986.37
2011 Feb	319,015	Drift_STL	321,070.59	-2,055.59
2011 Mar	448,224	Drift_STL	420,687.98	27,536.02
2011 Apr	517,979	Drift_STL	492,587.43	25,391.57
2011 May	575,401	Drift_STL	493,515.49	81,885.51
2011 Jun	519,950	Drift_STL	540,109.76	-20,159.76
2011 Jul	589,288	Drift_STL	561,137.19	28,150.81
2011 Aug	678,877	Drift_STL	689,684.18	-10,807.18
2011 Sep	577,108	Drift_STL	562,596.38	14,511.62
2011 Oct	471,268	Drift_STL	524,937.50	-53,669.50
2011 Nov	319,900	Drift_STL	381,898.33	-61,998.33
2011 Dec	262,266	Drift_STL	286,132.93	-23,866.93
2012 Jan	289,312	Drift_STL	291,062.17	-1,750.17
2012 Feb	329,299	Drift_STL	329,071.46	227.54
2012 Mar	399,988	Drift_STL	437,788.29	-37,800.29
2012 Apr	508,131	Drift_STL	456,945.86	51,185.14
2012 May	521,638	Drift_STL	501,214.54	20,423.46
2012 Jun	509,865	Drift_STL	486,635.64	23,229.36
2012 Jul	602,837	Drift_STL	551,168.61	51,668.39
2012 Aug	681,135	Drift_STL	692,029.84	-10,894.84
2012 Sep	562,007	Drift_STL	560,609.12	1,397.88
2012 Oct	468,951	Drift_STL	494,701.76	-25,750.76
2012 Nov	350,902	Drift_STL	362,904.02	-12,002.02
2012 Dec	283,620	Drift_STL	306,694.82	-23,074.82
2013 Jan	322,235	Drift_STL	308,370.18	13,864.82
2013 Feb	365,343	Drift_STL	359,401.40	5,941.60
2013 Mar	462,258	Drift_STL	466,164.90	-3,906.90
2013 Apr	516,930	Drift_STL	526,350.00	-9,420.00
2013 May	608,081	Drift_STL	523,429.67	84,651.33
2013 Jun	578,633	Drift_STL	572,571.14	6,061.86
2013 Jul	677,083	Drift_STL	628,706.39	48,376.61
2013 Aug	775,941	Drift_STL	761,857.33	14,083.67
2013 Sep	639,271	Drift_STL	652,411.24	-13,140.24
2013 Oct	535,649	Drift_STL	564,650.43	-29,001.43
2013 Nov	390,742	Drift_STL	426,392.56	-35,650.56
2013 Dec	342,783	Drift_STL	347,625.78	-4,842.78
2014 Jan	374,568	Drift_STL	372,116.03	2,451.97
2014 Feb	401,859	Drift_STL	415,192.92	-13,333.92
2014 Mar	503,533	Drift_STL	504,747.93	-1,214.93
2014 Apr	557,275	Drift_STL	570,687.72	-13,412.72
2014 May	610,148	Drift_STL	585,327.54	24,820.46
2014 Jun	595,332	Drift_STL	581,028.90	14,303.10
2014 Jul	687,207	Drift_STL	656,965.14	30,241.86
2014 Aug	787,020	Drift_STL	773,167.18	13,852.82
2014 Sep	652,671	Drift_STL	659,061.29	-6,390.29
2014 Oct	554,671	Drift_STL	567,235.74	-12,564.74
2014 Nov	415,750	Drift_STL	432,450.84	-16,700.84
2014 Dec	366,832	Drift_STL	367,462.92	-630.92
2015 Jan	399,040	Drift_STL	394,145.76	4,894.24
2015 Feb	442,963	Drift_STL	434,856.67	8,106.33
2015 Mar	545,523	Drift_STL	540,338.60	5,184.40
2015 Apr	586,230	Drift_STL	609,397.57	-23,167.57
2015 May	628,998	Drift_STL	624,601.68	4,396.32
2015 Jun	654,715	Drift_STL	604,045.52	50,669.48
2015 Jul	766,557	Drift_STL	720,981.98	45,575.02
2015 Aug	829,230	Drift_STL	848,506.32	-19,276.32
2015 Sep	696,849	Drift_STL	699,916.61	-3,067.61
2015 Oct	597,629	Drift_STL	606,944.12	-9,315.12
2015 Nov	475,257	Drift_STL	469,943.37	5,313.63
2015 Dec	407,035	Drift_STL	424,773.82	-17,738.82
2016 Jan	448,784	Drift_STL	438,024.21	10,759.79
2016 Feb	506,179	Drift_STL	485,553.05	20,625.95
2016 Mar	611,987	Drift_STL	600,942.42	11,044.58
2016 Apr	663,878	Drift_STL	669,807.18	-5,929.18
2016 May	726,980	Drift_STL	705,313.60	21,666.40
2016 Jun	759,256	Drift_STL	707,423.47	51,832.53
2016 Jul	849,148	Drift_STL	832,825.69	16,322.31
2016 Aug	891,091	Drift_STL	926,558.39	-35,467.39
2016 Sep	768,042	Drift_STL	763,170.26	4,871.74
2016 Oct	702,530	Drift_STL	675,203.79	27,326.21
2016 Nov	545,468	Drift_STL	569,832.69	-24,364.69
2016 Dec	457,565	Drift_STL	492,644.89	-35,079.89
2017 Jan	503,654	Drift_STL	495,816.83	7,837.17
2017 Feb	541,368	Drift_STL	546,190.37	-4,822.37
2017 Mar	647,679	Drift_STL	640,435.37	7,243.63
2017 Apr	710,409	Drift_STL	705,133.84	5,275.16
2017 May	745,096	Drift_STL	758,429.79	-13,333.79
2017 Jun	794,118	Drift_STL	738,439.22	55,678.78
2017 Jul	864,476	Drift_STL	871,662.24	-7,186.24
2017 Aug	939,077	Drift_STL	934,112.41	4,964.59
2017 Sep	818,705	Drift_STL	806,498.13	12,206.87
2017 Oct	734,287	Drift_STL	723,722.41	10,564.59
2017 Nov	582,743	Drift_STL	592,747.78	-10,004.78
2017 Dec	478,377	Drift_STL	519,497.42	-41,120.42
2018 Jan	534,281	Drift_STL	519,293.42	14,987.58
2018 Feb	555,841	Drift_STL	575,094.64	-19,253.64
2018 Mar	652,082	Drift_STL	657,121.65	-5,039.65
2018 Apr	689,214	Drift_STL	710,802.51	-21,588.51
2018 May	755,491	Drift_STL	741,857.90	13,633.10
2018 Jun	782,628	Drift_STL	761,643.24	20,984.76
2018 Jul	837,740	Drift_STL	862,720.43	-24,980.43
2018 Aug	936,644	Drift_STL	908,883.50	27,760.50
2018 Sep	806,267	Drift_STL	803,702.51	2,564.49
2018 Oct	721,989	Drift_STL	711,292.55	10,696.45
2018 Nov	575,096	Drift_STL	575,019.49	76.51
2018 Dec	496,993	Drift_STL	499,789.79	-2,796.79
2019 Jan	486,306	Drift_STL	536,629.94	-50,323.94
2019 Feb	498,081	Drift_STL	528,998.52	-30,917.52
2019 Mar	606,616	Drift_STL	604,636.81	1,979.19
2019 Apr	608,322	Drift_STL	662,420.30	-54,098.30
2019 May	665,724	Drift_STL	670,999.78	-5,275.78
2019 Jun	714,041	Drift_STL	686,369.18	27,671.82
2019 Jul	747,112	Drift_STL	792,085.31	-44,973.31
2019 Aug	828,426	Drift_STL	825,583.03	2,842.97
2019 Sep	719,254	Drift_STL	699,589.36	19,664.64
2019 Oct	629,555	Drift_STL	625,662.29	3,892.71
2019 Nov	508,290	Drift_STL	479,610.84	28,679.16
2019 Dec	445,470	Drift_STL	424,176.27	21,293.73
2020 Jan	488,461	Drift_STL	470,641.89	17,819.11
2020 Feb	540,254	Drift_STL	515,056.68	25,197.32
2020 Mar	297,649	Drift_STL	636,547.49	-338,898.49
2020 Apr	2,191	Drift_STL	380,020.88	-377,829.88
2020 May	2,955	Drift_STL	132,061.85	-129,106.85
2020 Jun	14,932	Drift_STL	89,432.12	-74,500.12
2020 Jul	95,576	Drift_STL	126,009.39	-30,433.39
2020 Aug	240,322	Drift_STL	193,837.94	46,484.06
2020 Sep	251,221	Drift_STL	113,925.71	137,295.29
2020 Oct	253,895	Drift_STL	134,867.93	119,027.07
2020 Nov	116,634	Drift_STL	71,169.87	45,464.13
2020 Dec	137,446	Drift_STL	2,752.45	134,693.55
2021 Jan	93,013	Drift_STL	127,356.80	-34,343.80
2021 Feb	40,883	Drift_STL	103,775.41	-62,892.41
2021 Mar	60,163	Drift_STL	75,807.16	-15,644.16
2021 Apr	95,116	Drift_STL	48,361.41	46,754.59
2021 May	179,599	Drift_STL	153,960.55	25,638.45
2021 Jun	321,985	Drift_STL	220,953.95	101,031.05
2021 Jul	552,399	Drift_STL	393,537.75	158,861.25
2021 Aug	780,123	Drift_STL	629,415.60	150,707.40
2021 Sep	697,572	Drift_STL	657,767.12	39,804.88
2021 Oct	655,682	Drift_STL	609,596.19	46,085.81
2021 Nov	521,638	Drift_STL	501,109.51	20,528.49
2021 Dec	397,592	Drift_STL	453,940.38	-56,348.38
2022 Jan	341,744	Drift_STL	422,077.18	-80,333.18
2022 Feb	391,699	Drift_STL	380,481.04	11,217.96
2022 Mar	569,482	Drift_STL	436,806.06	132,675.94
2022 Apr	727,326	Drift_STL	554,726.51	172,599.49
2022 May	779,426	Drift_STL	775,590.44	3,835.56
2022 Jun	833,955	Drift_STL	836,318.01	-2,363.01
2010 Jan	319,379	Drift_STL_log	328,457.48	-9,078.48
2010 Feb	329,697	Drift_STL_log	352,664.31	-22,967.31
2010 Mar	388,978	Drift_STL_log	420,114.20	-31,136.20
2010 Apr	427,950	Drift_STL_log	430,808.79	-2,858.79
2010 May	431,385	Drift_STL_log	406,477.50	24,907.50
2010 Jun	432,522	Drift_STL_log	405,519.75	27,002.25
2010 Jul	492,382	Drift_STL_log	464,627.97	27,754.03
2010 Aug	624,383	Drift_STL_log	576,910.87	47,472.13
2010 Sep	496,609	Drift_STL_log	505,921.52	-9,312.52
2010 Oct	450,841	Drift_STL_log	446,803.35	4,037.65
2010 Nov	327,330	Drift_STL_log	365,021.99	-37,691.99
2010 Dec	272,069	Drift_STL_log	292,675.99	-20,606.99
2011 Jan	286,010	Drift_STL_log	291,180.56	-5,170.56
2011 Feb	319,015	Drift_STL_log	314,908.35	4,106.65
2011 Mar	448,224	Drift_STL_log	402,757.34	45,466.66
2011 Apr	517,979	Drift_STL_log	486,640.11	31,338.89
2011 May	575,401	Drift_STL_log	491,437.86	83,963.14
2011 Jun	519,950	Drift_STL_log	534,832.62	-14,882.62
2011 Jul	589,288	Drift_STL_log	561,644.54	27,643.46
2011 Aug	678,877	Drift_STL_log	698,425.53	-19,548.53
2011 Sep	577,108	Drift_STL_log	556,355.64	20,752.36
2011 Oct	471,268	Drift_STL_log	520,248.42	-48,980.42
2011 Nov	319,900	Drift_STL_log	379,827.49	-59,927.49
2011 Dec	262,266	Drift_STL_log	289,230.16	-26,964.16
2012 Jan	289,312	Drift_STL_log	285,449.04	3,862.96
2012 Feb	329,299	Drift_STL_log	322,818.58	6,480.42
2012 Mar	399,988	Drift_STL_log	425,546.87	-25,558.87
2012 Apr	508,131	Drift_STL_log	447,461.38	60,669.62
2012 May	521,638	Drift_STL_log	498,243.80	23,394.20
2012 Jun	509,865	Drift_STL_log	485,554.81	24,310.19
2012 Jul	602,837	Drift_STL_log	549,586.47	53,250.53
2012 Aug	681,135	Drift_STL_log	697,670.91	-16,535.91
2012 Sep	562,007	Drift_STL_log	554,342.39	7,664.61
2012 Oct	468,951	Drift_STL_log	491,895.80	-22,944.80
2012 Nov	350,902	Drift_STL_log	361,681.59	-10,779.59
2012 Dec	283,620	Drift_STL_log	306,594.10	-22,974.10
2013 Jan	322,235	Drift_STL_log	306,704.95	15,530.05
2013 Feb	365,343	Drift_STL_log	358,772.74	6,570.26
2013 Mar	462,258	Drift_STL_log	467,367.76	-5,109.76
2013 Apr	516,930	Drift_STL_log	528,349.65	-11,419.65
2013 May	608,081	Drift_STL_log	522,781.05	85,299.95
2013 Jun	578,633	Drift_STL_log	569,148.61	9,484.39
2013 Jul	677,083	Drift_STL_log	635,292.64	41,790.36
2013 Aug	775,941	Drift_STL_log	780,004.66	-4,063.66
2013 Sep	639,271	Drift_STL_log	633,177.19	6,093.81
2013 Oct	535,649	Drift_STL_log	551,650.94	-16,001.94
2013 Nov	390,742	Drift_STL_log	406,788.95	-16,046.95
2013 Dec	342,783	Drift_STL_log	336,669.26	6,113.74
2014 Jan	374,568	Drift_STL_log	371,849.53	2,718.47
2014 Feb	401,859	Drift_STL_log	418,816.43	-16,957.43
2014 Mar	503,533	Drift_STL_log	517,040.57	-13,507.57
2014 Apr	557,275	Drift_STL_log	581,275.69	-24,000.69
2014 May	610,148	Drift_STL_log	588,513.39	21,634.61
2014 Jun	595,332	Drift_STL_log	580,933.75	14,398.25
2014 Jul	687,207	Drift_STL_log	666,910.13	20,296.87
2014 Aug	787,020	Drift_STL_log	791,673.43	-4,653.43
2014 Sep	652,671	Drift_STL_log	643,420.01	9,250.99
2014 Oct	554,671	Drift_STL_log	555,072.66	-401.66
2014 Nov	415,750	Drift_STL_log	411,260.38	4,489.62
2014 Dec	366,832	Drift_STL_log	353,640.87	13,191.13
2015 Jan	399,040	Drift_STL_log	395,007.99	4,032.01
2015 Feb	442,963	Drift_STL_log	439,640.06	3,322.94
2015 Mar	545,523	Drift_STL_log	560,967.34	-15,444.34
2015 Apr	586,230	Drift_STL_log	625,510.23	-39,280.23
2015 May	628,998	Drift_STL_log	631,268.81	-2,270.81
2015 Jun	654,715	Drift_STL_log	604,880.29	49,834.71
2015 Jul	766,557	Drift_STL_log	738,339.98	28,217.02
2015 Aug	829,230	Drift_STL_log	876,695.89	-47,465.89
2015 Sep	696,849	Drift_STL_log	683,379.92	13,469.08
2015 Oct	597,629	Drift_STL_log	591,110.68	6,518.32
2015 Nov	475,257	Drift_STL_log	440,115.11	35,141.89
2015 Dec	407,035	Drift_STL_log	401,336.27	5,698.73
2016 Jan	448,784	Drift_STL_log	438,498.53	10,285.47
2016 Feb	506,179	Drift_STL_log	491,901.22	14,277.78
2016 Mar	611,987	Drift_STL_log	632,191.98	-20,204.98
2016 Apr	663,878	Drift_STL_log	693,537.32	-29,659.32
2016 May	726,980	Drift_STL_log	720,675.06	6,304.94
2016 Jun	759,256	Drift_STL_log	709,001.79	50,254.21
2016 Jul	849,148	Drift_STL_log	864,989.03	-15,841.03
2016 Aug	891,091	Drift_STL_log	964,662.08	-73,571.08
2016 Sep	768,042	Drift_STL_log	745,026.81	23,015.19
2016 Oct	702,530	Drift_STL_log	653,187.58	49,342.42
2016 Nov	545,468	Drift_STL_log	518,698.75	26,769.25
2016 Dec	457,565	Drift_STL_log	458,174.82	-609.82
2017 Jan	503,654	Drift_STL_log	494,800.86	8,853.14
2017 Feb	541,368	Drift_STL_log	552,570.96	-11,202.96
2017 Mar	647,679	Drift_STL_log	671,501.67	-23,822.67
2017 Apr	710,409	Drift_STL_log	729,426.52	-19,017.52
2017 May	745,096	Drift_STL_log	778,628.21	-33,532.21
2017 Jun	794,118	Drift_STL_log	742,573.73	51,544.27
2017 Jul	864,476	Drift_STL_log	905,319.21	-40,843.21
2017 Aug	939,077	Drift_STL_log	967,891.53	-28,814.53
2017 Sep	818,705	Drift_STL_log	789,867.85	28,837.15
2017 Oct	734,287	Drift_STL_log	701,120.64	33,166.36
2017 Nov	582,743	Drift_STL_log	544,746.74	37,996.26
2017 Dec	478,377	Drift_STL_log	484,343.72	-5,966.72
2018 Jan	534,281	Drift_STL_log	516,480.17	17,800.83
2018 Feb	555,841	Drift_STL_log	579,397.10	-23,556.10
2018 Mar	652,082	Drift_STL_log	681,353.88	-29,271.88
2018 Apr	689,214	Drift_STL_log	729,404.58	-40,190.58
2018 May	755,491	Drift_STL_log	757,843.08	-2,352.08
2018 Jun	782,628	Drift_STL_log	767,138.14	15,489.86
2018 Jul	837,740	Drift_STL_log	889,089.87	-51,349.87
2018 Aug	936,644	Drift_STL_log	932,910.58	3,733.42
2018 Sep	806,267	Drift_STL_log	795,060.56	11,206.44
2018 Oct	721,989	Drift_STL_log	697,598.26	24,390.74
2018 Nov	575,096	Drift_STL_log	543,486.78	31,609.22
2018 Dec	496,993	Drift_STL_log	475,017.29	21,975.71
2019 Jan	486,306	Drift_STL_log	534,706.11	-48,400.11
2019 Feb	498,081	Drift_STL_log	527,783.90	-29,702.90
2019 Mar	606,616	Drift_STL_log	609,347.14	-2,731.14
2019 Apr	608,322	Drift_STL_log	669,770.35	-61,448.35
2019 May	665,724	Drift_STL_log	675,052.75	-9,328.75
2019 Jun	714,041	Drift_STL_log	688,508.64	25,532.36
2019 Jul	747,112	Drift_STL_log	801,976.82	-54,864.82
2019 Aug	828,426	Drift_STL_log	831,693.82	-3,267.82
2019 Sep	719,254	Drift_STL_log	709,051.95	10,202.05
2019 Oct	629,555	Drift_STL_log	628,692.58	862.42
2019 Nov	508,290	Drift_STL_log	482,250.10	26,039.90
2019 Dec	445,470	Drift_STL_log	422,393.68	23,076.32
2020 Jan	488,461	Drift_STL_log	469,403.97	19,057.03
2020 Feb	540,254	Drift_STL_log	515,546.31	24,707.69
2020 Mar	297,649	Drift_STL_log	645,563.83	-347,914.83
2020 Apr	2,191	Drift_STL_log	351,769.73	-349,578.73
2020 May	2,955	Drift_STL_log	5,268.28	-2,313.28
2020 Jun	14,932	Drift_STL_log	5,373.98	9,558.02
2020 Jul	95,576	Drift_STL_log	19,973.77	75,602.23
2020 Aug	240,322	Drift_STL_log	94,460.77	145,861.23
2020 Sep	251,221	Drift_STL_log	166,527.64	84,693.36
2020 Oct	253,895	Drift_STL_log	181,144.80	72,750.20
2020 Nov	116,634	Drift_STL_log	168,343.32	-51,709.32
2020 Dec	137,446	Drift_STL_log	95,282.48	42,163.52
2021 Jan	93,013	Drift_STL_log	140,962.93	-47,949.93
2021 Feb	40,883	Drift_STL_log	105,662.97	-64,779.97
2021 Mar	60,163	Drift_STL_log	52,117.99	8,045.01
2021 Apr	95,116	Drift_STL_log	31,438.31	63,677.69
2021 May	179,599	Drift_STL_log	125,599.76	53,999.24
2021 Jun	321,985	Drift_STL_log	281,438.03	40,546.97
2021 Jul	552,399	Drift_STL_log	528,770.48	23,628.52
2021 Aug	780,123	Drift_STL_log	753,446.88	26,676.12
2021 Sep	697,572	Drift_STL_log	742,087.87	-44,515.87
2021 Oct	655,682	Drift_STL_log	687,123.05	-31,441.05
2021 Nov	521,638	Drift_STL_log	514,211.43	7,426.57
2021 Dec	397,592	Drift_STL_log	520,892.61	-123,300.61
2022 Jan	341,744	Drift_STL_log	445,892.46	-104,148.46
2022 Feb	391,699	Drift_STL_log	368,289.34	23,409.66
2022 Mar	569,482	Drift_STL_log	498,989.16	70,492.84
2022 Apr	727,326	Drift_STL_log	311,311.73	416,014.27
2022 May	779,426	Drift_STL_log	1,040,977.68	-261,551.68
2022 Jun	833,955	Drift_STL_log	1,412,991.96	-579,036.96
2010 Jan	319,379	ETS_auto	325,493.63	-6,114.63
2010 Feb	329,697	ETS_auto	353,293.34	-23,596.34
2010 Mar	388,978	ETS_auto	421,481.29	-32,503.29
2010 Apr	427,950	ETS_auto	435,414.63	-7,464.63
2010 May	431,385	ETS_auto	391,695.93	39,689.07
2010 Jun	432,522	ETS_auto	404,252.92	28,269.08
2010 Jul	492,382	ETS_auto	466,090.87	26,291.13
2010 Aug	624,383	ETS_auto	580,705.66	43,677.34
2010 Sep	496,609	ETS_auto	503,595.76	-6,986.76
2010 Oct	450,841	ETS_auto	455,612.26	-4,771.26
2010 Nov	327,330	ETS_auto	371,685.00	-44,355.00
2010 Dec	272,069	ETS_auto	284,497.13	-12,428.13
2011 Jan	286,010	ETS_auto	290,384.99	-4,374.99
2011 Feb	319,015	ETS_auto	317,657.76	1,357.24
2011 Mar	448,224	ETS_auto	392,239.92	55,984.08
2011 Apr	517,979	ETS_auto	484,700.49	33,278.51
2011 May	575,401	ETS_auto	479,024.08	96,376.92
2011 Jun	519,950	ETS_auto	549,533.00	-29,583.00
2011 Jul	589,288	ETS_auto	562,714.77	26,573.23
2011 Aug	678,877	ETS_auto	691,255.44	-12,378.44
2011 Sep	577,108	ETS_auto	562,822.86	14,285.14
2011 Oct	471,268	ETS_auto	526,966.17	-55,698.17
2011 Nov	319,900	ETS_auto	378,244.69	-58,344.69
2011 Dec	262,266	ETS_auto	268,959.32	-6,693.32
2012 Jan	289,312	ETS_auto	279,243.28	10,068.72
2012 Feb	329,299	ETS_auto	317,955.34	11,343.66
2012 Mar	399,988	ETS_auto	424,509.93	-24,521.93
2012 Apr	508,131	ETS_auto	446,111.97	62,019.03
2012 May	521,638	ETS_auto	481,543.16	40,094.84
2012 Jun	509,865	ETS_auto	490,183.11	19,681.89
2012 Jul	602,837	ETS_auto	553,724.45	49,112.55
2012 Aug	681,135	ETS_auto	703,044.48	-21,909.48
2012 Sep	562,007	ETS_auto	562,400.99	-393.99
2012 Oct	468,951	ETS_auto	508,406.45	-39,455.45
2012 Nov	350,902	ETS_auto	365,059.60	-14,157.60
2012 Dec	283,620	ETS_auto	297,958.44	-14,338.44
2013 Jan	322,235	ETS_auto	300,301.18	21,933.82
2013 Feb	365,343	ETS_auto	351,301.97	14,041.03
2013 Mar	462,258	ETS_auto	459,247.41	3,010.59
2013 Apr	516,930	ETS_auto	517,003.33	-73.33
2013 May	608,081	ETS_auto	503,059.45	105,021.55
2013 Jun	578,633	ETS_auto	568,778.92	9,854.08
2013 Jul	677,083	ETS_auto	629,265.82	47,817.18
2013 Aug	775,941	ETS_auto	771,172.85	4,768.15
2013 Sep	639,271	ETS_auto	658,351.57	-19,080.57
2013 Oct	535,649	ETS_auto	574,750.94	-39,101.94
2013 Nov	390,742	ETS_auto	423,986.01	-33,244.01
2013 Dec	342,783	ETS_auto	335,193.84	7,589.16
2014 Jan	374,568	ETS_auto	360,371.70	14,196.30
2014 Feb	401,859	ETS_auto	401,238.41	620.59
2014 Mar	503,533	ETS_auto	496,077.25	7,455.75
2014 Apr	557,275	ETS_auto	552,669.69	4,605.31
2014 May	610,148	ETS_auto	559,037.83	51,110.17
2014 Jun	595,332	ETS_auto	573,282.52	22,049.48
2014 Jul	687,207	ETS_auto	647,283.17	39,923.83
2014 Aug	787,020	ETS_auto	776,894.98	10,125.02
2014 Sep	652,671	ETS_auto	658,586.25	-5,915.25
2014 Oct	554,671	ETS_auto	575,491.26	-20,820.26
2014 Nov	415,750	ETS_auto	438,736.88	-22,986.88
2014 Dec	366,832	ETS_auto	359,190.25	7,641.75
2015 Jan	399,040	ETS_auto	384,518.58	14,521.42
2015 Feb	442,963	ETS_auto	427,626.05	15,336.95
2015 Mar	545,523	ETS_auto	536,988.22	8,534.78
2015 Apr	586,230	ETS_auto	606,477.45	-20,247.45
2015 May	628,998	ETS_auto	588,137.99	40,860.01
2015 Jun	654,715	ETS_auto	600,875.64	53,839.36
2015 Jul	766,557	ETS_auto	713,453.87	53,103.13
2015 Aug	829,230	ETS_auto	859,307.02	-30,077.02
2015 Sep	696,849	ETS_auto	691,902.18	4,946.82
2015 Oct	597,629	ETS_auto	613,756.46	-16,127.46
2015 Nov	475,257	ETS_auto	478,188.74	-2,931.74
2015 Dec	407,035	ETS_auto	419,365.82	-12,330.82
2016 Jan	448,784	ETS_auto	424,918.80	23,865.20
2016 Feb	506,179	ETS_auto	478,674.44	27,504.56
2016 Mar	611,987	ETS_auto	590,585.80	21,401.20
2016 Apr	663,878	ETS_auto	655,755.66	8,122.34
2016 May	726,980	ETS_auto	686,187.95	40,792.05
2016 Jun	759,256	ETS_auto	700,768.16	58,487.84
2016 Jul	849,148	ETS_auto	829,224.75	19,923.25
2016 Aug	891,091	ETS_auto	932,671.45	-41,580.45
2016 Sep	768,042	ETS_auto	759,132.97	8,909.03
2016 Oct	702,530	ETS_auto	673,668.06	28,861.94
2016 Nov	545,468	ETS_auto	572,396.43	-26,928.43
2016 Dec	457,565	ETS_auto	482,183.78	-24,618.78
2017 Jan	503,654	ETS_auto	474,078.28	29,575.72
2017 Feb	541,368	ETS_auto	531,080.99	10,287.01
2017 Mar	647,679	ETS_auto	628,605.75	19,073.25
2017 Apr	710,409	ETS_auto	695,109.72	15,299.28
2017 May	745,096	ETS_auto	744,460.11	635.89
2017 Jun	794,118	ETS_auto	731,477.56	62,640.44
2017 Jul	864,476	ETS_auto	845,932.05	18,543.95
2017 Aug	939,077	ETS_auto	933,414.39	5,662.61
2017 Sep	818,705	ETS_auto	803,983.31	14,721.69
2017 Oct	734,287	ETS_auto	726,149.64	8,137.36
2017 Nov	582,743	ETS_auto	601,819.23	-19,076.23
2017 Dec	478,377	ETS_auto	521,128.66	-42,751.66
2018 Jan	534,281	ETS_auto	499,847.49	34,433.51
2018 Feb	555,841	ETS_auto	568,659.89	-12,818.89
2018 Mar	652,082	ETS_auto	651,834.46	247.54
2018 Apr	689,214	ETS_auto	708,045.98	-18,831.98
2018 May	755,491	ETS_auto	724,428.59	31,062.41
2018 Jun	782,628	ETS_auto	742,282.71	40,345.29
2018 Jul	837,740	ETS_auto	846,059.56	-8,319.56
2018 Aug	936,644	ETS_auto	921,017.80	15,626.20
2018 Sep	806,267	ETS_auto	812,018.61	-5,751.61
2018 Oct	721,989	ETS_auto	720,677.15	1,311.85
2018 Nov	575,096	ETS_auto	585,406.35	-10,310.35
2018 Dec	496,993	ETS_auto	509,033.87	-12,040.87
2019 Jan	486,306	ETS_auto	527,840.68	-41,534.68
2019 Feb	498,081	ETS_auto	519,774.31	-21,693.31
2019 Mar	606,616	ETS_auto	592,088.22	14,527.78
2019 Apr	608,322	ETS_auto	660,869.48	-52,547.48
2019 May	665,724	ETS_auto	655,403.09	10,320.91
2019 Jun	714,041	ETS_auto	666,186.76	47,854.24
2019 Jul	747,112	ETS_auto	789,284.92	-42,172.92
2019 Aug	828,426	ETS_auto	835,066.81	-6,640.81
2019 Sep	719,254	ETS_auto	701,086.04	18,167.96
2019 Oct	629,555	ETS_auto	628,151.85	1,403.15
2019 Nov	508,290	ETS_auto	488,036.87	20,253.13
2019 Dec	445,470	ETS_auto	434,524.01	10,945.99
2020 Jan	488,461	ETS_auto	472,249.83	16,211.17
2020 Feb	540,254	ETS_auto	519,252.57	21,001.43
2020 Mar	297,649	ETS_auto	640,303.77	-342,654.77
2020 Apr	2,191	ETS_auto	406,719.84	-404,528.84
2020 May	2,955	ETS_auto	-29,817.33	32,772.33
2020 Jun	14,932	ETS_auto	-72,012.56	86,944.56
2020 Jul	95,576	ETS_auto	25,257.81	70,318.19
2020 Aug	240,322	ETS_auto	127,109.20	113,212.80
2020 Sep	251,221	ETS_auto	116,947.60	134,273.40
2020 Oct	253,895	ETS_auto	162,766.10	91,128.90
2020 Nov	116,634	ETS_auto	119,762.79	-3,128.79
2020 Dec	137,446	ETS_auto	52,370.78	85,075.22
2021 Jan	93,013	ETS_auto	176,020.67	-83,007.67
2021 Feb	40,883	ETS_auto	134,499.37	-93,616.37
2021 Mar	60,163	ETS_auto	105,110.15	-44,947.15
2021 Apr	95,116	ETS_auto	75,493.24	19,622.76
2021 May	179,599	ETS_auto	144,013.08	35,585.92
2021 Jun	321,985	ETS_auto	196,489.63	125,495.37
2021 Jul	552,399	ETS_auto	403,921.88	148,477.12
2021 Aug	780,123	ETS_auto	641,415.45	138,707.55
2021 Sep	697,572	ETS_auto	668,100.95	29,471.05
2021 Oct	655,682	ETS_auto	615,730.07	39,951.93
2021 Nov	521,638	ETS_auto	514,650.15	6,987.85
2021 Dec	397,592	ETS_auto	457,493.56	-59,901.56
2022 Jan	341,744	ETS_auto	417,217.30	-75,473.30
2022 Feb	391,699	ETS_auto	360,219.83	31,479.17
2022 Mar	569,482	ETS_auto	437,670.48	131,811.52
2022 Apr	727,326	ETS_auto	570,919.77	156,406.23
2022 May	779,426	ETS_auto	760,834.97	18,591.03
2022 Jun	833,955	ETS_auto	790,603.59	43,351.41
2010 Jan	319,379	ETS_auto_log	324,404.68	-5,025.68
2010 Feb	329,697	ETS_auto_log	349,588.66	-19,891.66
2010 Mar	388,978	ETS_auto_log	405,889.51	-16,911.51
2010 Apr	427,950	ETS_auto_log	427,506.15	443.85
2010 May	431,385	ETS_auto_log	393,483.77	37,901.23
2010 Jun	432,522	ETS_auto_log	404,166.71	28,355.29
2010 Jul	492,382	ETS_auto_log	466,799.26	25,582.74
2010 Aug	624,383	ETS_auto_log	583,516.92	40,866.08
2010 Sep	496,609	ETS_auto_log	514,116.04	-17,507.04
2010 Oct	450,841	ETS_auto_log	457,731.47	-6,890.47
2010 Nov	327,330	ETS_auto_log	378,241.27	-50,911.27
2010 Dec	272,069	ETS_auto_log	296,698.36	-24,629.36
2011 Jan	286,010	ETS_auto_log	288,926.65	-2,916.65
2011 Feb	319,015	ETS_auto_log	314,302.12	4,712.88
2011 Mar	448,224	ETS_auto_log	389,886.50	58,337.50
2011 Apr	517,979	ETS_auto_log	479,702.11	38,276.89
2011 May	575,401	ETS_auto_log	479,527.34	95,873.66
2011 Jun	519,950	ETS_auto_log	556,580.53	-36,630.53
2011 Jul	589,288	ETS_auto_log	572,984.10	16,303.90
2011 Aug	678,877	ETS_auto_log	713,021.02	-34,144.02
2011 Sep	577,108	ETS_auto_log	561,647.88	15,460.12
2011 Oct	471,268	ETS_auto_log	530,228.24	-58,960.24
2011 Nov	319,900	ETS_auto_log	383,097.45	-63,197.45
2011 Dec	262,266	ETS_auto_log	278,907.19	-16,641.19
2012 Jan	289,312	ETS_auto_log	278,250.36	11,061.64
2012 Feb	329,299	ETS_auto_log	314,215.51	15,083.49
2012 Mar	399,988	ETS_auto_log	409,900.00	-9,912.00
2012 Apr	508,131	ETS_auto_log	438,396.70	69,734.30
2012 May	521,638	ETS_auto_log	488,328.88	33,309.12
2012 Jun	509,865	ETS_auto_log	493,411.31	16,453.69
2012 Jul	602,837	ETS_auto_log	563,432.47	39,404.53
2012 Aug	681,135	ETS_auto_log	727,938.11	-46,803.11
2012 Sep	562,007	ETS_auto_log	562,895.63	-888.63
2012 Oct	468,951	ETS_auto_log	508,186.25	-39,235.25
2012 Nov	350,902	ETS_auto_log	371,044.40	-20,142.40
2012 Dec	283,620	ETS_auto_log	307,570.88	-23,950.88
2013 Jan	322,235	ETS_auto_log	300,150.20	22,084.80
2013 Feb	365,343	ETS_auto_log	349,147.06	16,195.94
2013 Mar	462,258	ETS_auto_log	455,625.26	6,632.74
2013 Apr	516,930	ETS_auto_log	516,617.56	312.44
2013 May	608,081	ETS_auto_log	506,077.20	102,003.80
2013 Jun	578,633	ETS_auto_log	581,063.37	-2,430.37
2013 Jul	677,083	ETS_auto_log	653,161.43	23,921.57
2013 Aug	775,941	ETS_auto_log	807,261.64	-31,320.64
2013 Sep	639,271	ETS_auto_log	640,970.43	-1,699.43
2013 Oct	535,649	ETS_auto_log	568,939.45	-33,290.45
2013 Nov	390,742	ETS_auto_log	419,609.78	-28,867.78
2013 Dec	342,783	ETS_auto_log	341,291.02	1,491.98
2014 Jan	374,568	ETS_auto_log	368,086.74	6,481.26
2014 Feb	401,859	ETS_auto_log	404,860.25	-3,001.25
2014 Mar	503,533	ETS_auto_log	504,860.37	-1,327.37
2014 Apr	557,275	ETS_auto_log	567,343.11	-10,068.11
2014 May	610,148	ETS_auto_log	562,802.39	47,345.61
2014 Jun	595,332	ETS_auto_log	585,489.12	9,842.88
2014 Jul	687,207	ETS_auto_log	666,940.95	20,266.05
2014 Aug	787,020	ETS_auto_log	809,502.23	-22,482.23
2014 Sep	652,671	ETS_auto_log	644,897.35	7,773.65
2014 Oct	554,671	ETS_auto_log	571,427.00	-16,756.00
2014 Nov	415,750	ETS_auto_log	424,880.58	-9,130.58
2014 Dec	366,832	ETS_auto_log	355,410.88	11,421.12
2015 Jan	399,040	ETS_auto_log	390,160.54	8,879.46
2015 Feb	442,963	ETS_auto_log	436,188.92	6,774.08
2015 Mar	545,523	ETS_auto_log	563,210.15	-17,687.15
2015 Apr	586,230	ETS_auto_log	617,195.09	-30,965.09
2015 May	628,998	ETS_auto_log	599,263.25	29,734.75
2015 Jun	654,715	ETS_auto_log	601,639.93	53,075.07
2015 Jul	766,557	ETS_auto_log	730,583.06	35,973.94
2015 Aug	829,230	ETS_auto_log	900,269.38	-71,039.38
2015 Sep	696,849	ETS_auto_log	684,429.50	12,419.50
2015 Oct	597,629	ETS_auto_log	607,385.54	-9,756.54
2015 Nov	475,257	ETS_auto_log	454,146.77	21,110.23
2015 Dec	407,035	ETS_auto_log	407,316.80	-281.80
2016 Jan	448,784	ETS_auto_log	433,717.91	15,066.09
2016 Feb	506,179	ETS_auto_log	497,421.89	8,757.11
2016 Mar	611,987	ETS_auto_log	634,932.78	-22,945.78
2016 Apr	663,878	ETS_auto_log	686,913.75	-23,035.75
2016 May	726,980	ETS_auto_log	688,128.18	38,851.82
2016 Jun	759,256	ETS_auto_log	699,893.25	59,362.75
2016 Jul	849,148	ETS_auto_log	862,277.42	-13,129.42
2016 Aug	891,091	ETS_auto_log	980,474.03	-89,383.03
2016 Sep	768,042	ETS_auto_log	737,405.71	30,636.29
2016 Oct	702,530	ETS_auto_log	659,642.88	42,887.12
2016 Nov	545,468	ETS_auto_log	531,521.64	13,946.36
2016 Dec	457,565	ETS_auto_log	462,577.81	-5,012.81
2017 Jan	503,654	ETS_auto_log	488,976.75	14,677.25
2017 Feb	541,368	ETS_auto_log	558,068.32	-16,700.32
2017 Mar	647,679	ETS_auto_log	677,317.73	-29,638.73
2017 Apr	710,409	ETS_auto_log	722,496.02	-12,087.02
2017 May	745,096	ETS_auto_log	751,357.77	-6,261.77
2017 Jun	794,118	ETS_auto_log	731,627.78	62,490.22
2017 Jul	864,476	ETS_auto_log	895,050.51	-30,574.51
2017 Aug	939,077	ETS_auto_log	988,009.64	-48,932.64
2017 Sep	818,705	ETS_auto_log	778,848.61	39,856.39
2017 Oct	734,287	ETS_auto_log	696,818.59	37,468.41
2017 Nov	582,743	ETS_auto_log	550,936.31	31,806.69
2017 Dec	478,377	ETS_auto_log	493,419.88	-15,042.88
2018 Jan	534,281	ETS_auto_log	519,581.60	14,699.40
2018 Feb	555,841	ETS_auto_log	588,516.45	-32,675.45
2018 Mar	652,082	ETS_auto_log	693,312.83	-41,230.83
2018 Apr	689,214	ETS_auto_log	734,241.60	-45,027.60
2018 May	755,491	ETS_auto_log	732,833.22	22,657.78
2018 Jun	782,628	ETS_auto_log	748,182.07	34,445.93
2018 Jul	837,740	ETS_auto_log	883,361.05	-45,621.05
2018 Aug	936,644	ETS_auto_log	951,717.66	-15,073.66
2018 Sep	806,267	ETS_auto_log	779,589.60	26,677.40
2018 Oct	721,989	ETS_auto_log	690,117.10	31,871.90
2018 Nov	575,096	ETS_auto_log	541,233.83	33,862.17
2018 Dec	496,993	ETS_auto_log	483,723.77	13,269.23
2019 Jan	486,306	ETS_auto_log	540,924.27	-54,618.27
2019 Feb	498,081	ETS_auto_log	531,426.63	-33,345.63
2019 Mar	606,616	ETS_auto_log	613,715.45	-7,099.45
2019 Apr	608,322	ETS_auto_log	675,360.76	-67,038.76
2019 May	665,724	ETS_auto_log	657,128.70	8,595.30
2019 Jun	714,041	ETS_auto_log	662,380.24	51,660.76
2019 Jul	747,112	ETS_auto_log	808,367.25	-61,255.25
2019 Aug	828,426	ETS_auto_log	844,200.29	-15,774.29
2019 Sep	719,254	ETS_auto_log	695,543.18	23,710.82
2019 Oct	629,555	ETS_auto_log	623,555.02	5,999.98
2019 Nov	508,290	ETS_auto_log	475,669.76	32,620.24
2019 Dec	445,470	ETS_auto_log	426,521.94	18,948.06
2020 Jan	488,461	ETS_auto_log	480,776.74	7,684.26
2020 Feb	540,254	ETS_auto_log	534,035.06	6,218.94
2020 Mar	297,649	ETS_auto_log	665,168.90	-367,519.90
2020 Apr	2,191	ETS_auto_log	542,734.29	-540,543.29
2020 May	2,955	ETS_auto_log	17.69	2,937.31
2020 Jun	14,932	ETS_auto_log	3,297.00	11,635.00
2020 Jul	95,576	ETS_auto_log	16,823.45	78,752.55
2020 Aug	240,322	ETS_auto_log	109,049.64	131,272.36
2020 Sep	251,221	ETS_auto_log	275,039.16	-23,818.16
2020 Oct	253,895	ETS_auto_log	287,530.07	-33,635.07
2020 Nov	116,634	ETS_auto_log	290,481.37	-173,847.37
2020 Dec	137,446	ETS_auto_log	133,733.70	3,712.30
2021 Jan	93,013	ETS_auto_log	157,596.87	-64,583.87
2021 Feb	40,883	ETS_auto_log	106,710.52	-65,827.52
2021 Mar	60,163	ETS_auto_log	47,002.68	13,160.32
2021 Apr	95,116	ETS_auto_log	69,193.00	25,923.00
2021 May	179,599	ETS_auto_log	109,471.50	70,127.50
2021 Jun	321,985	ETS_auto_log	207,001.22	114,983.78
2021 Jul	552,399	ETS_auto_log	371,557.27	180,841.73
2021 Aug	780,123	ETS_auto_log	638,097.75	142,025.25
2021 Sep	697,572	ETS_auto_log	901,454.74	-203,882.74
2021 Oct	655,682	ETS_auto_log	806,017.09	-150,335.09
2021 Nov	521,638	ETS_auto_log	757,204.66	-235,566.66
2021 Dec	397,592	ETS_auto_log	602,444.39	-204,852.39
2022 Jan	341,744	ETS_auto_log	459,305.03	-117,561.03
2022 Feb	391,699	ETS_auto_log	394,781.91	-3,082.91
2022 Mar	569,482	ETS_auto_log	452,456.64	117,025.36
2022 Apr	727,326	ETS_auto_log	658,168.22	69,157.78
2022 May	779,426	ETS_auto_log	840,550.39	-61,124.39
2022 Jun	833,955	ETS_auto_log	900,790.83	-66,835.83
2010 Jan	319,379	HWA	327,508.10	-8,129.10
2010 Feb	329,697	HWA	354,438.25	-24,741.25
2010 Mar	388,978	HWA	421,701.40	-32,723.40
2010 Apr	427,950	HWA	434,422.48	-6,472.48
2010 May	431,385	HWA	383,410.95	47,974.05
2010 Jun	432,522	HWA	403,575.14	28,946.86
2010 Jul	492,382	HWA	477,278.70	15,103.30
2010 Aug	624,383	HWA	591,341.27	33,041.73
2010 Sep	496,609	HWA	510,288.44	-13,679.44
2010 Oct	450,841	HWA	455,713.31	-4,872.31
2010 Nov	327,330	HWA	374,267.94	-46,937.94
2010 Dec	272,069	HWA	285,355.00	-13,286.00
2011 Jan	286,010	HWA	292,157.46	-6,147.46
2011 Feb	319,015	HWA	319,343.14	-328.14
2011 Mar	448,224	HWA	411,310.35	36,913.65
2011 Apr	517,979	HWA	485,827.50	32,151.50
2011 May	575,401	HWA	482,807.07	92,593.93
2011 Jun	519,950	HWA	549,118.68	-29,168.68
2011 Jul	589,288	HWA	563,303.37	25,984.63
2011 Aug	678,877	HWA	688,256.97	-9,379.97
2011 Sep	577,108	HWA	559,513.18	17,594.82
2011 Oct	471,268	HWA	524,713.10	-53,445.10
2011 Nov	319,900	HWA	380,672.59	-60,772.59
2011 Dec	262,266	HWA	269,036.05	-6,770.05
2012 Jan	289,312	HWA	277,910.04	11,401.96
2012 Feb	329,299	HWA	318,707.68	10,591.32
2012 Mar	399,988	HWA	425,797.05	-25,809.05
2012 Apr	508,131	HWA	447,480.36	60,650.64
2012 May	521,638	HWA	483,392.12	38,245.88
2012 Jun	509,865	HWA	489,485.95	20,379.05
2012 Jul	602,837	HWA	548,955.18	53,881.82
2012 Aug	681,135	HWA	696,663.93	-15,528.93
2012 Sep	562,007	HWA	560,441.55	1,565.45
2012 Oct	468,951	HWA	503,551.75	-34,600.75
2012 Nov	350,902	HWA	363,656.74	-12,754.74
2012 Dec	283,620	HWA	299,056.66	-15,436.66
2013 Jan	322,235	HWA	298,588.32	23,646.68
2013 Feb	365,343	HWA	352,269.66	13,073.34
2013 Mar	462,258	HWA	458,961.37	3,296.63
2013 Apr	516,930	HWA	517,006.14	-76.14
2013 May	608,081	HWA	505,247.53	102,833.47
2013 Jun	578,633	HWA	572,969.50	5,663.50
2013 Jul	677,083	HWA	626,632.58	50,450.42
2013 Aug	775,941	HWA	774,921.65	1,019.35
2013 Sep	639,271	HWA	658,808.07	-19,537.07
2013 Oct	535,649	HWA	573,104.10	-37,455.10
2013 Nov	390,742	HWA	422,867.66	-32,125.66
2013 Dec	342,783	HWA	334,774.38	8,008.62
2014 Jan	374,568	HWA	358,468.30	16,099.70
2014 Feb	401,859	HWA	402,279.56	-420.56
2014 Mar	503,533	HWA	499,689.21	3,843.79
2014 Apr	557,275	HWA	559,479.05	-2,204.05
2014 May	610,148	HWA	563,386.25	46,761.75
2014 Jun	595,332	HWA	590,387.55	4,944.45
2014 Jul	687,207	HWA	658,921.45	28,285.55
2014 Aug	787,020	HWA	776,517.69	10,502.31
2014 Sep	652,671	HWA	665,126.83	-12,455.83
2014 Oct	554,671	HWA	578,257.67	-23,586.67
2014 Nov	415,750	HWA	437,553.98	-21,803.98
2014 Dec	366,832	HWA	358,763.37	8,068.63
2015 Jan	399,040	HWA	384,521.85	14,518.15
2015 Feb	442,963	HWA	429,568.64	13,394.36
2015 Mar	545,523	HWA	543,649.62	1,873.38
2015 Apr	586,230	HWA	606,652.46	-20,422.46
2015 May	628,998	HWA	601,047.84	27,950.16
2015 Jun	654,715	HWA	604,814.32	49,900.68
2015 Jul	766,557	HWA	712,453.29	54,103.71
2015 Aug	829,230	HWA	852,169.48	-22,939.48
2015 Sep	696,849	HWA	699,751.97	-2,902.97
2015 Oct	597,629	HWA	618,286.26	-20,657.26
2015 Nov	475,257	HWA	476,193.84	-936.84
2015 Dec	407,035	HWA	419,535.67	-12,500.67
2016 Jan	448,784	HWA	425,575.99	23,208.01
2016 Feb	506,179	HWA	482,119.30	24,059.70
2016 Mar	611,987	HWA	606,922.73	5,064.27
2016 Apr	663,878	HWA	669,389.16	-5,511.16
2016 May	726,980	HWA	689,663.33	37,316.67
2016 Jun	759,256	HWA	712,519.06	46,736.94
2016 Jul	849,148	HWA	831,295.32	17,852.68
2016 Aug	891,091	HWA	938,945.19	-47,854.19
2016 Sep	768,042	HWA	765,194.46	2,847.54
2016 Oct	702,530	HWA	681,709.01	20,820.99
2016 Nov	545,468	HWA	578,263.71	-32,795.71
2016 Dec	457,565	HWA	485,615.05	-28,050.05
2017 Jan	503,654	HWA	477,390.98	26,263.02
2017 Feb	541,368	HWA	537,876.77	3,491.23
2017 Mar	647,679	HWA	637,196.86	10,482.14
2017 Apr	710,409	HWA	699,718.07	10,690.93
2017 May	745,096	HWA	744,460.11	635.89
2017 Jun	794,118	HWA	731,477.56	62,640.44
2017 Jul	864,476	HWA	866,318.02	-1,842.02
2017 Aug	939,077	HWA	947,060.36	-7,983.36
2017 Sep	818,705	HWA	810,311.80	8,393.20
2017 Oct	734,287	HWA	729,861.52	4,425.48
2017 Nov	582,743	HWA	601,819.23	-19,076.23
2017 Dec	478,377	HWA	520,582.75	-42,205.75
2018 Jan	534,281	HWA	502,461.90	31,819.10
2018 Feb	555,841	HWA	568,659.89	-12,818.89
2018 Mar	652,082	HWA	651,834.46	247.54
2018 Apr	689,214	HWA	709,821.88	-20,607.88
2018 May	755,491	HWA	726,029.35	29,461.65
2018 Jun	782,628	HWA	752,356.93	30,271.07
2018 Jul	837,740	HWA	857,418.11	-19,678.11
2018 Aug	936,644	HWA	921,535.62	15,108.38
2018 Sep	806,267	HWA	811,062.27	-4,795.27
2018 Oct	721,989	HWA	719,516.41	2,472.59
2018 Nov	575,096	HWA	585,097.49	-10,001.49
2018 Dec	496,993	HWA	509,287.05	-12,294.05
2019 Jan	486,306	HWA	528,310.08	-42,004.08
2019 Feb	498,081	HWA	520,650.75	-22,569.75
2019 Mar	606,616	HWA	593,432.75	13,183.25
2019 Apr	608,322	HWA	662,112.80	-53,790.80
2019 May	665,724	HWA	658,714.81	7,009.19
2019 Jun	714,041	HWA	668,127.08	45,913.92
2019 Jul	747,112	HWA	789,284.92	-42,172.92
2019 Aug	828,426	HWA	835,066.81	-6,640.81
2019 Sep	719,254	HWA	701,086.04	18,167.96
2019 Oct	629,555	HWA	629,023.04	531.96
2019 Nov	508,290	HWA	490,041.39	18,248.61
2019 Dec	445,470	HWA	437,878.96	7,591.04
2020 Jan	488,461	HWA	475,764.11	12,696.89
2020 Feb	540,254	HWA	522,336.25	17,917.75
2020 Mar	297,649	HWA	640,303.77	-342,654.77
2020 Apr	2,191	HWA	515,348.72	-513,157.72
2020 May	2,955	HWA	-29,817.33	32,772.33
2020 Jun	14,932	HWA	-72,012.56	86,944.56
2020 Jul	95,576	HWA	25,257.81	70,318.19
2020 Aug	240,322	HWA	127,109.20	113,212.80
2020 Sep	251,221	HWA	90,846.06	160,374.94
2020 Oct	253,895	HWA	153,763.66	100,131.34
2020 Nov	116,634	HWA	116,073.38	560.62
2020 Dec	137,446	HWA	48,279.69	89,166.31
2021 Jan	93,013	HWA	174,827.80	-81,814.80
2021 Feb	40,883	HWA	126,772.04	-85,889.04
2021 Mar	60,163	HWA	96,762.90	-36,599.90
2021 Apr	95,116	HWA	65,473.52	29,642.48
2021 May	179,599	HWA	135,394.97	44,204.03
2021 Jun	321,985	HWA	189,264.47	132,720.53
2021 Jul	552,399	HWA	401,174.78	151,224.22
2021 Aug	780,123	HWA	642,262.43	137,860.57
2021 Sep	697,572	HWA	655,513.21	42,058.79
2021 Oct	655,682	HWA	624,961.85	30,720.15
2021 Nov	521,638	HWA	528,412.76	-6,774.76
2021 Dec	397,592	HWA	483,409.55	-85,817.55
2022 Jan	341,744	HWA	422,132.52	-80,388.52
2022 Feb	391,699	HWA	364,755.62	26,943.38
2022 Mar	569,482	HWA	442,425.50	127,056.50
2022 Apr	727,326	HWA	576,466.34	150,859.66
2022 May	779,426	HWA	811,884.10	-32,458.10
2022 Jun	833,955	HWA	831,250.68	2,704.32
2010 Jan	319,379	HWA_log	326,441.44	-7,062.44
2010 Feb	329,697	HWA_log	365,575.85	-35,878.85
2010 Mar	388,978	HWA_log	462,293.70	-73,315.70
2010 Apr	427,950	HWA_log	470,641.50	-42,691.50
2010 May	431,385	HWA_log	429,568.79	1,816.21
2010 Jun	432,522	HWA_log	408,925.18	23,596.82
2010 Jul	492,382	HWA_log	447,133.18	45,248.82
2010 Aug	624,383	HWA_log	541,192.34	83,190.66
2010 Sep	496,609	HWA_log	444,919.12	51,689.88
2010 Oct	450,841	HWA_log	421,902.39	28,938.61
2010 Nov	327,330	HWA_log	334,616.17	-7,286.17
2010 Dec	272,069	HWA_log	294,636.43	-22,567.43
2011 Jan	286,010	HWA_log	301,884.14	-15,874.14
2011 Feb	319,015	HWA_log	315,625.66	3,389.34
2011 Mar	448,224	HWA_log	402,825.09	45,398.91
2011 Apr	517,979	HWA_log	450,869.10	67,109.90
2011 May	575,401	HWA_log	464,388.48	111,012.52
2011 Jun	519,950	HWA_log	481,574.83	38,375.17
2011 Jul	589,288	HWA_log	577,229.11	12,058.89
2011 Aug	678,877	HWA_log	691,138.93	-12,261.93
2011 Sep	577,108	HWA_log	539,609.55	37,498.45
2011 Oct	471,268	HWA_log	488,443.70	-17,175.70
2011 Nov	319,900	HWA_log	357,143.18	-37,243.18
2011 Dec	262,266	HWA_log	299,261.39	-36,995.39
2012 Jan	289,312	HWA_log	302,464.86	-13,152.86
2012 Feb	329,299	HWA_log	331,029.16	-1,730.16
2012 Mar	399,988	HWA_log	445,148.33	-45,160.33
2012 Apr	508,131	HWA_log	480,975.45	27,155.55
2012 May	521,638	HWA_log	514,915.31	6,722.69
2012 Jun	509,865	HWA_log	466,106.90	43,758.10
2012 Jul	602,837	HWA_log	540,974.38	61,862.62
2012 Aug	681,135	HWA_log	647,163.41	33,971.59
2012 Sep	562,007	HWA_log	547,664.44	14,342.56
2012 Oct	468,951	HWA_log	460,261.75	8,689.25
2012 Nov	350,902	HWA_log	326,749.27	24,152.73
2012 Dec	283,620	HWA_log	286,967.53	-3,347.53
2013 Jan	322,235	HWA_log	325,275.45	-3,040.45
2013 Feb	365,343	HWA_log	369,539.19	-4,196.19
2013 Mar	462,258	HWA_log	460,412.23	1,845.77
2013 Apr	516,930	HWA_log	575,663.32	-58,733.32
2013 May	608,081	HWA_log	572,913.84	35,167.16
2013 Jun	578,633	HWA_log	553,671.48	24,961.52
2013 Jul	677,083	HWA_log	644,372.90	32,710.10
2013 Aug	775,941	HWA_log	730,091.17	45,849.83
2013 Sep	639,271	HWA_log	611,722.42	27,548.58
2013 Oct	535,649	HWA_log	516,227.06	19,421.94
2013 Nov	390,742	HWA_log	381,834.50	8,907.50
2013 Dec	342,783	HWA_log	313,687.46	29,095.54
2014 Jan	374,568	HWA_log	373,473.54	1,094.46
2014 Feb	401,859	HWA_log	429,865.65	-28,006.65
2014 Mar	503,533	HWA_log	511,140.40	-7,607.40
2014 Apr	557,275	HWA_log	594,544.85	-37,269.85
2014 May	610,148	HWA_log	661,512.73	-51,364.73
2014 Jun	595,332	HWA_log	621,984.35	-26,652.35
2014 Jul	687,207	HWA_log	703,781.37	-16,574.37
2014 Aug	787,020	HWA_log	767,105.71	19,914.29
2014 Sep	652,671	HWA_log	634,651.13	18,019.87
2014 Oct	554,671	HWA_log	528,945.10	25,725.90
2014 Nov	415,750	HWA_log	389,668.49	26,081.51
2014 Dec	366,832	HWA_log	337,511.49	29,320.51
2015 Jan	399,040	HWA_log	377,867.68	21,172.32
2015 Feb	442,963	HWA_log	451,376.13	-8,413.13
2015 Mar	545,523	HWA_log	566,137.78	-20,614.78
2015 Apr	586,230	HWA_log	606,637.19	-20,407.19
2015 May	628,998	HWA_log	675,853.43	-46,855.43
2015 Jun	654,715	HWA_log	652,335.64	2,379.36
2015 Jul	766,557	HWA_log	759,375.82	7,181.18
2015 Aug	829,230	HWA_log	860,416.33	-31,186.33
2015 Sep	696,849	HWA_log	678,496.86	18,352.14
2015 Oct	597,629	HWA_log	576,987.78	20,641.22
2015 Nov	475,257	HWA_log	449,314.60	25,942.40
2015 Dec	407,035	HWA_log	392,814.89	14,220.11
2016 Jan	448,784	HWA_log	453,501.76	-4,717.76
2016 Feb	506,179	HWA_log	466,658.17	39,520.83
2016 Mar	611,987	HWA_log	617,600.35	-5,613.35
2016 Apr	663,878	HWA_log	699,939.46	-36,061.46
2016 May	726,980	HWA_log	729,906.01	-2,926.01
2016 Jun	759,256	HWA_log	703,755.77	55,500.23
2016 Jul	849,148	HWA_log	841,375.55	7,772.45
2016 Aug	891,091	HWA_log	925,554.67	-34,463.67
2016 Sep	768,042	HWA_log	748,484.53	19,557.47
2016 Oct	702,530	HWA_log	641,716.00	60,814.00
2016 Nov	545,468	HWA_log	538,021.77	7,446.23
2016 Dec	457,565	HWA_log	451,342.53	6,222.47
2017 Jan	503,654	HWA_log	488,601.82	15,052.18
2017 Feb	541,368	HWA_log	560,090.12	-18,722.12
2017 Mar	647,679	HWA_log	664,034.77	-16,355.77
2017 Apr	710,409	HWA_log	765,042.48	-54,633.48
2017 May	745,096	HWA_log	776,408.64	-31,312.64
2017 Jun	794,118	HWA_log	725,186.57	68,931.43
2017 Jul	864,476	HWA_log	866,057.54	-1,581.54
2017 Aug	939,077	HWA_log	992,020.45	-52,943.45
2017 Sep	818,705	HWA_log	806,012.73	12,692.27
2017 Oct	734,287	HWA_log	705,825.67	28,461.33
2017 Nov	582,743	HWA_log	547,317.33	35,425.67
2017 Dec	478,377	HWA_log	479,949.99	-1,572.99
2018 Jan	534,281	HWA_log	505,705.60	28,575.40
2018 Feb	555,841	HWA_log	593,999.26	-38,158.26
2018 Mar	652,082	HWA_log	692,309.82	-40,227.82
2018 Apr	689,214	HWA_log	742,523.03	-53,309.03
2018 May	755,491	HWA_log	780,599.38	-25,108.38
2018 Jun	782,628	HWA_log	810,187.65	-27,559.65
2018 Jul	837,740	HWA_log	885,032.00	-47,292.00
2018 Aug	936,644	HWA_log	923,110.78	13,533.22
2018 Sep	806,267	HWA_log	816,029.02	-9,762.02
2018 Oct	721,989	HWA_log	706,460.80	15,528.20
2018 Nov	575,096	HWA_log	543,821.07	31,274.93
2018 Dec	496,993	HWA_log	469,356.76	27,636.24
2019 Jan	486,306	HWA_log	532,243.01	-45,937.01
2019 Feb	498,081	HWA_log	534,076.50	-35,995.50
2019 Mar	606,616	HWA_log	618,106.87	-11,490.87
2019 Apr	608,322	HWA_log	662,441.16	-54,119.16
2019 May	665,724	HWA_log	700,266.41	-34,542.41
2019 Jun	714,041	HWA_log	721,752.38	-7,711.38
2019 Jul	747,112	HWA_log	799,130.72	-52,018.72
2019 Aug	828,426	HWA_log	865,431.33	-37,005.33
2019 Sep	719,254	HWA_log	743,510.15	-24,256.15
2019 Oct	629,555	HWA_log	664,069.46	-34,514.46
2019 Nov	508,290	HWA_log	506,748.76	1,541.24
2019 Dec	445,470	HWA_log	424,850.11	20,619.89
2020 Jan	488,461	HWA_log	452,280.90	36,180.10
2020 Feb	540,254	HWA_log	461,985.64	78,268.36
2020 Mar	297,649	HWA_log	620,544.08	-322,895.08
2020 Apr	2,191	HWA_log	525,529.79	-523,338.79
2020 May	2,955	HWA_log	6,373.71	-3,418.71
2020 Jun	14,932	HWA_log	2,147.00	12,785.00
2020 Jul	95,576	HWA_log	15,499.55	80,076.45
2020 Aug	240,322	HWA_log	117,960.21	122,361.79
2020 Sep	251,221	HWA_log	238,998.65	12,222.35
2020 Oct	253,895	HWA_log	226,684.20	27,210.80
2020 Nov	116,634	HWA_log	215,918.83	-99,284.83
2020 Dec	137,446	HWA_log	119,888.88	17,557.12
2021 Jan	93,013	HWA_log	169,276.03	-76,263.03
2021 Feb	40,883	HWA_log	103,456.59	-62,573.59
2021 Mar	60,163	HWA_log	57,014.32	3,148.68
2021 Apr	95,116	HWA_log	41,968.65	53,147.35
2021 May	179,599	HWA_log	122,505.35	57,093.65
2021 Jun	321,985	HWA_log	231,098.92	90,886.08
2021 Jul	552,399	HWA_log	454,941.98	97,457.02
2021 Aug	780,123	HWA_log	732,991.82	47,131.18
2021 Sep	697,572	HWA_log	771,200.37	-73,628.37
2021 Oct	655,682	HWA_log	728,971.42	-73,289.42
2021 Nov	521,638	HWA_log	493,756.66	27,881.34
2021 Dec	397,592	HWA_log	471,204.33	-73,612.33
2022 Jan	341,744	HWA_log	437,454.39	-95,710.39
2022 Feb	391,699	HWA_log	352,861.54	38,837.46
2022 Mar	569,482	HWA_log	540,573.71	28,908.29
2022 Apr	727,326	HWA_log	460,455.91	266,870.09
2022 May	779,426	HWA_log	1,092,618.19	-313,192.19
2022 Jun	833,955	HWA_log	1,206,962.87	-373,007.87
2010 Jan	319,379	Naive	308,080.00	11,299.00
2010 Feb	329,697	Naive	319,379.00	10,318.00
2010 Mar	388,978	Naive	329,697.00	59,281.00
2010 Apr	427,950	Naive	388,978.00	38,972.00
2010 May	431,385	Naive	427,950.00	3,435.00
2010 Jun	432,522	Naive	431,385.00	1,137.00
2010 Jul	492,382	Naive	432,522.00	59,860.00
2010 Aug	624,383	Naive	492,382.00	132,001.00
2010 Sep	496,609	Naive	624,383.00	-127,774.00
2010 Oct	450,841	Naive	496,609.00	-45,768.00
2010 Nov	327,330	Naive	450,841.00	-123,511.00
2010 Dec	272,069	Naive	327,330.00	-55,261.00
2011 Jan	286,010	Naive	272,069.00	13,941.00
2011 Feb	319,015	Naive	286,010.00	33,005.00
2011 Mar	448,224	Naive	319,015.00	129,209.00
2011 Apr	517,979	Naive	448,224.00	69,755.00
2011 May	575,401	Naive	517,979.00	57,422.00
2011 Jun	519,950	Naive	575,401.00	-55,451.00
2011 Jul	589,288	Naive	519,950.00	69,338.00
2011 Aug	678,877	Naive	589,288.00	89,589.00
2011 Sep	577,108	Naive	678,877.00	-101,769.00
2011 Oct	471,268	Naive	577,108.00	-105,840.00
2011 Nov	319,900	Naive	471,268.00	-151,368.00
2011 Dec	262,266	Naive	319,900.00	-57,634.00
2012 Jan	289,312	Naive	262,266.00	27,046.00
2012 Feb	329,299	Naive	289,312.00	39,987.00
2012 Mar	399,988	Naive	329,299.00	70,689.00
2012 Apr	508,131	Naive	399,988.00	108,143.00
2012 May	521,638	Naive	508,131.00	13,507.00
2012 Jun	509,865	Naive	521,638.00	-11,773.00
2012 Jul	602,837	Naive	509,865.00	92,972.00
2012 Aug	681,135	Naive	602,837.00	78,298.00
2012 Sep	562,007	Naive	681,135.00	-119,128.00
2012 Oct	468,951	Naive	562,007.00	-93,056.00
2012 Nov	350,902	Naive	468,951.00	-118,049.00
2012 Dec	283,620	Naive	350,902.00	-67,282.00
2013 Jan	322,235	Naive	283,620.00	38,615.00
2013 Feb	365,343	Naive	322,235.00	43,108.00
2013 Mar	462,258	Naive	365,343.00	96,915.00
2013 Apr	516,930	Naive	462,258.00	54,672.00
2013 May	608,081	Naive	516,930.00	91,151.00
2013 Jun	578,633	Naive	608,081.00	-29,448.00
2013 Jul	677,083	Naive	578,633.00	98,450.00
2013 Aug	775,941	Naive	677,083.00	98,858.00
2013 Sep	639,271	Naive	775,941.00	-136,670.00
2013 Oct	535,649	Naive	639,271.00	-103,622.00
2013 Nov	390,742	Naive	535,649.00	-144,907.00
2013 Dec	342,783	Naive	390,742.00	-47,959.00
2014 Jan	374,568	Naive	342,783.00	31,785.00
2014 Feb	401,859	Naive	374,568.00	27,291.00
2014 Mar	503,533	Naive	401,859.00	101,674.00
2014 Apr	557,275	Naive	503,533.00	53,742.00
2014 May	610,148	Naive	557,275.00	52,873.00
2014 Jun	595,332	Naive	610,148.00	-14,816.00
2014 Jul	687,207	Naive	595,332.00	91,875.00
2014 Aug	787,020	Naive	687,207.00	99,813.00
2014 Sep	652,671	Naive	787,020.00	-134,349.00
2014 Oct	554,671	Naive	652,671.00	-98,000.00
2014 Nov	415,750	Naive	554,671.00	-138,921.00
2014 Dec	366,832	Naive	415,750.00	-48,918.00
2015 Jan	399,040	Naive	366,832.00	32,208.00
2015 Feb	442,963	Naive	399,040.00	43,923.00
2015 Mar	545,523	Naive	442,963.00	102,560.00
2015 Apr	586,230	Naive	545,523.00	40,707.00
2015 May	628,998	Naive	586,230.00	42,768.00
2015 Jun	654,715	Naive	628,998.00	25,717.00
2015 Jul	766,557	Naive	654,715.00	111,842.00
2015 Aug	829,230	Naive	766,557.00	62,673.00
2015 Sep	696,849	Naive	829,230.00	-132,381.00
2015 Oct	597,629	Naive	696,849.00	-99,220.00
2015 Nov	475,257	Naive	597,629.00	-122,372.00
2015 Dec	407,035	Naive	475,257.00	-68,222.00
2016 Jan	448,784	Naive	407,035.00	41,749.00
2016 Feb	506,179	Naive	448,784.00	57,395.00
2016 Mar	611,987	Naive	506,179.00	105,808.00
2016 Apr	663,878	Naive	611,987.00	51,891.00
2016 May	726,980	Naive	663,878.00	63,102.00
2016 Jun	759,256	Naive	726,980.00	32,276.00
2016 Jul	849,148	Naive	759,256.00	89,892.00
2016 Aug	891,091	Naive	849,148.00	41,943.00
2016 Sep	768,042	Naive	891,091.00	-123,049.00
2016 Oct	702,530	Naive	768,042.00	-65,512.00
2016 Nov	545,468	Naive	702,530.00	-157,062.00
2016 Dec	457,565	Naive	545,468.00	-87,903.00
2017 Jan	503,654	Naive	457,565.00	46,089.00
2017 Feb	541,368	Naive	503,654.00	37,714.00
2017 Mar	647,679	Naive	541,368.00	106,311.00
2017 Apr	710,409	Naive	647,679.00	62,730.00
2017 May	745,096	Naive	710,409.00	34,687.00
2017 Jun	794,118	Naive	745,096.00	49,022.00
2017 Jul	864,476	Naive	794,118.00	70,358.00
2017 Aug	939,077	Naive	864,476.00	74,601.00
2017 Sep	818,705	Naive	939,077.00	-120,372.00
2017 Oct	734,287	Naive	818,705.00	-84,418.00
2017 Nov	582,743	Naive	734,287.00	-151,544.00
2017 Dec	478,377	Naive	582,743.00	-104,366.00
2018 Jan	534,281	Naive	478,377.00	55,904.00
2018 Feb	555,841	Naive	534,281.00	21,560.00
2018 Mar	652,082	Naive	555,841.00	96,241.00
2018 Apr	689,214	Naive	652,082.00	37,132.00
2018 May	755,491	Naive	689,214.00	66,277.00
2018 Jun	782,628	Naive	755,491.00	27,137.00
2018 Jul	837,740	Naive	782,628.00	55,112.00
2018 Aug	936,644	Naive	837,740.00	98,904.00
2018 Sep	806,267	Naive	936,644.00	-130,377.00
2018 Oct	721,989	Naive	806,267.00	-84,278.00
2018 Nov	575,096	Naive	721,989.00	-146,893.00
2018 Dec	496,993	Naive	575,096.00	-78,103.00
2019 Jan	486,306	Naive	496,993.00	-10,687.00
2019 Feb	498,081	Naive	486,306.00	11,775.00
2019 Mar	606,616	Naive	498,081.00	108,535.00
2019 Apr	608,322	Naive	606,616.00	1,706.00
2019 May	665,724	Naive	608,322.00	57,402.00
2019 Jun	714,041	Naive	665,724.00	48,317.00
2019 Jul	747,112	Naive	714,041.00	33,071.00
2019 Aug	828,426	Naive	747,112.00	81,314.00
2019 Sep	719,254	Naive	828,426.00	-109,172.00
2019 Oct	629,555	Naive	719,254.00	-89,699.00
2019 Nov	508,290	Naive	629,555.00	-121,265.00
2019 Dec	445,470	Naive	508,290.00	-62,820.00
2020 Jan	488,461	Naive	445,470.00	42,991.00
2020 Feb	540,254	Naive	488,461.00	51,793.00
2020 Mar	297,649	Naive	540,254.00	-242,605.00
2020 Apr	2,191	Naive	297,649.00	-295,458.00
2020 May	2,955	Naive	2,191.00	764.00
2020 Jun	14,932	Naive	2,955.00	11,977.00
2020 Jul	95,576	Naive	14,932.00	80,644.00
2020 Aug	240,322	Naive	95,576.00	144,746.00
2020 Sep	251,221	Naive	240,322.00	10,899.00
2020 Oct	253,895	Naive	251,221.00	2,674.00
2020 Nov	116,634	Naive	253,895.00	-137,261.00
2020 Dec	137,446	Naive	116,634.00	20,812.00
2021 Jan	93,013	Naive	137,446.00	-44,433.00
2021 Feb	40,883	Naive	93,013.00	-52,130.00
2021 Mar	60,163	Naive	40,883.00	19,280.00
2021 Apr	95,116	Naive	60,163.00	34,953.00
2021 May	179,599	Naive	95,116.00	84,483.00
2021 Jun	321,985	Naive	179,599.00	142,386.00
2021 Jul	552,399	Naive	321,985.00	230,414.00
2021 Aug	780,123	Naive	552,399.00	227,724.00
2021 Sep	697,572	Naive	780,123.00	-82,551.00
2021 Oct	655,682	Naive	697,572.00	-41,890.00
2021 Nov	521,638	Naive	655,682.00	-134,044.00
2021 Dec	397,592	Naive	521,638.00	-124,046.00
2022 Jan	341,744	Naive	397,592.00	-55,848.00
2022 Feb	391,699	Naive	341,744.00	49,955.00
2022 Mar	569,482	Naive	391,699.00	177,783.00
2022 Apr	727,326	Naive	569,482.00	157,844.00
2022 May	779,426	Naive	727,326.00	52,100.00
2022 Jun	833,955	Naive	779,426.00	54,529.00
2010 Jan	319,379	Naive_log	310,979.74	8,399.26
2010 Feb	329,697	Naive_log	322,374.61	7,322.39
2010 Mar	388,978	Naive_log	332,707.83	56,270.17
2010 Apr	427,950	Naive_log	392,572.01	35,377.99
2010 May	431,385	Naive_log	431,867.18	-482.18
2010 Jun	432,522	Naive_log	435,310.52	-2,788.52
2010 Jul	492,382	Naive_log	436,432.95	55,949.05
2010 Aug	624,383	Naive_log	496,832.99	127,550.01
2010 Sep	496,609	Naive_log	630,100.10	-133,491.10
2010 Oct	450,841	Naive_log	501,264.62	-50,423.62
2010 Nov	327,330	Naive_log	455,085.11	-127,755.11
2010 Dec	272,069	Naive_log	330,509.97	-58,440.97
2011 Jan	286,010	Naive_log	274,739.61	11,270.39
2011 Feb	319,015	Naive_log	288,807.01	30,207.99
2011 Mar	448,224	Naive_log	322,147.81	126,076.19
2011 Apr	517,979	Naive_log	452,761.91	65,217.09
2011 May	575,401	Naive_log	523,236.20	52,164.80
2011 Jun	519,950	Naive_log	581,265.07	-61,315.07
2011 Jul	589,288	Naive_log	525,248.16	64,039.84
2011 Aug	678,877	Naive_log	595,290.76	83,586.24
2011 Sep	577,108	Naive_log	685,760.03	-108,652.03
2011 Oct	471,268	Naive_log	583,016.65	-111,748.65
2011 Nov	319,900	Naive_log	476,159.22	-156,259.22
2011 Dec	262,266	Naive_log	323,389.10	-61,123.10
2012 Jan	289,312	Naive_log	265,169.66	24,142.34
2012 Feb	329,299	Naive_log	292,506.48	36,792.52
2012 Mar	399,988	Naive_log	332,874.52	67,113.48
2012 Apr	508,131	Naive_log	404,393.21	103,737.79
2012 May	521,638	Naive_log	513,790.84	7,847.16
2012 Jun	509,865	Naive_log	527,446.02	-17,581.02
2012 Jul	602,837	Naive_log	515,533.90	87,303.10
2012 Aug	681,135	Naive_log	609,492.88	71,642.12
2012 Sep	562,007	Naive_log	688,574.33	-126,567.33
2012 Oct	468,951	Naive_log	568,218.88	-99,267.88
2012 Nov	350,902	Naive_log	474,168.36	-123,266.36
2012 Dec	283,620	Naive_log	354,907.22	-71,287.22
2013 Jan	322,235	Naive_log	286,901.77	35,333.23
2013 Feb	365,343	Naive_log	325,976.27	39,366.73
2013 Mar	462,258	Naive_log	369,544.06	92,713.94
2013 Apr	516,930	Naive_log	467,667.46	49,262.54
2013 May	608,081	Naive_log	522,959.46	85,121.54
2013 Jun	578,633	Naive_log	615,230.87	-36,597.87
2013 Jul	677,083	Naive_log	585,425.08	91,657.92
2013 Aug	775,941	Naive_log	684,975.32	90,965.68
2013 Sep	639,271	Naive_log	784,909.06	-145,638.06
2013 Oct	535,649	Naive_log	646,746.65	-111,097.65
2013 Nov	390,742	Naive_log	541,911.72	-151,169.72
2013 Dec	342,783	Naive_log	395,458.53	-52,675.53
2014 Jan	374,568	Naive_log	346,944.05	27,623.95
2014 Feb	401,859	Naive_log	379,091.21	22,767.79
2014 Mar	503,533	Naive_log	406,689.50	96,843.50
2014 Apr	557,275	Naive_log	509,673.85	47,601.15
2014 May	610,148	Naive_log	564,073.96	46,074.04
2014 Jun	595,332	Naive_log	617,564.93	-22,232.93
2014 Jul	687,207	Naive_log	602,524.56	84,682.44
2014 Aug	787,020	Naive_log	695,460.63	91,559.37
2014 Sep	652,671	Naive_log	796,458.67	-143,787.67
2014 Oct	554,671	Naive_log	660,593.05	-105,922.05
2014 Nov	415,750	Naive_log	561,371.21	-145,621.21
2014 Dec	366,832	Naive_log	420,892.07	-54,060.07
2015 Jan	399,040	Naive_log	371,368.17	27,671.83
2015 Feb	442,963	Naive_log	403,986.12	38,976.88
2015 Mar	545,523	Naive_log	448,420.07	97,102.93
2015 Apr	586,230	Naive_log	552,342.35	33,887.65
2015 May	628,998	Naive_log	593,564.84	35,433.16
2015 Jun	654,715	Naive_log	636,880.34	17,834.66
2015 Jul	766,557	Naive_log	662,893.56	103,663.44
2015 Aug	829,230	Naive_log	776,056.04	53,173.96
2015 Sep	696,849	Naive_log	839,386.69	-142,537.69
2015 Oct	597,629	Naive_log	705,462.51	-107,833.51
2015 Nov	475,257	Naive_log	604,989.56	-129,732.56
2015 Dec	407,035	Naive_log	481,185.29	-74,150.29
2016 Jan	448,784	Naive_log	412,147.69	36,636.31
2016 Feb	506,179	Naive_log	454,438.30	51,740.70
2016 Mar	611,987	Naive_log	512,472.48	99,514.52
2016 Apr	663,878	Naive_log	619,634.47	44,243.53
2016 May	726,980	Naive_log	672,160.61	54,819.39
2016 Jun	759,256	Naive_log	736,060.25	23,195.75
2016 Jul	849,148	Naive_log	768,724.22	80,423.78
2016 Aug	891,091	Naive_log	859,607.11	31,483.89
2016 Sep	768,042	Naive_log	901,914.21	-133,872.21
2016 Oct	702,530	Naive_log	777,417.75	-74,887.75
2016 Nov	545,468	Naive_log	710,987.38	-165,519.38
2016 Dec	457,565	Naive_log	552,161.18	-94,596.18
2017 Jan	503,654	Naive_log	463,236.74	40,417.26
2017 Feb	541,368	Naive_log	509,906.87	31,461.13
2017 Mar	647,679	Naive_log	547,932.05	99,746.95
2017 Apr	710,409	Naive_log	655,577.49	54,831.51
2017 May	745,096	Naive_log	719,085.38	26,010.62
2017 Jun	794,118	Naive_log	754,194.19	39,923.81
2017 Jul	864,476	Naive_log	803,785.30	60,690.70
2017 Aug	939,077	Naive_log	874,948.98	64,128.02
2017 Sep	818,705	Naive_log	950,342.26	-131,637.26
2017 Oct	734,287	Naive_log	828,554.54	-94,267.54
2017 Nov	582,743	Naive_log	743,095.26	-160,352.26
2017 Dec	478,377	Naive_log	589,791.20	-111,414.20
2018 Jan	534,281	Naive_log	484,234.62	50,046.38
2018 Feb	555,841	Naive_log	540,806.39	15,034.61
2018 Mar	652,082	Naive_log	562,504.09	89,577.91
2018 Apr	689,214	Naive_log	659,967.05	29,246.95
2018 May	755,491	Naive_log	697,556.78	57,934.22
2018 Jun	782,628	Naive_log	764,653.42	17,974.58
2018 Jul	837,740	Naive_log	792,091.08	45,648.92
2018 Aug	936,644	Naive_log	847,827.36	88,816.64
2018 Sep	806,267	Naive_log	947,848.71	-141,581.71
2018 Oct	721,989	Naive_log	815,930.95	-93,941.95
2018 Nov	575,096	Naive_log	730,492.05	-155,396.05
2018 Dec	496,993	Naive_log	581,943.83	-84,950.83
2019 Jan	486,306	Naive_log	502,954.82	-16,648.82
2019 Feb	498,081	Naive_log	492,121.42	5,959.58
2019 Mar	606,616	Naive_log	503,913.94	102,702.06
2019 Apr	608,322	Naive_log	613,791.63	-5,469.63
2019 May	665,724	Naive_log	615,515.75	50,208.25
2019 Jun	714,041	Naive_log	673,618.43	40,422.57
2019 Jul	747,112	Naive_log	722,517.86	24,594.14
2019 Aug	828,426	Naive_log	755,892.09	72,533.91
2019 Sep	719,254	Naive_log	838,077.71	-118,823.71
2019 Oct	629,555	Naive_log	727,642.99	-98,087.99
2019 Nov	508,290	Naive_log	636,765.90	-128,475.90
2019 Dec	445,470	Naive_log	514,174.70	-68,704.70
2020 Jan	488,461	Naive_log	450,657.55	37,803.45
2020 Feb	540,254	Naive_log	494,164.54	46,089.46
2020 Mar	297,649	Naive_log	546,523.29	-248,874.29
2020 Apr	2,191	Naive_log	301,536.05	-299,345.05
2020 May	2,955	Naive_log	2,441.69	513.31
2020 Jun	14,932	Naive_log	3,294.22	11,637.78
2020 Jul	95,576	Naive_log	16,809.70	78,766.30
2020 Aug	240,322	Naive_log	108,955.99	131,366.01
2020 Sep	251,221	Naive_log	274,770.99	-23,549.99
2020 Oct	253,895	Naive_log	287,224.52	-33,329.52
2020 Nov	116,634	Naive_log	290,172.52	-173,538.52
2020 Dec	137,446	Naive_log	133,578.90	3,867.10
2021 Jan	93,013	Naive_log	157,428.65	-64,415.65
2021 Feb	40,883	Naive_log	106,590.67	-65,707.67
2021 Mar	60,163	Naive_log	46,947.15	13,215.85
2021 Apr	95,116	Naive_log	69,119.38	25,996.62
2021 May	179,599	Naive_log	109,355.22	70,243.78
2021 Jun	321,985	Naive_log	206,782.77	115,202.23
2021 Jul	552,399	Naive_log	371,159.90	181,239.10
2021 Aug	780,123	Naive_log	637,393.43	142,729.57
2021 Sep	697,572	Naive_log	900,460.09	-202,888.09
2021 Oct	655,682	Naive_log	805,091.63	-149,409.63
2021 Nov	521,638	Naive_log	756,342.01	-234,704.01
2021 Dec	397,592	Naive_log	601,747.79	-204,155.79
2022 Jan	341,744	Naive_log	458,758.70	-117,014.70
2022 Feb	391,699	Naive_log	394,327.71	-2,628.71
2022 Mar	569,482	Naive_log	451,937.62	117,544.38
2022 Apr	727,326	Naive_log	657,259.60	70,066.40
2022 May	779,426	Naive_log	839,613.82	-60,187.82
2022 Jun	833,955	Naive_log	899,771.22	-65,816.22
2010 Jan	319,379	Prophet	386,395.78	-67,016.78
2010 Feb	329,697	Prophet	408,874.79	-79,177.79
2010 Mar	388,978	Prophet	490,345.59	-101,367.59
2010 Apr	427,950	Prophet	520,735.13	-92,785.13
2010 May	431,385	Prophet	454,687.23	-23,302.23
2010 Jun	432,522	Prophet	423,373.72	9,148.28
2010 Jul	492,382	Prophet	466,871.60	25,510.40
2010 Aug	624,383	Prophet	563,707.27	60,675.73
2010 Sep	496,609	Prophet	460,407.12	36,201.88
2010 Oct	450,841	Prophet	422,118.93	28,722.07
2010 Nov	327,330	Prophet	344,647.16	-17,317.16
2010 Dec	272,069	Prophet	292,258.11	-20,189.11
2011 Jan	286,010	Prophet	307,263.50	-21,253.50
2011 Feb	319,015	Prophet	338,739.09	-19,724.09
2011 Mar	448,224	Prophet	414,098.44	34,125.56
2011 Apr	517,979	Prophet	463,267.16	54,711.84
2011 May	575,401	Prophet	412,037.69	163,363.31
2011 Jun	519,950	Prophet	418,259.47	101,690.53
2011 Jul	589,288	Prophet	471,942.47	117,345.53
2011 Aug	678,877	Prophet	590,893.00	87,984.00
2011 Sep	577,108	Prophet	483,350.29	93,757.71
2011 Oct	471,268	Prophet	448,826.51	22,441.49
2011 Nov	319,900	Prophet	367,034.21	-47,134.21
2011 Dec	262,266	Prophet	316,810.14	-54,544.14
2012 Jan	289,312	Prophet	328,983.27	-39,671.27
2012 Feb	329,299	Prophet	364,663.86	-35,364.86
2012 Mar	399,988	Prophet	459,811.88	-59,823.88
2012 Apr	508,131	Prophet	490,812.38	17,318.62
2012 May	521,638	Prophet	463,550.80	58,087.20
2012 Jun	509,865	Prophet	439,431.40	70,433.60
2012 Jul	602,837	Prophet	487,716.60	115,120.40
2012 Aug	681,135	Prophet	597,897.51	83,237.49
2012 Sep	562,007	Prophet	495,141.75	66,865.25
2012 Oct	468,951	Prophet	452,103.63	16,847.37
2012 Nov	350,902	Prophet	356,557.99	-5,655.99
2012 Dec	283,620	Prophet	311,857.15	-28,237.15
2013 Jan	322,235	Prophet	329,284.52	-7,049.52
2013 Feb	365,343	Prophet	353,342.79	12,000.21
2013 Mar	462,258	Prophet	452,012.21	10,245.79
2013 Apr	516,930	Prophet	507,616.92	9,313.08
2013 May	608,081	Prophet	491,724.70	116,356.30
2013 Jun	578,633	Prophet	471,678.64	106,954.36
2013 Jul	677,083	Prophet	529,927.55	147,155.45
2013 Aug	775,941	Prophet	640,327.08	135,613.92
2013 Sep	639,271	Prophet	554,047.21	85,223.79
2013 Oct	535,649	Prophet	510,493.59	25,155.41
2013 Nov	390,742	Prophet	409,875.99	-19,133.99
2013 Dec	342,783	Prophet	359,092.67	-16,309.67
2014 Jan	374,568	Prophet	382,774.36	-8,206.36
2014 Feb	401,859	Prophet	413,800.05	-11,941.05
2014 Mar	503,533	Prophet	511,918.28	-8,385.28
2014 Apr	557,275	Prophet	566,619.81	-9,344.81
2014 May	610,148	Prophet	568,975.58	41,172.42
2014 Jun	595,332	Prophet	543,385.96	51,946.04
2014 Jul	687,207	Prophet	610,013.81	77,193.19
2014 Aug	787,020	Prophet	723,986.70	63,033.30
2014 Sep	652,671	Prophet	619,107.32	33,563.68
2014 Oct	554,671	Prophet	559,749.96	-5,078.96
2014 Nov	415,750	Prophet	451,702.45	-35,952.45
2014 Dec	366,832	Prophet	399,199.90	-32,367.90
2015 Jan	399,040	Prophet	415,218.27	-16,178.27
2015 Feb	442,963	Prophet	452,219.96	-9,256.96
2015 Mar	545,523	Prophet	544,558.14	964.86
2015 Apr	586,230	Prophet	611,344.90	-25,114.90
2015 May	628,998	Prophet	618,549.01	10,448.99
2015 Jun	654,715	Prophet	595,938.28	58,776.72
2015 Jul	766,557	Prophet	664,708.79	101,848.21
2015 Aug	829,230	Prophet	777,478.82	51,751.18
2015 Sep	696,849	Prophet	662,847.49	34,001.51
2015 Oct	597,629	Prophet	596,514.63	1,114.37
2015 Nov	475,257	Prophet	484,174.25	-8,917.25
2015 Dec	407,035	Prophet	433,697.07	-26,662.07
2016 Jan	448,784	Prophet	457,447.03	-8,663.03
2016 Feb	506,179	Prophet	497,810.24	8,368.76
2016 Mar	611,987	Prophet	599,897.40	12,089.60
2016 Apr	663,878	Prophet	659,839.93	4,038.07
2016 May	726,980	Prophet	677,540.04	49,439.96
2016 Jun	759,256	Prophet	659,044.96	100,211.04
2016 Jul	849,148	Prophet	732,278.42	116,869.58
2016 Aug	891,091	Prophet	836,133.35	54,957.65
2016 Sep	768,042	Prophet	723,715.86	44,326.14
2016 Oct	702,530	Prophet	656,267.73	46,262.27
2016 Nov	545,468	Prophet	547,769.54	-2,301.54
2016 Dec	457,565	Prophet	506,408.62	-48,843.62
2017 Jan	503,654	Prophet	523,613.33	-19,959.33
2017 Feb	541,368	Prophet	550,869.88	-9,501.88
2017 Mar	647,679	Prophet	661,197.68	-13,518.68
2017 Apr	710,409	Prophet	716,652.79	-6,243.79
2017 May	745,096	Prophet	745,761.14	-665.14
2017 Jun	794,118	Prophet	736,702.57	57,415.43
2017 Jul	864,476	Prophet	819,610.67	44,865.33
2017 Aug	939,077	Prophet	912,394.31	26,682.69
2017 Sep	818,705	Prophet	799,624.27	19,080.73
2017 Oct	734,287	Prophet	726,450.48	7,836.52
2017 Nov	582,743	Prophet	604,759.62	-22,016.62
2017 Dec	478,377	Prophet	547,080.01	-68,703.01
2018 Jan	534,281	Prophet	569,243.91	-34,962.91
2018 Feb	555,841	Prophet	605,130.79	-49,289.79
2018 Mar	652,082	Prophet	706,449.21	-54,367.21
2018 Apr	689,214	Prophet	756,880.74	-67,666.74
2018 May	755,491	Prophet	792,513.45	-37,022.45
2018 Jun	782,628	Prophet	784,776.55	-2,148.55
2018 Jul	837,740	Prophet	865,517.39	-27,777.39
2018 Aug	936,644	Prophet	958,399.63	-21,755.63
2018 Sep	806,267	Prophet	836,422.39	-30,155.39
2018 Oct	721,989	Prophet	746,581.96	-24,592.96
2018 Nov	575,096	Prophet	609,302.36	-34,206.36
2018 Dec	496,993	Prophet	544,399.66	-47,406.66
2019 Jan	486,306	Prophet	568,505.81	-82,199.81
2019 Feb	498,081	Prophet	597,796.03	-99,715.03
2019 Mar	606,616	Prophet	695,388.62	-88,772.62
2019 Apr	608,322	Prophet	728,844.33	-120,522.33
2019 May	665,724	Prophet	762,192.03	-96,468.03
2019 Jun	714,041	Prophet	741,650.87	-27,609.87
2019 Jul	747,112	Prophet	812,188.49	-65,076.49
2019 Aug	828,426	Prophet	895,416.02	-66,990.02
2019 Sep	719,254	Prophet	761,058.42	-41,804.42
2019 Oct	629,555	Prophet	654,346.90	-24,791.90
2019 Nov	508,290	Prophet	507,381.44	908.56
2019 Dec	445,470	Prophet	436,050.85	9,419.15
2020 Jan	488,461	Prophet	450,102.92	38,358.08
2020 Feb	540,254	Prophet	481,806.35	58,447.65
2020 Mar	297,649	Prophet	584,950.45	-287,301.45
2020 Apr	2,191	Prophet	637,095.01	-634,904.01
2020 May	2,955	Prophet	669,781.78	-666,826.78
2020 Jun	14,932	Prophet	616,771.52	-601,839.52
2020 Jul	95,576	Prophet	667,355.09	-571,779.09
2020 Aug	240,322	Prophet	693,950.60	-453,628.60
2020 Sep	251,221	Prophet	537,796.58	-286,575.58
2020 Oct	253,895	Prophet	429,074.04	-175,179.04
2020 Nov	116,634	Prophet	282,898.31	-166,264.31
2020 Dec	137,446	Prophet	154,277.90	-16,831.90
2021 Jan	93,013	Prophet	199,822.75	-106,809.75
2021 Feb	40,883	Prophet	219,192.95	-178,309.95
2021 Mar	60,163	Prophet	225,071.36	-164,908.36
2021 Apr	95,116	Prophet	222,257.84	-127,141.84
2021 May	179,599	Prophet	214,935.93	-35,336.93
2021 Jun	321,985	Prophet	215,462.89	106,522.11
2021 Jul	552,399	Prophet	318,370.39	234,028.61
2021 Aug	780,123	Prophet	415,133.15	364,989.85
2021 Sep	697,572	Prophet	324,315.58	373,256.42
2021 Oct	655,682	Prophet	281,506.05	374,175.95
2021 Nov	521,638	Prophet	189,819.95	331,818.05
2021 Dec	397,592	Prophet	163,779.53	233,812.47
2022 Jan	341,744	Prophet	214,265.49	127,478.51
2022 Feb	391,699	Prophet	250,290.76	141,408.24
2022 Mar	569,482	Prophet	312,067.53	257,414.47
2022 Apr	727,326	Prophet	352,880.46	374,445.54
2022 May	779,426	Prophet	413,869.39	365,556.61
2022 Jun	833,955	Prophet	458,489.44	375,465.56
2010 Jan	319,379	Prophet_log	353,629.36	-34,250.36
2010 Feb	329,697	Prophet_log	373,837.49	-44,140.49
2010 Mar	388,978	Prophet_log	446,284.52	-57,306.52
2010 Apr	427,950	Prophet_log	468,697.44	-40,747.44
2010 May	431,385	Prophet_log	410,251.57	21,133.43
2010 Jun	432,522	Prophet_log	389,671.03	42,850.97
2010 Jul	492,382	Prophet_log	425,406.56	66,975.44
2010 Aug	624,383	Prophet_log	517,103.86	107,279.14
2010 Sep	496,609	Prophet_log	432,428.75	64,180.25
2010 Oct	450,841	Prophet_log	403,075.57	47,765.43
2010 Nov	327,330	Prophet_log	341,287.57	-13,957.57
2010 Dec	272,069	Prophet_log	295,343.13	-23,274.13
2011 Jan	286,010	Prophet_log	304,444.47	-18,434.47
2011 Feb	319,015	Prophet_log	330,747.66	-11,732.66
2011 Mar	448,224	Prophet_log	393,628.69	54,595.31
2011 Apr	517,979	Prophet_log	436,760.76	81,218.24
2011 May	575,401	Prophet_log	397,523.21	177,877.79
2011 Jun	519,950	Prophet_log	404,045.54	115,904.46
2011 Jul	589,288	Prophet_log	455,427.57	133,860.43
2011 Aug	678,877	Prophet_log	586,495.52	92,381.48
2011 Sep	577,108	Prophet_log	486,730.03	90,377.97
2011 Oct	471,268	Prophet_log	461,562.22	9,705.78
2011 Nov	319,900	Prophet_log	393,010.05	-73,110.05
2011 Dec	262,266	Prophet_log	340,165.70	-77,899.70
2012 Jan	289,312	Prophet_log	348,030.71	-58,718.71
2012 Feb	329,299	Prophet_log	384,242.05	-54,943.05
2012 Mar	399,988	Prophet_log	462,433.14	-62,445.14
2012 Apr	508,131	Prophet_log	495,443.18	12,687.82
2012 May	521,638	Prophet_log	477,368.76	44,269.24
2012 Jun	509,865	Prophet_log	458,924.43	50,940.57
2012 Jul	602,837	Prophet_log	508,993.31	93,843.69
2012 Aug	681,135	Prophet_log	617,722.46	63,412.54
2012 Sep	562,007	Prophet_log	514,286.63	47,720.37
2012 Oct	468,951	Prophet_log	479,345.25	-10,394.25
2012 Nov	350,902	Prophet_log	383,793.54	-32,891.54
2012 Dec	283,620	Prophet_log	341,033.89	-57,413.89
2013 Jan	322,235	Prophet_log	360,479.63	-38,244.63
2013 Feb	365,343	Prophet_log	377,399.46	-12,056.46
2013 Mar	462,258	Prophet_log	471,735.45	-9,477.45
2013 Apr	516,930	Prophet_log	523,544.14	-6,614.14
2013 May	608,081	Prophet_log	505,584.19	102,496.81
2013 Jun	578,633	Prophet_log	490,044.70	88,588.30
2013 Jul	677,083	Prophet_log	560,650.52	116,432.48
2013 Aug	775,941	Prophet_log	679,645.22	96,295.78
2013 Sep	639,271	Prophet_log	574,363.45	64,907.55
2013 Oct	535,649	Prophet_log	523,825.67	11,823.33
2013 Nov	390,742	Prophet_log	417,792.59	-27,050.59
2013 Dec	342,783	Prophet_log	362,201.93	-19,418.93
2014 Jan	374,568	Prophet_log	389,439.68	-14,871.68
2014 Feb	401,859	Prophet_log	423,804.08	-21,945.08
2014 Mar	503,533	Prophet_log	535,455.64	-31,922.64
2014 Apr	557,275	Prophet_log	599,817.48	-42,542.48
2014 May	610,148	Prophet_log	593,862.62	16,285.38
2014 Jun	595,332	Prophet_log	566,367.72	28,964.28
2014 Jul	687,207	Prophet_log	640,963.43	46,243.57
2014 Aug	787,020	Prophet_log	778,058.25	8,961.75
2014 Sep	652,671	Prophet_log	649,207.84	3,463.16
2014 Oct	554,671	Prophet_log	580,101.74	-25,430.74
2014 Nov	415,750	Prophet_log	446,156.41	-30,406.41
2014 Dec	366,832	Prophet_log	380,245.33	-13,413.33
2015 Jan	399,040	Prophet_log	405,178.79	-6,138.79
2015 Feb	442,963	Prophet_log	446,064.85	-3,101.85
2015 Mar	545,523	Prophet_log	572,484.96	-26,961.96
2015 Apr	586,230	Prophet_log	645,876.78	-59,646.78
2015 May	628,998	Prophet_log	646,377.44	-17,379.44
2015 Jun	654,715	Prophet_log	607,890.08	46,824.92
2015 Jul	766,557	Prophet_log	689,754.13	76,802.87
2015 Aug	829,230	Prophet_log	834,797.25	-5,567.25
2015 Sep	696,849	Prophet_log	690,719.47	6,129.53
2015 Oct	597,629	Prophet_log	606,671.98	-9,042.98
2015 Nov	475,257	Prophet_log	462,870.29	12,386.71
2015 Dec	407,035	Prophet_log	395,127.43	11,907.57
2016 Jan	448,784	Prophet_log	425,979.56	22,804.44
2016 Feb	506,179	Prophet_log	478,102.44	28,076.56
2016 Mar	611,987	Prophet_log	613,382.92	-1,395.92
2016 Apr	663,878	Prophet_log	693,881.28	-30,003.28
2016 May	726,980	Prophet_log	714,820.75	12,159.25
2016 Jun	759,256	Prophet_log	692,118.07	67,137.93
2016 Jul	849,148	Prophet_log	790,737.50	58,410.50
2016 Aug	891,091	Prophet_log	932,966.86	-41,875.86
2016 Sep	768,042	Prophet_log	772,413.74	-4,371.74
2016 Oct	702,530	Prophet_log	673,711.41	28,818.59
2016 Nov	545,468	Prophet_log	519,449.18	26,018.82
2016 Dec	457,565	Prophet_log	456,862.41	702.59
2017 Jan	503,654	Prophet_log	491,262.64	12,391.36
2017 Feb	541,368	Prophet_log	542,506.97	-1,138.97
2017 Mar	647,679	Prophet_log	695,296.05	-47,617.05
2017 Apr	710,409	Prophet_log	777,677.34	-67,268.34
2017 May	745,096	Prophet_log	814,336.30	-69,240.30
2017 Jun	794,118	Prophet_log	792,861.05	1,256.95
2017 Jul	864,476	Prophet_log	900,327.21	-35,851.21
2017 Aug	939,077	Prophet_log	1,024,696.62	-85,619.62
2017 Sep	818,705	Prophet_log	847,784.31	-29,079.31
2017 Oct	734,287	Prophet_log	735,089.24	-802.24
2017 Nov	582,743	Prophet_log	558,702.20	24,040.80
2017 Dec	478,377	Prophet_log	479,186.45	-809.45
2018 Jan	534,281	Prophet_log	515,020.18	19,260.82
2018 Feb	555,841	Prophet_log	568,869.48	-13,028.48
2018 Mar	652,082	Prophet_log	717,536.80	-65,454.80
2018 Apr	689,214	Prophet_log	783,739.76	-94,525.76
2018 May	755,491	Prophet_log	824,168.38	-68,677.38
2018 Jun	782,628	Prophet_log	798,366.16	-15,738.16
2018 Jul	837,740	Prophet_log	902,498.15	-64,758.15
2018 Aug	936,644	Prophet_log	1,022,794.65	-86,150.65
2018 Sep	806,267	Prophet_log	842,917.96	-36,650.96
2018 Oct	721,989	Prophet_log	719,354.84	2,634.16
2018 Nov	575,096	Prophet_log	533,243.67	41,852.33
2018 Dec	496,993	Prophet_log	454,656.59	42,336.41
2019 Jan	486,306	Prophet_log	496,856.70	-10,550.70
2019 Feb	498,081	Prophet_log	543,665.34	-45,584.34
2019 Mar	606,616	Prophet_log	678,627.10	-72,011.10
2019 Apr	608,322	Prophet_log	725,665.07	-117,343.07
2019 May	665,724	Prophet_log	765,655.14	-99,931.14
2019 Jun	714,041	Prophet_log	731,166.68	-17,125.68
2019 Jul	747,112	Prophet_log	818,307.69	-71,195.69
2019 Aug	828,426	Prophet_log	929,057.94	-100,631.94
2019 Sep	719,254	Prophet_log	760,024.61	-40,770.61
2019 Oct	629,555	Prophet_log	637,518.61	-7,963.61
2019 Nov	508,290	Prophet_log	465,886.34	42,403.66
2019 Dec	445,470	Prophet_log	396,104.33	49,365.67
2020 Jan	488,461	Prophet_log	421,497.49	66,963.51
2020 Feb	540,254	Prophet_log	468,148.05	72,105.95
2020 Mar	297,649	Prophet_log	585,859.98	-288,210.98
2020 Apr	2,191	Prophet_log	635,017.01	-632,826.01
2020 May	2,955	Prophet_log	655,031.18	-652,076.18
2020 Jun	14,932	Prophet_log	472,240.61	-457,308.61
2020 Jul	95,576	Prophet_log	378,598.55	-283,022.55
2020 Aug	240,322	Prophet_log	284,321.15	-43,999.15
2020 Sep	251,221	Prophet_log	215,462.17	35,758.83
2020 Oct	253,895	Prophet_log	152,510.04	101,384.96
2020 Nov	116,634	Prophet_log	109,874.84	6,759.16
2020 Dec	137,446	Prophet_log	95,107.32	42,338.68
2021 Jan	93,013	Prophet_log	112,200.42	-19,187.42
2021 Feb	40,883	Prophet_log	120,074.35	-79,191.35
2021 Mar	60,163	Prophet_log	125,515.75	-65,352.75
2021 Apr	95,116	Prophet_log	61,429.21	33,686.79
2021 May	179,599	Prophet_log	65,138.61	114,460.39
2021 Jun	321,985	Prophet_log	91,075.42	230,909.58
2021 Jul	552,399	Prophet_log	142,361.55	410,037.45
2021 Aug	780,123	Prophet_log	198,803.59	581,319.41
2021 Sep	697,572	Prophet_log	193,914.56	503,657.44
2021 Oct	655,682	Prophet_log	187,139.43	468,542.57
2021 Nov	521,638	Prophet_log	151,430.21	370,207.79
2021 Dec	397,592	Prophet_log	147,363.85	250,228.15
2022 Jan	341,744	Prophet_log	163,299.53	178,444.47
2022 Feb	391,699	Prophet_log	167,823.27	223,875.73
2022 Mar	569,482	Prophet_log	194,956.55	374,525.45
2022 Apr	727,326	Prophet_log	155,596.52	571,729.48
2022 May	779,426	Prophet_log	214,771.32	564,654.68
2022 Jun	833,955	Prophet_log	277,516.80	556,438.20
2010 Jan	319,379	SNaive	337,043.00	-17,664.00
2010 Feb	329,697	SNaive	371,317.00	-41,620.00
2010 Mar	388,978	SNaive	473,879.00	-84,901.00
2010 Apr	427,950	SNaive	525,648.00	-97,698.00
2010 May	431,385	SNaive	510,850.00	-79,465.00
2010 Jun	432,522	SNaive	501,923.00	-69,401.00
2010 Jul	492,382	SNaive	523,383.00	-31,001.00
2010 Aug	624,383	SNaive	623,297.00	1,086.00
2010 Sep	496,609	SNaive	517,222.00	-20,613.00
2010 Oct	450,841	SNaive	454,129.00	-3,288.00
2010 Nov	327,330	SNaive	350,155.00	-22,825.00
2010 Dec	272,069	SNaive	308,080.00	-36,011.00
2011 Jan	286,010	SNaive	319,379.00	-33,369.00
2011 Feb	319,015	SNaive	329,697.00	-10,682.00
2011 Mar	448,224	SNaive	388,978.00	59,246.00
2011 Apr	517,979	SNaive	427,950.00	90,029.00
2011 May	575,401	SNaive	431,385.00	144,016.00
2011 Jun	519,950	SNaive	432,522.00	87,428.00
2011 Jul	589,288	SNaive	492,382.00	96,906.00
2011 Aug	678,877	SNaive	624,383.00	54,494.00
2011 Sep	577,108	SNaive	496,609.00	80,499.00
2011 Oct	471,268	SNaive	450,841.00	20,427.00
2011 Nov	319,900	SNaive	327,330.00	-7,430.00
2011 Dec	262,266	SNaive	272,069.00	-9,803.00
2012 Jan	289,312	SNaive	286,010.00	3,302.00
2012 Feb	329,299	SNaive	319,015.00	10,284.00
2012 Mar	399,988	SNaive	448,224.00	-48,236.00
2012 Apr	508,131	SNaive	517,979.00	-9,848.00
2012 May	521,638	SNaive	575,401.00	-53,763.00
2012 Jun	509,865	SNaive	519,950.00	-10,085.00
2012 Jul	602,837	SNaive	589,288.00	13,549.00
2012 Aug	681,135	SNaive	678,877.00	2,258.00
2012 Sep	562,007	SNaive	577,108.00	-15,101.00
2012 Oct	468,951	SNaive	471,268.00	-2,317.00
2012 Nov	350,902	SNaive	319,900.00	31,002.00
2012 Dec	283,620	SNaive	262,266.00	21,354.00
2013 Jan	322,235	SNaive	289,312.00	32,923.00
2013 Feb	365,343	SNaive	329,299.00	36,044.00
2013 Mar	462,258	SNaive	399,988.00	62,270.00
2013 Apr	516,930	SNaive	508,131.00	8,799.00
2013 May	608,081	SNaive	521,638.00	86,443.00
2013 Jun	578,633	SNaive	509,865.00	68,768.00
2013 Jul	677,083	SNaive	602,837.00	74,246.00
2013 Aug	775,941	SNaive	681,135.00	94,806.00
2013 Sep	639,271	SNaive	562,007.00	77,264.00
2013 Oct	535,649	SNaive	468,951.00	66,698.00
2013 Nov	390,742	SNaive	350,902.00	39,840.00
2013 Dec	342,783	SNaive	283,620.00	59,163.00
2014 Jan	374,568	SNaive	322,235.00	52,333.00
2014 Feb	401,859	SNaive	365,343.00	36,516.00
2014 Mar	503,533	SNaive	462,258.00	41,275.00
2014 Apr	557,275	SNaive	516,930.00	40,345.00
2014 May	610,148	SNaive	608,081.00	2,067.00
2014 Jun	595,332	SNaive	578,633.00	16,699.00
2014 Jul	687,207	SNaive	677,083.00	10,124.00
2014 Aug	787,020	SNaive	775,941.00	11,079.00
2014 Sep	652,671	SNaive	639,271.00	13,400.00
2014 Oct	554,671	SNaive	535,649.00	19,022.00
2014 Nov	415,750	SNaive	390,742.00	25,008.00
2014 Dec	366,832	SNaive	342,783.00	24,049.00
2015 Jan	399,040	SNaive	374,568.00	24,472.00
2015 Feb	442,963	SNaive	401,859.00	41,104.00
2015 Mar	545,523	SNaive	503,533.00	41,990.00
2015 Apr	586,230	SNaive	557,275.00	28,955.00
2015 May	628,998	SNaive	610,148.00	18,850.00
2015 Jun	654,715	SNaive	595,332.00	59,383.00
2015 Jul	766,557	SNaive	687,207.00	79,350.00
2015 Aug	829,230	SNaive	787,020.00	42,210.00
2015 Sep	696,849	SNaive	652,671.00	44,178.00
2015 Oct	597,629	SNaive	554,671.00	42,958.00
2015 Nov	475,257	SNaive	415,750.00	59,507.00
2015 Dec	407,035	SNaive	366,832.00	40,203.00
2016 Jan	448,784	SNaive	399,040.00	49,744.00
2016 Feb	506,179	SNaive	442,963.00	63,216.00
2016 Mar	611,987	SNaive	545,523.00	66,464.00
2016 Apr	663,878	SNaive	586,230.00	77,648.00
2016 May	726,980	SNaive	628,998.00	97,982.00
2016 Jun	759,256	SNaive	654,715.00	104,541.00
2016 Jul	849,148	SNaive	766,557.00	82,591.00
2016 Aug	891,091	SNaive	829,230.00	61,861.00
2016 Sep	768,042	SNaive	696,849.00	71,193.00
2016 Oct	702,530	SNaive	597,629.00	104,901.00
2016 Nov	545,468	SNaive	475,257.00	70,211.00
2016 Dec	457,565	SNaive	407,035.00	50,530.00
2017 Jan	503,654	SNaive	448,784.00	54,870.00
2017 Feb	541,368	SNaive	506,179.00	35,189.00
2017 Mar	647,679	SNaive	611,987.00	35,692.00
2017 Apr	710,409	SNaive	663,878.00	46,531.00
2017 May	745,096	SNaive	726,980.00	18,116.00
2017 Jun	794,118	SNaive	759,256.00	34,862.00
2017 Jul	864,476	SNaive	849,148.00	15,328.00
2017 Aug	939,077	SNaive	891,091.00	47,986.00
2017 Sep	818,705	SNaive	768,042.00	50,663.00
2017 Oct	734,287	SNaive	702,530.00	31,757.00
2017 Nov	582,743	SNaive	545,468.00	37,275.00
2017 Dec	478,377	SNaive	457,565.00	20,812.00
2018 Jan	534,281	SNaive	503,654.00	30,627.00
2018 Feb	555,841	SNaive	541,368.00	14,473.00
2018 Mar	652,082	SNaive	647,679.00	4,403.00
2018 Apr	689,214	SNaive	710,409.00	-21,195.00
2018 May	755,491	SNaive	745,096.00	10,395.00
2018 Jun	782,628	SNaive	794,118.00	-11,490.00
2018 Jul	837,740	SNaive	864,476.00	-26,736.00
2018 Aug	936,644	SNaive	939,077.00	-2,433.00
2018 Sep	806,267	SNaive	818,705.00	-12,438.00
2018 Oct	721,989	SNaive	734,287.00	-12,298.00
2018 Nov	575,096	SNaive	582,743.00	-7,647.00
2018 Dec	496,993	SNaive	478,377.00	18,616.00
2019 Jan	486,306	SNaive	534,281.00	-47,975.00
2019 Feb	498,081	SNaive	555,841.00	-57,760.00
2019 Mar	606,616	SNaive	652,082.00	-45,466.00
2019 Apr	608,322	SNaive	689,214.00	-80,892.00
2019 May	665,724	SNaive	755,491.00	-89,767.00
2019 Jun	714,041	SNaive	782,628.00	-68,587.00
2019 Jul	747,112	SNaive	837,740.00	-90,628.00
2019 Aug	828,426	SNaive	936,644.00	-108,218.00
2019 Sep	719,254	SNaive	806,267.00	-87,013.00
2019 Oct	629,555	SNaive	721,989.00	-92,434.00
2019 Nov	508,290	SNaive	575,096.00	-66,806.00
2019 Dec	445,470	SNaive	496,993.00	-51,523.00
2020 Jan	488,461	SNaive	486,306.00	2,155.00
2020 Feb	540,254	SNaive	498,081.00	42,173.00
2020 Mar	297,649	SNaive	606,616.00	-308,967.00
2020 Apr	2,191	SNaive	608,322.00	-606,131.00
2020 May	2,955	SNaive	665,724.00	-662,769.00
2020 Jun	14,932	SNaive	714,041.00	-699,109.00
2020 Jul	95,576	SNaive	747,112.00	-651,536.00
2020 Aug	240,322	SNaive	828,426.00	-588,104.00
2020 Sep	251,221	SNaive	719,254.00	-468,033.00
2020 Oct	253,895	SNaive	629,555.00	-375,660.00
2020 Nov	116,634	SNaive	508,290.00	-391,656.00
2020 Dec	137,446	SNaive	445,470.00	-308,024.00
2021 Jan	93,013	SNaive	488,461.00	-395,448.00
2021 Feb	40,883	SNaive	540,254.00	-499,371.00
2021 Mar	60,163	SNaive	297,649.00	-237,486.00
2021 Apr	95,116	SNaive	2,191.00	92,925.00
2021 May	179,599	SNaive	2,955.00	176,644.00
2021 Jun	321,985	SNaive	14,932.00	307,053.00
2021 Jul	552,399	SNaive	95,576.00	456,823.00
2021 Aug	780,123	SNaive	240,322.00	539,801.00
2021 Sep	697,572	SNaive	251,221.00	446,351.00
2021 Oct	655,682	SNaive	253,895.00	401,787.00
2021 Nov	521,638	SNaive	116,634.00	405,004.00
2021 Dec	397,592	SNaive	137,446.00	260,146.00
2022 Jan	341,744	SNaive	93,013.00	248,731.00
2022 Feb	391,699	SNaive	40,883.00	350,816.00
2022 Mar	569,482	SNaive	60,163.00	509,319.00
2022 Apr	727,326	SNaive	95,116.00	632,210.00
2022 May	779,426	SNaive	179,599.00	599,827.00
2022 Jun	833,955	SNaive	321,985.00	511,970.00
2010 Jan	319,379	SNaive_log	338,055.14	-18,676.14
2010 Feb	329,697	SNaive_log	372,428.22	-42,731.22
2010 Mar	388,978	SNaive_log	475,313.40	-86,335.40
2010 Apr	427,950	SNaive_log	527,301.37	-99,351.37
2010 May	431,385	SNaive_log	512,550.81	-81,165.81
2010 Jun	432,522	SNaive_log	503,637.04	-71,115.04
2010 Jul	492,382	SNaive_log	525,144.99	-32,762.99
2010 Aug	624,383	SNaive_log	625,326.08	-943.08
2010 Sep	496,609	SNaive_log	518,842.21	-22,233.21
2010 Oct	450,841	SNaive_log	455,504.50	-4,663.50
2010 Nov	327,330	SNaive_log	351,190.69	-23,860.69
2010 Dec	272,069	SNaive_log	308,994.72	-36,925.72
2011 Jan	286,010	SNaive_log	320,343.83	-34,333.83
2011 Feb	319,015	SNaive_log	330,711.07	-11,696.07
2011 Mar	448,224	SNaive_log	390,176.31	58,047.69
2011 Apr	517,979	SNaive_log	429,225.75	88,753.25
2011 May	575,401	SNaive_log	432,741.61	142,659.39
2011 Jun	519,950	SNaive_log	434,036.58	85,913.42
2011 Jul	589,288	SNaive_log	494,183.45	95,104.55
2011 Aug	678,877	SNaive_log	626,756.12	52,120.88
2011 Sep	577,108	SNaive_log	498,507.38	78,600.62
2011 Oct	471,268	SNaive_log	452,610.94	18,657.06
2011 Nov	319,900	SNaive_log	328,617.95	-8,717.95
2011 Dec	262,266	SNaive_log	273,137.68	-10,871.68
2012 Jan	289,312	SNaive_log	287,135.01	2,176.99
2012 Feb	329,299	SNaive_log	320,264.77	9,034.23
2012 Mar	399,988	SNaive_log	449,981.66	-49,993.66
2012 Apr	508,131	SNaive_log	520,039.58	-11,908.58
2012 May	521,638	SNaive_log	577,671.40	-56,033.40
2012 Jun	509,865	SNaive_log	521,998.47	-12,133.47
2012 Jul	602,837	SNaive_log	591,610.69	11,226.31
2012 Aug	681,135	SNaive_log	681,553.23	-418.23
2012 Sep	562,007	SNaive_log	579,382.55	-17,375.55
2012 Oct	468,951	SNaive_log	473,126.33	-4,175.33
2012 Nov	350,902	SNaive_log	321,160.80	29,741.20
2012 Dec	283,620	SNaive_log	263,308.77	20,311.23
2013 Jan	322,235	SNaive_log	290,470.48	31,764.52
2013 Feb	365,343	SNaive_log	330,629.04	34,713.96
2013 Mar	462,258	SNaive_log	401,623.50	60,634.50
2013 Apr	516,930	SNaive_log	510,247.40	6,682.60
2013 May	608,081	SNaive_log	523,804.18	84,276.82
2013 Jun	578,633	SNaive_log	512,037.76	66,595.24
2013 Jul	677,083	SNaive_log	605,434.01	71,648.99
2013 Aug	775,941	SNaive_log	684,109.60	91,831.40
2013 Sep	639,271	SNaive_log	564,500.69	74,770.31
2013 Oct	535,649	SNaive_log	471,067.51	64,581.49
2013 Nov	390,742	SNaive_log	352,508.61	38,233.39
2013 Dec	342,783	SNaive_log	284,931.91	57,851.09
2014 Jan	374,568	SNaive_log	323,778.79	50,789.21
2014 Feb	401,859	SNaive_log	367,110.62	34,748.38
2014 Mar	503,533	SNaive_log	464,512.13	39,020.87
2014 Apr	557,275	SNaive_log	519,468.14	37,806.86
2014 May	610,148	SNaive_log	611,067.52	-919.52
2014 Jun	595,332	SNaive_log	581,472.89	13,859.11
2014 Jul	687,207	SNaive_log	680,381.42	6,825.58
2014 Aug	787,020	SNaive_log	779,707.48	7,312.52
2014 Sep	652,671	SNaive_log	642,350.73	10,320.27
2014 Oct	554,671	SNaive_log	538,226.76	16,444.24
2014 Nov	415,750	SNaive_log	392,624.59	23,125.41
2014 Dec	366,832	SNaive_log	344,440.05	22,391.95
2015 Jan	399,040	SNaive_log	376,386.19	22,653.81
2015 Feb	442,963	SNaive_log	403,811.89	39,151.11
2015 Mar	545,523	SNaive_log	505,997.66	39,525.34
2015 Apr	586,230	SNaive_log	560,018.37	26,211.63
2015 May	628,998	SNaive_log	613,097.49	15,900.51
2015 Jun	654,715	SNaive_log	598,189.80	56,525.20
2015 Jul	766,557	SNaive_log	690,530.14	76,026.86
2015 Aug	829,230	SNaive_log	790,868.64	38,361.36
2015 Sep	696,849	SNaive_log	655,870.28	40,978.72
2015 Oct	597,629	SNaive_log	557,400.77	40,228.23
2015 Nov	475,257	SNaive_log	417,806.05	57,450.95
2015 Dec	407,035	SNaive_log	368,671.55	38,363.45
2016 Jan	448,784	SNaive_log	401,059.83	47,724.17
2016 Feb	506,179	SNaive_log	445,228.46	60,950.54
2016 Mar	611,987	SNaive_log	548,357.93	63,629.07
2016 Apr	663,878	SNaive_log	589,308.39	74,569.61
2016 May	726,980	SNaive_log	632,345.15	94,634.85
2016 Jun	759,256	SNaive_log	658,251.97	101,004.03
2016 Jul	849,148	SNaive_log	770,755.99	78,392.01
2016 Aug	891,091	SNaive_log	833,768.31	57,322.69
2016 Sep	768,042	SNaive_log	700,676.29	67,365.71
2016 Oct	702,530	SNaive_log	600,930.13	101,599.87
2016 Nov	545,468	SNaive_log	477,936.99	67,531.01
2016 Dec	457,565	SNaive_log	409,342.13	48,222.87
2017 Jan	503,654	SNaive_log	451,353.84	52,300.16
2017 Feb	541,368	SNaive_log	509,101.00	32,267.00
2017 Mar	647,679	SNaive_log	615,484.72	32,194.28
2017 Apr	710,409	SNaive_log	667,655.72	42,753.28
2017 May	745,096	SNaive_log	731,132.05	13,963.95
2017 Jun	794,118	SNaive_log	763,579.67	30,538.33
2017 Jul	864,476	SNaive_log	853,975.35	10,500.65
2017 Aug	939,077	SNaive_log	896,147.81	42,929.19
2017 Sep	818,705	SNaive_log	772,406.39	46,298.61
2017 Oct	734,287	SNaive_log	706,529.06	27,757.94
2017 Nov	582,743	SNaive_log	548,577.21	34,165.79
2017 Dec	478,377	SNaive_log	460,165.37	18,211.63
2018 Jan	534,281	SNaive_log	506,512.18	27,768.82
2018 Feb	555,841	SNaive_log	544,404.03	11,436.97
2018 Mar	652,082	SNaive_log	651,219.07	862.93
2018 Apr	689,214	SNaive_log	714,198.52	-24,984.52
2018 May	755,491	SNaive_log	749,046.35	6,444.65
2018 Jun	782,628	SNaive_log	798,271.43	-15,643.43
2018 Jul	837,740	SNaive_log	868,967.04	-31,227.04
2018 Aug	936,644	SNaive_log	943,867.27	-7,223.27
2018 Sep	806,267	SNaive_log	822,843.32	-16,576.32
2018 Oct	721,989	SNaive_log	737,958.17	-15,969.17
2018 Nov	575,096	SNaive_log	585,624.47	-10,528.47
2018 Dec	496,993	SNaive_log	480,710.11	16,282.89
2019 Jan	486,306	SNaive_log	536,862.93	-50,556.93
2019 Feb	498,081	SNaive_log	558,542.44	-60,461.44
2019 Mar	606,616	SNaive_log	655,244.86	-48,628.86
2019 Apr	608,322	SNaive_log	692,449.26	-84,127.26
2019 May	665,724	SNaive_log	758,944.01	-93,220.01
2019 Jun	714,041	SNaive_log	786,159.43	-72,118.43
2019 Jul	747,112	SNaive_log	841,466.85	-94,354.85
2019 Aug	828,426	SNaive_log	940,851.52	-112,425.52
2019 Sep	719,254	SNaive_log	809,945.11	-90,691.11
2019 Oct	629,555	SNaive_log	725,320.70	-95,765.70
2019 Nov	508,290	SNaive_log	577,799.68	-69,509.68
2019 Dec	445,470	SNaive_log	499,354.12	-53,884.12
2020 Jan	488,461	SNaive_log	488,608.53	-147.53
2020 Feb	540,254	SNaive_log	500,411.25	39,842.75
2020 Mar	297,649	SNaive_log	609,469.53	-311,820.53
2020 Apr	2,191	SNaive_log	612,554.59	-610,363.59
2020 May	2,955	SNaive_log	767,808.47	-764,853.47
2020 Jun	14,932	SNaive_log	920,277.17	-905,345.17
2020 Jul	95,576	SNaive_log	1,014,517.02	-918,941.02
2020 Aug	240,322	SNaive_log	1,141,027.98	-900,705.98
2020 Sep	251,221	SNaive_log	995,737.00	-744,516.00
2020 Oct	253,895	SNaive_log	874,716.59	-620,821.59
2020 Nov	116,634	SNaive_log	708,164.42	-591,530.42
2020 Dec	137,446	SNaive_log	625,109.44	-487,663.44
2021 Jan	93,013	SNaive_log	688,560.78	-595,547.78
2021 Feb	40,883	SNaive_log	768,450.60	-727,567.60
2021 Mar	60,163	SNaive_log	432,552.84	-372,389.84
2021 Apr	95,116	SNaive_log	3,209.83	91,906.17
2021 May	179,599	SNaive_log	4,523.60	175,075.40
2021 Jun	321,985	SNaive_log	24,023.87	297,961.13
2021 Jul	552,399	SNaive_log	157,943.67	394,455.33
2021 Aug	780,123	SNaive_log	400,566.72	379,556.28
2021 Sep	697,572	SNaive_log	420,345.59	277,226.41
2021 Oct	655,682	SNaive_log	426,044.90	229,637.10
2021 Nov	521,638	SNaive_log	196,202.07	325,435.93
2021 Dec	397,592	SNaive_log	232,634.42	164,957.58
2022 Jan	341,744	SNaive_log	157,912.49	183,831.51
2022 Feb	391,699	SNaive_log	69,727.29	321,971.71
2022 Mar	569,482	SNaive_log	104,029.31	465,452.69
2022 Apr	727,326	SNaive_log	166,682.84	560,643.16
2022 May	779,426	SNaive_log	318,172.88	461,253.12
2022 Jun	833,955	SNaive_log	573,596.84	260,358.16
2010 Jan	319,379	TSLM	406,210.22	-86,831.22
2010 Feb	329,697	TSLM	438,956.45	-109,259.45
2010 Mar	388,978	TSLM	527,792.00	-138,814.00
2010 Apr	427,950	TSLM	566,345.80	-138,395.80
2010 May	431,385	TSLM	515,439.58	-84,054.58
2010 Jun	432,522	TSLM	487,661.06	-55,139.06
2010 Jul	492,382	TSLM	530,133.27	-37,751.27
2010 Aug	624,383	TSLM	626,038.95	-1,655.95
2010 Sep	496,609	TSLM	518,296.35	-21,687.35
2010 Oct	450,841	TSLM	477,630.83	-26,789.83
2010 Nov	327,330	TSLM	403,332.73	-76,002.73
2010 Dec	272,069	TSLM	351,913.47	-79,844.47
2011 Jan	286,010	TSLM	369,016.16	-83,006.16
2011 Feb	319,015	TSLM	399,435.11	-80,420.11
2011 Mar	448,224	TSLM	484,710.31	-36,486.31
2011 Apr	517,979	TSLM	525,484.93	-7,505.93
2011 May	575,401	TSLM	486,346.24	89,054.76
2011 Jun	519,950	TSLM	468,140.24	51,809.76
2011 Jul	589,288	TSLM	516,069.29	73,218.71
2011 Aug	678,877	TSLM	623,583.75	55,293.25
2011 Sep	577,108	TSLM	513,831.70	63,276.30
2011 Oct	471,268	TSLM	473,067.56	-1,799.56
2011 Nov	319,900	TSLM	388,634.38	-68,734.38
2011 Dec	262,266	TSLM	338,867.96	-76,601.96
2012 Jan	289,312	TSLM	354,613.54	-65,301.54
2012 Feb	329,299	TSLM	384,554.01	-55,255.01
2012 Mar	399,988	TSLM	481,603.78	-81,615.78
2012 Apr	508,131	TSLM	521,074.89	-12,943.89
2012 May	521,638	TSLM	493,053.27	28,584.73
2012 Jun	509,865	TSLM	467,833.43	42,031.57
2012 Jul	602,837	TSLM	517,122.77	85,714.23
2012 Aug	681,135	TSLM	625,977.24	55,157.76
2012 Sep	562,007	TSLM	515,625.71	46,381.29
2012 Oct	468,951	TSLM	466,017.69	2,933.31
2012 Nov	350,902	TSLM	369,990.00	-19,088.00
2012 Dec	283,620	TSLM	321,240.93	-37,620.93
2013 Jan	322,235	TSLM	339,999.58	-17,764.58
2013 Feb	365,343	TSLM	370,847.97	-5,504.97
2013 Mar	462,258	TSLM	465,009.30	-2,751.30
2013 Apr	516,930	TSLM	518,636.47	-1,706.47
2013 May	608,081	TSLM	501,429.85	106,651.15
2013 Jun	578,633	TSLM	476,327.75	102,305.25
2013 Jul	677,083	TSLM	533,258.48	143,824.52
2013 Aug	775,941	TSLM	639,803.30	136,137.70
2013 Sep	639,271	TSLM	530,954.04	108,316.96
2013 Oct	535,649	TSLM	477,361.67	58,287.33
2013 Nov	390,742	TSLM	376,673.61	14,068.39
2013 Dec	342,783	TSLM	326,719.61	16,063.39
2014 Jan	374,568	TSLM	347,865.47	26,702.53
2014 Feb	401,859	TSLM	380,613.09	21,245.91
2014 Mar	503,533	TSLM	476,182.78	27,350.22
2014 Apr	557,275	TSLM	531,107.28	26,167.72
2014 May	610,148	TSLM	530,972.82	79,175.18
2014 Jun	595,332	TSLM	505,172.44	90,159.56
2014 Jul	687,207	TSLM	566,630.11	120,576.89
2014 Aug	787,020	TSLM	670,377.78	116,642.22
2014 Sep	652,671	TSLM	557,681.31	94,989.69
2014 Oct	554,671	TSLM	496,842.31	57,828.69
2014 Nov	415,750	TSLM	390,117.34	25,632.66
2014 Dec	366,832	TSLM	339,961.02	26,870.98
2015 Jan	399,040	TSLM	364,016.26	35,023.74
2015 Feb	442,963	TSLM	395,433.33	47,529.67
2015 Mar	545,523	TSLM	495,880.66	49,642.34
2015 Apr	586,230	TSLM	552,362.09	33,867.91
2015 May	628,998	TSLM	561,752.98	67,245.02
2015 Jun	654,715	TSLM	539,972.02	114,742.98
2015 Jul	766,557	TSLM	606,304.52	160,252.48
2015 Aug	829,230	TSLM	711,569.13	117,660.87
2015 Sep	696,849	TSLM	595,137.14	101,711.86
2015 Oct	597,629	TSLM	526,514.34	71,114.66
2015 Nov	475,257	TSLM	415,555.06	59,701.94
2015 Dec	407,035	TSLM	366,674.65	40,360.35
2016 Jan	448,784	TSLM	390,250.93	58,533.07
2016 Feb	506,179	TSLM	426,250.91	79,928.09
2016 Mar	611,987	TSLM	530,255.95	81,731.05
2016 Apr	663,878	TSLM	591,600.38	72,277.62
2016 May	726,980	TSLM	611,453.56	115,526.44
2016 Jun	759,256	TSLM	595,908.02	163,347.98
2016 Jul	849,148	TSLM	670,388.44	178,759.56
2016 Aug	891,091	TSLM	770,176.47	120,914.53
2016 Sep	768,042	TSLM	652,843.30	115,198.70
2016 Oct	702,530	TSLM	578,221.94	124,308.06
2016 Nov	545,468	TSLM	465,043.65	80,424.35
2016 Dec	457,565	TSLM	414,765.17	42,799.83
2017 Jan	503,654	TSLM	441,105.24	62,548.76
2017 Feb	541,368	TSLM	482,504.28	58,863.72
2017 Mar	647,679	TSLM	587,100.58	60,578.42
2017 Apr	710,409	TSLM	646,755.45	63,653.55
2017 May	745,096	TSLM	679,618.29	65,477.71
2017 Jun	794,118	TSLM	670,945.54	123,172.46
2017 Jul	864,476	TSLM	750,806.99	113,669.01
2017 Aug	939,077	TSLM	842,300.59	96,776.41
2017 Sep	818,705	TSLM	725,231.41	93,473.59
2017 Oct	734,287	TSLM	649,174.08	85,112.92
2017 Nov	582,743	TSLM	529,862.03	52,880.97
2017 Dec	478,377	TSLM	475,709.77	2,667.23
2018 Jan	534,281	TSLM	505,753.21	28,527.79
2018 Feb	555,841	TSLM	549,025.50	6,815.50
2018 Mar	652,082	TSLM	653,226.66	-1,144.66
2018 Apr	689,214	TSLM	713,257.32	-24,043.32
2018 May	755,491	TSLM	751,840.50	3,650.50
2018 Jun	782,628	TSLM	751,140.75	31,487.25
2018 Jul	837,740	TSLM	831,051.28	6,688.72
2018 Aug	936,644	TSLM	919,606.73	17,037.27
2018 Sep	806,267	TSLM	800,998.47	5,268.53
2018 Oct	721,989	TSLM	720,875.89	1,113.11
2018 Nov	575,096	TSLM	591,653.43	-16,557.43
2018 Dec	496,993	TSLM	531,764.25	-34,771.25
2019 Jan	486,306	TSLM	564,426.04	-78,120.04
2019 Feb	498,081	TSLM	600,549.14	-102,468.14
2019 Mar	606,616	TSLM	698,344.84	-91,728.84
2019 Apr	608,322	TSLM	756,418.23	-148,096.23
2019 May	665,724	TSLM	797,043.23	-131,319.23
2019 Jun	714,041	TSLM	796,815.99	-82,774.99
2019 Jul	747,112	TSLM	872,069.78	-124,957.78
2019 Aug	828,426	TSLM	956,120.90	-127,694.90
2019 Sep	719,254	TSLM	829,534.03	-110,280.03
2019 Oct	629,555	TSLM	742,734.51	-113,179.51
2019 Nov	508,290	TSLM	604,867.54	-96,577.54
2019 Dec	445,470	TSLM	538,427.54	-92,957.54
2020 Jan	488,461	TSLM	567,352.64	-78,891.64
2020 Feb	540,254	TSLM	599,910.74	-59,656.74
2020 Mar	297,649	TSLM	697,382.10	-399,733.10
2020 Apr	2,191	TSLM	739,393.39	-737,202.39
2020 May	2,955	TSLM	768,640.60	-765,685.60
2020 Jun	14,932	TSLM	754,280.03	-739,348.03
2020 Jul	95,576	TSLM	809,918.17	-714,342.17
2020 Aug	240,322	TSLM	873,630.69	-633,308.69
2020 Sep	251,221	TSLM	730,925.10	-479,704.10
2020 Oct	253,895	TSLM	628,011.92	-374,116.92
2020 Nov	116,634	TSLM	477,949.29	-361,315.29
2020 Dec	137,446	TSLM	398,067.44	-260,621.44
2021 Jan	93,013	TSLM	420,597.52	-327,584.52
2021 Feb	40,883	TSLM	445,457.96	-404,574.96
2021 Mar	60,163	TSLM	498,760.30	-438,597.30
2021 Apr	95,116	TSLM	503,709.11	-408,593.11
2021 May	179,599	TSLM	540,128.56	-360,529.56
2021 Jun	321,985	TSLM	538,048.75	-216,063.75
2021 Jul	552,399	TSLM	608,432.97	-56,033.97
2021 Aug	780,123	TSLM	690,006.06	90,116.94
2021 Sep	697,572	TSLM	578,461.56	119,110.44
2021 Oct	655,682	TSLM	495,374.31	160,307.69
2021 Nov	521,638	TSLM	355,699.66	165,938.34
2021 Dec	397,592	TSLM	294,493.71	103,098.29
2022 Jan	341,744	TSLM	318,138.41	23,605.59
2022 Feb	391,699	TSLM	341,876.74	49,822.26
2022 Mar	569,482	TSLM	394,815.98	174,666.02
2022 Apr	727,326	TSLM	409,699.59	317,626.41
2022 May	779,426	TSLM	466,678.72	312,747.28
2022 Jun	833,955	TSLM	499,934.42	334,020.58
2010 Jan	319,379	TSLM_log	397,141.32	-77,762.32
2010 Feb	329,697	TSLM_log	432,177.72	-102,480.72
2010 Mar	388,978	TSLM_log	526,007.02	-137,029.02
2010 Apr	427,950	TSLM_log	567,030.30	-139,080.30
2010 May	431,385	TSLM_log	512,175.53	-80,790.53
2010 Jun	432,522	TSLM_log	482,857.87	-50,335.87
2010 Jul	492,382	TSLM_log	526,604.05	-34,222.05
2010 Aug	624,383	TSLM_log	624,565.41	-182.41
2010 Sep	496,609	TSLM_log	514,791.38	-18,182.38
2010 Oct	450,841	TSLM_log	474,191.42	-23,350.42
2010 Nov	327,330	TSLM_log	399,571.79	-72,241.79
2010 Dec	272,069	TSLM_log	348,092.06	-76,023.06
2011 Jan	286,010	TSLM_log	364,595.55	-78,585.55
2011 Feb	319,015	TSLM_log	394,198.48	-75,183.48
2011 Mar	448,224	TSLM_log	477,085.03	-28,861.03
2011 Apr	517,979	TSLM_log	517,426.83	552.17
2011 May	575,401	TSLM_log	479,140.45	96,260.55
2011 Jun	519,950	TSLM_log	461,670.55	58,279.45
2011 Jul	589,288	TSLM_log	508,955.40	80,332.60
2011 Aug	678,877	TSLM_log	615,541.61	63,335.39
2011 Sep	577,108	TSLM_log	507,317.39	69,790.61
2011 Oct	471,268	TSLM_log	467,349.63	3,918.37
2011 Nov	319,900	TSLM_log	383,405.52	-63,505.52
2011 Dec	262,266	TSLM_log	334,316.13	-72,050.13
2012 Jan	289,312	TSLM_log	349,157.34	-59,845.34
2012 Feb	329,299	TSLM_log	378,025.69	-48,726.69
2012 Mar	399,988	TSLM_log	472,165.18	-72,177.18
2012 Apr	508,131	TSLM_log	510,550.57	-2,419.57
2012 May	521,638	TSLM_log	482,969.03	38,668.97
2012 Jun	509,865	TSLM_log	459,330.07	50,534.93
2012 Jul	602,837	TSLM_log	506,804.93	96,032.07
2012 Aug	681,135	TSLM_log	612,788.68	68,346.32
2012 Sep	562,007	TSLM_log	506,093.20	55,913.80
2012 Oct	468,951	TSLM_log	458,677.53	10,273.47
2012 Nov	350,902	TSLM_log	364,954.52	-14,052.52
2012 Dec	283,620	TSLM_log	317,612.08	-33,992.08
2013 Jan	322,235	TSLM_log	335,441.11	-13,206.11
2013 Feb	365,343	TSLM_log	365,217.66	125.34
2013 Mar	462,258	TSLM_log	455,721.44	6,536.56
2013 Apr	516,930	TSLM_log	508,311.01	8,618.99
2013 May	608,081	TSLM_log	491,698.02	116,382.98
2013 Jun	578,633	TSLM_log	467,576.97	111,056.03
2013 Jul	677,083	TSLM_log	522,580.83	154,502.17
2013 Aug	775,941	TSLM_log	627,509.84	148,431.16
2013 Sep	639,271	TSLM_log	520,694.28	118,576.72
2013 Oct	535,649	TSLM_log	468,422.94	67,226.06
2013 Nov	390,742	TSLM_log	368,012.40	22,729.60
2013 Dec	342,783	TSLM_log	318,215.74	24,567.26
2014 Jan	374,568	TSLM_log	339,318.49	35,249.51
2014 Feb	401,859	TSLM_log	372,064.84	29,794.16
2014 Mar	503,533	TSLM_log	467,158.24	36,374.76
2014 Apr	557,275	TSLM_log	522,916.95	34,358.05
2014 May	610,148	TSLM_log	522,064.53	88,083.47
2014 Jun	595,332	TSLM_log	496,426.50	98,905.50
2014 Jul	687,207	TSLM_log	557,063.33	130,143.67
2014 Aug	787,020	TSLM_log	662,417.41	124,602.59
2014 Sep	652,671	TSLM_log	548,935.32	103,735.68
2014 Oct	554,671	TSLM_log	488,355.05	66,315.95
2014 Nov	415,750	TSLM_log	379,160.09	36,589.91
2014 Dec	366,832	TSLM_log	327,586.59	39,245.41
2015 Jan	399,040	TSLM_log	352,158.52	46,881.48
2015 Feb	442,963	TSLM_log	384,813.43	58,149.57
2015 Mar	545,523	TSLM_log	488,479.14	57,043.86
2015 Apr	586,230	TSLM_log	548,154.15	38,075.85
2015 May	628,998	TSLM_log	556,836.21	72,161.79
2015 Jun	654,715	TSLM_log	534,690.54	120,024.46
2015 Jul	766,557	TSLM_log	602,568.25	163,988.75
2015 Aug	829,230	TSLM_log	714,384.63	114,845.37
2015 Sep	696,849	TSLM_log	591,254.07	105,594.93
2015 Oct	597,629	TSLM_log	519,435.93	78,193.07
2015 Nov	475,257	TSLM_log	400,289.16	74,967.84
2015 Dec	407,035	TSLM_log	346,971.72	60,063.28
2016 Jan	448,784	TSLM_log	372,470.85	76,313.15
2016 Feb	506,179	TSLM_log	411,446.84	94,732.16
2016 Mar	611,987	TSLM_log	525,162.51	86,824.49
2016 Apr	663,878	TSLM_log	594,250.34	69,627.66
2016 May	726,980	TSLM_log	614,995.94	111,984.06
2016 Jun	759,256	TSLM_log	596,780.89	162,475.11
2016 Jul	849,148	TSLM_log	678,112.09	171,035.91
2016 Aug	891,091	TSLM_log	793,181.05	97,909.95
2016 Sep	768,042	TSLM_log	658,719.58	109,322.42
2016 Oct	702,530	TSLM_log	573,876.21	128,653.79
2016 Nov	545,468	TSLM_log	441,364.60	104,103.40
2016 Dec	457,565	TSLM_log	381,724.47	75,840.53
2017 Jan	503,654	TSLM_log	412,022.44	91,631.56
2017 Feb	541,368	TSLM_log	459,952.85	81,415.15
2017 Mar	647,679	TSLM_log	584,608.10	63,070.90
2017 Apr	710,409	TSLM_log	658,071.65	52,337.35
2017 May	745,096	TSLM_log	695,452.94	49,643.06
2017 Jun	794,118	TSLM_log	682,722.81	111,395.19
2017 Jul	864,476	TSLM_log	778,627.61	85,848.39
2017 Aug	939,077	TSLM_log	895,816.63	43,260.37
2017 Sep	818,705	TSLM_log	748,635.85	70,069.15
2017 Oct	734,287	TSLM_log	652,651.49	81,635.51
2017 Nov	582,743	TSLM_log	500,197.30	82,545.70
2017 Dec	478,377	TSLM_log	430,249.91	48,127.09
2018 Jan	534,281	TSLM_log	467,456.18	66,824.82
2018 Feb	555,841	TSLM_log	522,624.43	33,216.57
2018 Mar	652,082	TSLM_log	659,549.37	-7,467.37
2018 Apr	689,214	TSLM_log	740,907.40	-51,693.40
2018 May	755,491	TSLM_log	790,030.31	-34,539.31
2018 Jun	782,628	TSLM_log	784,950.62	-2,322.62
2018 Jul	837,740	TSLM_log	891,659.47	-53,919.47
2018 Aug	936,644	TSLM_log	1,017,698.41	-81,054.41
2018 Sep	806,267	TSLM_log	853,848.79	-47,581.79
2018 Oct	721,989	TSLM_log	742,895.76	-20,906.76
2018 Nov	575,096	TSLM_log	563,039.01	12,056.99
2018 Dec	496,993	TSLM_log	480,825.18	16,167.82
2019 Jan	486,306	TSLM_log	523,911.96	-37,605.96
2019 Feb	498,081	TSLM_log	575,188.29	-77,107.29
2019 Mar	606,616	TSLM_log	713,983.04	-107,367.04
2019 Apr	608,322	TSLM_log	798,735.78	-190,413.78
2019 May	665,724	TSLM_log	853,426.35	-187,702.35
2019 Jun	714,041	TSLM_log	848,770.40	-134,729.40
2019 Jul	747,112	TSLM_log	954,711.93	-207,599.93
2019 Aug	828,426	TSLM_log	1,078,370.56	-249,944.56
2019 Sep	719,254	TSLM_log	900,475.52	-181,221.52
2019 Oct	629,555	TSLM_log	778,984.54	-149,429.54
2019 Nov	508,290	TSLM_log	586,724.05	-78,434.05
2019 Dec	445,470	TSLM_log	496,714.80	-51,244.80
2020 Jan	488,461	TSLM_log	536,752.26	-48,291.26
2020 Feb	540,254	TSLM_log	583,016.80	-42,762.80
2020 Mar	297,649	TSLM_log	718,108.74	-420,459.74
2020 Apr	2,191	TSLM_log	778,408.33	-776,217.33
2020 May	2,955	TSLM_log	841,339.76	-838,384.76
2020 Jun	14,932	TSLM_log	820,659.34	-805,727.34
2020 Jul	95,576	TSLM_log	874,314.16	-778,738.16
2020 Aug	240,322	TSLM_log	938,542.73	-698,220.73
2020 Sep	251,221	TSLM_log	764,356.03	-513,135.03
2020 Oct	253,895	TSLM_log	642,630.60	-388,735.60
2020 Nov	116,634	TSLM_log	474,538.90	-357,904.90
2020 Dec	137,446	TSLM_log	386,626.64	-249,180.64
2021 Jan	93,013	TSLM_log	405,814.22	-312,801.22
2021 Feb	40,883	TSLM_log	424,674.18	-383,791.18
2021 Mar	60,163	TSLM_log	458,250.13	-398,087.13
2021 Apr	95,116	TSLM_log	292,432.82	-197,316.82
2021 May	179,599	TSLM_log	320,200.78	-140,601.78
2021 Jun	321,985	TSLM_log	376,551.92	-54,566.92
2021 Jul	552,399	TSLM_log	502,369.88	50,029.12
2021 Aug	780,123	TSLM_log	604,941.52	175,181.48
2021 Sep	697,572	TSLM_log	523,905.66	173,666.34
2021 Oct	655,682	TSLM_log	459,998.49	195,683.51
2021 Nov	521,638	TSLM_log	333,616.23	188,021.77
2021 Dec	397,592	TSLM_log	292,819.72	104,772.28
2022 Jan	341,744	TSLM_log	302,387.99	39,356.01
2022 Feb	391,699	TSLM_log	298,527.15	93,171.85
2022 Mar	569,482	TSLM_log	342,490.36	226,991.64
2022 Apr	727,326	TSLM_log	238,633.52	488,692.48
2022 May	779,426	TSLM_log	293,998.40	485,427.60
2022 Jun	833,955	TSLM_log	387,618.14	446,336.86

# Show Point Forecasts in Plot: 2000-2022
error_fc_madeira_slide %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_until2022, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2000-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2010-2022
error_fc_madeira_slide %>%
  filter(year(Month) >= 2010) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_from2010, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2010-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2019-2022
error_fc_madeira_slide %>%
  filter(year(Month) >= 2019) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_from2019, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2019-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2020-2022
error_fc_madeira_slide %>%
  filter(year(Month) >= 2020) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_madeira_from2020, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2020-2022") +
  ylab("Overnight_Stays")

2.1.2.4 Change of RMSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_slide, tourism_madeira_until2019) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_slide, tourism_madeira_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
Drift_STL	7	26,363.61	1	60,452.48
ETS_auto	10	30,306.75	2	62,458.92
ARIMA_auto	2	24,567.87	3	62,917.47
ARIMA_d1D1	3	24,793.46	4	63,294.54
HWA	8	28,906.75	5	67,655.80
ARIMA_auto_log	6	26,318.15	6	70,546.17
ETS_auto_log	12	33,847.93	7	77,582.25
HWA_log	11	33,727.42	8	78,631.71
ARIMA_d0D1	1	24,247.36	9	79,891.52
Drift_STL_log	9	29,259.07	10	82,411.91
ARIMA_d0D1_log	4	25,531.56	11	85,187.45
ARIMA_d1D1_log	5	26,108.28	12	86,942.82
Naive	18	82,367.68	13	91,659.07
Naive_log	19	83,041.75	14	93,786.23
Prophet	16	57,399.43	15	155,237.13
Prophet_log	15	54,980.47	16	163,721.16
TSLM	17	79,276.66	17	188,328.39
TSLM_log	20	88,413.58	18	202,003.88
SNaive	14	53,807.75	19	204,508.35
SNaive_log	13	53,100.30	20	231,796.75

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Save best models according to the RMSE of Forecasts from 2010-2022
best_models_fc_madeira_slide <- c("ARIMA_d0D1", "Drift_STL", "ARIMA_d1D1", "ARIMA_auto", "HWA", "ETS_auto", "Naive", "Prophet", "TSLM", "SNaive")

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_slide, tourism_madeira_until2019) %>%
  filter(.model %in% best_models_fc_madeira_slide) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_slide, tourism_madeira_until2022) %>%
  filter(.model %in% best_models_fc_madeira_slide) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
Drift_STL	4	26,363.61	1	60,452.48
ETS_auto	6	30,306.75	2	62,458.92
ARIMA_auto	2	24,567.87	3	62,917.47
ARIMA_d1D1	3	24,793.46	4	63,294.54
HWA	5	28,906.75	5	67,655.80
ARIMA_d0D1	1	24,247.36	6	79,891.52
Naive	10	82,367.68	7	91,659.07
Prophet	8	57,399.43	8	155,237.13
TSLM	9	79,276.66	9	188,328.39
SNaive	7	53,807.75	10	204,508.35

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.1.2.5 RMSE Development by including more Years in Time Series

# Compute RMSE and RMSSE for 2010 and create tibble
tourism_until_i <- tourism_madeira_until2022 %>%
    filter(year(Month) <= 2010)

accuracy_madeira_slide <- accuracy(fc_madeira_slide, tourism_until_i) %>%
  select(c(.model, RMSE, RMSSE)) %>%
  mutate(Until_Year = 2010)

# Create tsibble of summarized RMSE and RMSSE, beginning in 2010 and including more years
for (i in 2011:2022){
  tourism_until_i <- tourism_madeira_until2022 %>%
    filter(year(Month) <= i)

  accuracy_next_year <- accuracy(fc_madeira_slide, tourism_until_i) %>%
    select(c(.model, RMSE, RMSSE)) %>%
    mutate(Until_Year = i)

  accuracy_madeira_slide <- rbind(accuracy_madeira_slide, accuracy_next_year)
}

rm(accuracy_next_year, tourism_until_i) # remove variables from R environment

accuracy_madeira_slide <- accuracy_madeira_slide %>%
  rename(Model = .model) %>%
  select(c(Until_Year, Model, RMSE, RMSSE)) %>%
  as_tsibble(key = Model, index = Until_Year)

# Show table
accuracy_madeira_slide %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	27,048.19	0.70
2011	ARIMA_auto	31,802.61	0.75
2012	ARIMA_auto	28,826.53	0.70
2013	ARIMA_auto	28,639.17	0.66
2014	ARIMA_auto	25,988.15	0.61
2015	ARIMA_auto	25,311.05	0.59
2016	ARIMA_auto	25,017.26	0.55
2017	ARIMA_auto	24,200.64	0.53
2018	ARIMA_auto	23,637.91	0.53
2019	ARIMA_auto	24,567.87	0.53
2020	ARIMA_auto	59,117.03	0.51
2021	ARIMA_auto	62,054.25	0.44
2022	ARIMA_auto	62,917.47	0.41
2010	ARIMA_auto_log	26,851.51	0.70
2011	ARIMA_auto_log	32,966.24	0.77
2012	ARIMA_auto_log	30,066.30	0.73
2013	ARIMA_auto_log	29,440.35	0.68
2014	ARIMA_auto_log	26,804.42	0.63
2015	ARIMA_auto_log	26,483.06	0.62
2016	ARIMA_auto_log	26,678.49	0.58
2017	ARIMA_auto_log	26,041.70	0.57
2018	ARIMA_auto_log	25,459.91	0.58
2019	ARIMA_auto_log	26,318.15	0.57
2020	ARIMA_auto_log	62,357.26	0.53
2021	ARIMA_auto_log	70,176.98	0.50
2022	ARIMA_auto_log	70,546.17	0.46
2010	ARIMA_d0D1	27,833.95	0.72
2011	ARIMA_d0D1	30,889.70	0.73
2012	ARIMA_d0D1	28,156.94	0.68
2013	ARIMA_d0D1	28,135.13	0.65
2014	ARIMA_d0D1	25,543.90	0.60
2015	ARIMA_d0D1	24,845.06	0.58
2016	ARIMA_d0D1	24,771.02	0.54
2017	ARIMA_d0D1	23,924.67	0.53
2018	ARIMA_d0D1	23,329.63	0.53
2019	ARIMA_d0D1	24,247.36	0.52
2020	ARIMA_d0D1	79,371.45	0.68
2021	ARIMA_d0D1	79,848.48	0.57
2022	ARIMA_d0D1	79,891.52	0.52
2010	ARIMA_d0D1_log	27,463.48	0.71
2011	ARIMA_d0D1_log	31,035.85	0.73
2012	ARIMA_d0D1_log	28,663.85	0.69
2013	ARIMA_d0D1_log	28,371.81	0.65
2014	ARIMA_d0D1_log	25,866.14	0.61
2015	ARIMA_d0D1_log	25,610.47	0.60
2016	ARIMA_d0D1_log	25,848.15	0.56
2017	ARIMA_d0D1_log	25,142.17	0.55
2018	ARIMA_d0D1_log	24,595.23	0.56
2019	ARIMA_d0D1_log	25,531.56	0.55
2020	ARIMA_d0D1_log	63,074.98	0.54
2021	ARIMA_d0D1_log	64,764.00	0.46
2022	ARIMA_d0D1_log	85,187.45	0.55
2010	ARIMA_d1D1	26,026.60	0.67
2011	ARIMA_d1D1	33,564.31	0.79
2012	ARIMA_d1D1	30,902.53	0.75
2013	ARIMA_d1D1	30,108.06	0.69
2014	ARIMA_d1D1	27,321.11	0.64
2015	ARIMA_d1D1	26,432.59	0.62
2016	ARIMA_d1D1	25,992.41	0.57
2017	ARIMA_d1D1	25,083.76	0.55
2018	ARIMA_d1D1	24,438.85	0.55
2019	ARIMA_d1D1	24,793.46	0.53
2020	ARIMA_d1D1	59,202.59	0.51
2021	ARIMA_d1D1	62,173.10	0.44
2022	ARIMA_d1D1	63,294.54	0.41
2010	ARIMA_d1D1_log	26,851.51	0.70
2011	ARIMA_d1D1_log	34,453.47	0.81
2012	ARIMA_d1D1_log	31,819.11	0.77
2013	ARIMA_d1D1_log	30,328.74	0.70
2014	ARIMA_d1D1_log	27,625.77	0.65
2015	ARIMA_d1D1_log	27,248.95	0.64
2016	ARIMA_d1D1_log	27,331.59	0.60
2017	ARIMA_d1D1_log	26,627.71	0.59
2018	ARIMA_d1D1_log	25,967.11	0.59
2019	ARIMA_d1D1_log	26,108.28	0.56
2020	ARIMA_d1D1_log	60,706.92	0.52
2021	ARIMA_d1D1_log	66,700.84	0.48
2022	ARIMA_d1D1_log	86,942.82	0.56
2010	Drift_STL	26,282.69	0.68
2011	Drift_STL	32,458.74	0.76
2012	Drift_STL	30,922.91	0.75
2013	Drift_STL	31,226.69	0.72
2014	Drift_STL	28,744.68	0.67
2015	Drift_STL	27,814.65	0.65
2016	Drift_STL	27,532.79	0.60
2017	Drift_STL	26,857.53	0.59
2018	Drift_STL	25,906.50	0.59
2019	Drift_STL	26,363.61	0.57
2020	Drift_STL	56,441.00	0.48
2021	Drift_STL	58,581.75	0.42
2022	Drift_STL	60,452.48	0.39
2010	Drift_STL_log	25,673.11	0.67
2011	Drift_STL_log	33,271.59	0.78
2012	Drift_STL_log	31,813.47	0.77
2013	Drift_STL_log	31,156.00	0.72
2014	Drift_STL_log	28,587.80	0.67
2015	Drift_STL_log	28,351.39	0.66
2016	Drift_STL_log	29,150.98	0.64
2017	Drift_STL_log	29,262.66	0.65
2018	Drift_STL_log	28,971.22	0.65
2019	Drift_STL_log	29,259.07	0.63
2020	Drift_STL_log	54,422.58	0.47
2021	Drift_STL_log	54,367.15	0.39
2022	Drift_STL_log	82,411.91	0.53
2010	ETS_auto	27,192.31	0.70
2011	ETS_auto	35,889.88	0.84
2012	ETS_auto	34,335.64	0.83
2013	ETS_auto	35,243.40	0.81
2014	ETS_auto	33,103.25	0.78
2015	ETS_auto	32,364.33	0.76
2016	ETS_auto	32,130.82	0.70
2017	ETS_auto	31,469.87	0.69
2018	ETS_auto	30,424.56	0.69
2019	ETS_auto	30,306.75	0.65
2020	ETS_auto	58,514.19	0.50
2021	ETS_auto	60,919.93	0.43
2022	ETS_auto	62,458.92	0.40
2010	ETS_auto_log	27,118.12	0.70
2011	ETS_auto_log	37,458.40	0.88
2012	ETS_auto_log	35,989.65	0.87
2013	ETS_auto_log	35,746.20	0.82
2014	ETS_auto_log	32,989.33	0.77
2015	ETS_auto_log	32,793.79	0.77
2016	ETS_auto_log	33,626.91	0.73
2017	ETS_auto_log	33,542.15	0.74
2018	ETS_auto_log	33,344.04	0.75
2019	ETS_auto_log	33,847.93	0.73
2020	ETS_auto_log	68,553.85	0.59
2021	ETS_auto_log	77,385.21	0.55
2022	ETS_auto_log	77,582.25	0.50
2010	HWA	27,142.79	0.70
2011	HWA	34,380.07	0.81
2012	HWA	33,156.87	0.80
2013	HWA	34,263.81	0.79
2014	HWA	31,886.49	0.75
2015	HWA	30,986.71	0.72
2016	HWA	30,627.52	0.67
2017	HWA	29,921.52	0.66
2018	HWA	28,904.40	0.65
2019	HWA	28,906.75	0.62
2020	HWA	64,642.95	0.55
2021	HWA	66,637.75	0.48
2022	HWA	67,655.80	0.44
2010	HWA_log	42,948.46	1.11
2011	HWA_log	44,493.53	1.05
2012	HWA_log	40,236.05	0.97
2013	HWA_log	37,874.71	0.87
2014	HWA_log	35,970.97	0.84
2015	HWA_log	34,127.71	0.80
2016	HWA_log	33,680.31	0.74
2017	HWA_log	33,832.01	0.75
2018	HWA_log	33,679.14	0.76
2019	HWA_log	33,727.42	0.73
2020	HWA_log	64,824.92	0.56
2021	HWA_log	64,951.56	0.46
2022	HWA_log	78,631.71	0.51
2010	Naive	72,466.89	1.88
2011	Naive	79,807.28	1.87
2012	Naive	79,633.17	1.92
2013	Naive	82,332.93	1.89
2014	Naive	82,777.15	1.94
2015	Naive	82,680.03	1.93
2016	Naive	82,937.73	1.81
2017	Naive	83,303.36	1.84
2018	Naive	83,341.41	1.88
2019	Naive	82,367.68	1.77
2020	Naive	87,551.46	0.75
2021	Naive	90,996.94	0.65
2022	Naive	91,659.07	0.59
2010	Naive_log	73,057.36	1.89
2011	Naive_log	80,428.81	1.89
2012	Naive_log	80,230.27	1.94
2013	Naive_log	82,914.40	1.91
2014	Naive_log	83,377.66	1.96
2015	Naive_log	83,282.76	1.94
2016	Naive_log	83,534.33	1.82
2017	Naive_log	83,923.14	1.85
2018	Naive_log	83,977.18	1.90
2019	Naive_log	83,041.75	1.79
2020	Naive_log	88,677.32	0.76
2021	Naive_log	94,244.03	0.67
2022	Naive_log	93,786.23	0.61
2010	Prophet	55,862.08	1.45
2011	Prophet	69,365.00	1.63
2012	Prophet	65,887.05	1.59
2013	Prophet	69,254.51	1.59
2014	Prophet	64,343.18	1.51
2015	Prophet	61,003.72	1.42
2016	Prophet	60,149.97	1.31
2017	Prophet	57,398.12	1.27
2018	Prophet	55,695.47	1.26
2019	Prophet	57,399.43	1.23
2020	Prophet	133,887.54	1.15
2021	Prophet	146,663.36	1.05
2022	Prophet	155,237.13	1.00
2010	Prophet_log	52,820.73	1.37
2011	Prophet_log	74,927.19	1.76
2012	Prophet_log	68,599.28	1.66
2013	Prophet_log	67,360.51	1.55
2014	Prophet_log	61,429.48	1.44
2015	Prophet_log	57,685.17	1.35
2016	Prophet_log	54,896.44	1.20
2017	Prophet_log	53,514.79	1.18
2018	Prophet_log	53,589.85	1.21
2019	Prophet_log	54,980.47	1.18
2020	Prophet_log	109,604.25	0.94
2021	Prophet_log	140,513.13	1.00
2022	Prophet_log	163,721.16	1.06
2010	SNaive	52,554.91	1.36
2011	SNaive	62,510.14	1.47
2012	SNaive	53,007.37	1.28
2013	SNaive	55,845.42	1.28
2014	SNaive	51,535.61	1.21
2015	SNaive	50,711.51	1.18
2016	SNaive	55,292.47	1.21
2017	SNaive	53,422.12	1.18
2018	SNaive	50,668.17	1.15
2019	SNaive	53,807.75	1.16
2020	SNaive	153,714.16	1.32
2021	SNaive	182,718.86	1.30
2022	SNaive	204,508.35	1.32
2010	SNaive_log	53,749.18	1.39
2011	SNaive_log	62,398.12	1.47
2012	SNaive_log	53,020.37	1.28
2013	SNaive_log	55,304.27	1.27
2014	SNaive_log	50,868.47	1.19
2015	SNaive_log	49,766.24	1.16
2016	SNaive_log	53,924.34	1.18
2017	SNaive_log	51,880.53	1.14
2018	SNaive_log	49,266.74	1.11
2019	SNaive_log	53,100.30	1.14
2020	SNaive_log	202,213.92	1.73
2021	SNaive_log	222,212.55	1.59
2022	SNaive_log	231,796.75	1.50
2010	TSLM	83,052.69	2.15
2011	TSLM	73,923.03	1.74
2012	TSLM	67,125.38	1.62
2013	TSLM	70,594.42	1.62
2014	TSLM	70,486.00	1.65
2015	TSLM	72,934.75	1.70
2016	TSLM	79,308.65	1.73
2017	TSLM	79,318.54	1.75
2018	TSLM	75,047.45	1.70
2019	TSLM	79,276.66	1.70
2020	TSLM	175,810.63	1.51
2021	TSLM	185,897.27	1.33
2022	TSLM	188,328.39	1.22
2010	TSLM_log	79,987.38	2.07
2011	TSLM_log	72,650.65	1.71
2012	TSLM_log	66,744.38	1.61
2013	TSLM_log	72,477.85	1.67
2014	TSLM_log	73,577.82	1.73
2015	TSLM_log	76,493.64	1.78
2016	TSLM_log	82,472.73	1.80
2017	TSLM_log	81,516.09	1.80
2018	TSLM_log	78,172.88	1.77
2019	TSLM_log	88,413.58	1.90
2020	TSLM_log	190,138.24	1.63
2021	TSLM_log	193,387.27	1.38
2022	TSLM_log	202,003.88	1.31

All Models

# Plot development of RMSE for period 2010-2022
accuracy_madeira_slide %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_madeira_slide %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_madeira_slide %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_madeira_slide %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_madeira_slide %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	82,367.68	87,551.46	5,183.78	0.0629
Naive_log	83,041.75	88,677.32	5,635.57	0.0679
Drift_STL_log	29,259.07	54,422.58	25,163.51	0.8600
HWA_log	33,727.42	64,824.92	31,097.50	0.9220
ETS_auto	30,306.75	58,514.19	28,207.44	0.9307
Prophet_log	54,980.47	109,604.25	54,623.78	0.9935
ETS_auto_log	33,847.93	68,553.85	34,705.92	1.0253
Drift_STL	26,363.61	56,441.00	30,077.39	1.1409
TSLM_log	88,413.58	190,138.24	101,724.66	1.1506
TSLM	79,276.66	175,810.63	96,533.97	1.2177
HWA	28,906.75	64,642.95	35,736.21	1.2363
ARIMA_d1D1_log	26,108.28	60,706.92	34,598.65	1.3252
Prophet	57,399.43	133,887.54	76,488.11	1.3326
ARIMA_auto_log	26,318.15	62,357.26	36,039.11	1.3694
ARIMA_d1D1	24,793.46	59,202.59	34,409.13	1.3878
ARIMA_auto	24,567.87	59,117.03	34,549.17	1.4063
ARIMA_d0D1_log	25,531.56	63,074.98	37,543.43	1.4705
SNaive	53,807.75	153,714.16	99,906.41	1.8567
ARIMA_d0D1	24,247.36	79,371.45	55,124.10	2.2734
SNaive_log	53,100.30	202,213.92	149,113.63	2.8082

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

Each Model once

# Plot development of RMSE for period 2010-2022
accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	82,367.68	87,551.46	5,183.78	0.0629
ETS_auto	30,306.75	58,514.19	28,207.44	0.9307
Drift_STL	26,363.61	56,441.00	30,077.39	1.1409
TSLM	79,276.66	175,810.63	96,533.97	1.2177
HWA	28,906.75	64,642.95	35,736.21	1.2363
Prophet	57,399.43	133,887.54	76,488.11	1.3326
ARIMA_d1D1	24,793.46	59,202.59	34,409.13	1.3878
ARIMA_auto	24,567.87	59,117.03	34,549.17	1.4063
SNaive	53,807.75	153,714.16	99,906.41	1.8567
ARIMA_d0D1	24,247.36	79,371.45	55,124.10	2.2734

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

2.1.2.6 RMSE per Year

All Models

# Calculate RMSE per year and save as tsibble
rmse_pyear_madeira_slide <- error_fc_madeira_slide %>%
  mutate(Year = year(Month)) %>%
  index_by(Year) %>%
  group_by(Model) %>%
  summarise(RMSE = (mean(Forecast_Error**2))**0.5)

# Create Plot for 2010-2022
rmse_pyear_madeira_slide %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Create Plot for 2020-2022
rmse_pyear_madeira_slide %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_madeira_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	128,349.1	55,326.97	0.7577
Naive_log	132,442.5	58,349.10	0.7875
TSLM_log	565,250.8	413,031.79	2.7134
TSLM	526,455.4	416,188.41	3.7744
Prophet_log	319,242.0	253,047.83	3.8228
Drift_STL_log	154,980.8	123,248.41	3.8840
ETS_auto_log	200,596.9	162,512.84	4.2672
HWA_log	186,680.4	152,521.54	4.4651
Drift_STL	167,603.9	137,436.34	4.5558
ARIMA_auto	180,020.2	148,286.19	4.6728
Prophet	405,262.5	334,346.51	4.7147
ARIMA_auto_log	189,331.1	156,276.84	4.7279
ETS_auto	168,754.3	139,529.24	4.7743
ARIMA_d0D1_log	192,988.0	160,211.93	4.8881
SNaive	480,578.5	404,110.50	5.2847
ARIMA_d1D1	180,020.2	152,238.19	5.4797
HWA	193,932.5	165,004.68	5.7040
ARIMA_d1D1_log	183,636.1	156,290.11	5.7153
ARIMA_d0D1	251,830.8	220,511.52	7.0408
SNaive_log	649,306.4	569,609.99	7.1472

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_madeira_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_d0D1	84,919.07	-166,911.75	-0.6628
Drift_STL_log	53,753.68	-101,227.16	-0.6532
HWA_log	66,328.64	-120,351.79	-0.6447
TSLM_log	226,065.42	-339,185.34	-0.6001
ARIMA_d0D1_log	81,052.56	-111,935.48	-0.5800
HWA	85,564.34	-108,368.19	-0.5588
Drift_STL	78,360.70	-89,243.15	-0.5325
ARIMA_auto	88,123.23	-91,896.93	-0.5105
ETS_auto	82,896.53	-85,857.81	-0.5088
ARIMA_d1D1	88,495.88	-91,524.28	-0.5084
TSLM	273,295.48	-253,159.89	-0.4809
SNaive_log	377,817.21	-271,489.16	-0.4181
Prophet	246,854.33	-158,408.15	-0.3909
ARIMA_d1D1_log	113,355.13	-70,280.97	-0.3827
ARIMA_auto_log	127,769.29	-61,561.78	-0.3252
ETS_auto_log	142,006.03	-58,590.87	-0.2921
SNaive	375,134.24	-105,444.30	-0.2194
Naive	122,668.21	-5,680.89	-0.0443
Prophet_log	323,702.47	4,460.43	0.0140
Naive_log	141,714.15	9,271.68	0.0700

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_madeira_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ETS_auto_log	82,169.60	-59,836.43	-0.4214
Naive_log	82,036.25	-59,677.90	-0.4211
ARIMA_auto_log	78,890.25	-48,879.04	-0.3826
Naive	106,320.15	-16,348.06	-0.1333
TSLM	239,379.35	-33,916.13	-0.1241
ARIMA_auto	80,917.70	-7,205.53	-0.0818
ARIMA_d0D1	80,917.70	-4,001.37	-0.0471
ARIMA_d1D1	85,924.97	-2,570.91	-0.0291
HWA	88,648.27	3,083.93	0.0360
SNaive_log	397,694.94	19,877.72	0.0526
ETS_auto	91,968.58	9,072.05	0.1094
Prophet	293,633.77	46,779.45	0.1895
Drift_STL	94,862.22	16,501.52	0.2106
SNaive	494,290.74	119,156.50	0.3176
Prophet_log	443,013.36	119,310.89	0.3686
TSLM_log	350,102.84	124,037.42	0.5487
ARIMA_d1D1_log	286,705.98	173,350.86	1.5293
HWA_log	230,921.48	164,592.84	2.4815
ARIMA_d0D1_log	284,178.69	203,126.12	2.5061
Drift_STL_log	314,410.85	260,657.17	4.8491

Each Model once

# Create Plot for 2010-2022
rmse_pyear_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022")

# Create Plot for 2020-2022
rmse_pyear_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022")

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	128,349.1	55,326.97	0.7577
TSLM	526,455.4	416,188.41	3.7744
Drift_STL	167,603.9	137,436.34	4.5558
ARIMA_auto	180,020.2	148,286.19	4.6728
Prophet	405,262.5	334,346.51	4.7147
ETS_auto	168,754.3	139,529.24	4.7743
SNaive	480,578.5	404,110.50	5.2847
ARIMA_d1D1	180,020.2	152,238.19	5.4797
HWA	193,932.5	165,004.68	5.7040
ARIMA_d0D1	251,830.8	220,511.52	7.0408

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_d0D1	84,919.07	-166,911.75	-0.6628
HWA	85,564.34	-108,368.19	-0.5588
Drift_STL	78,360.70	-89,243.15	-0.5325
ARIMA_auto	88,123.23	-91,896.93	-0.5105
ETS_auto	82,896.53	-85,857.81	-0.5088
ARIMA_d1D1	88,495.88	-91,524.28	-0.5084
TSLM	273,295.48	-253,159.89	-0.4809
Prophet	246,854.33	-158,408.15	-0.3909
SNaive	375,134.24	-105,444.30	-0.2194
Naive	122,668.21	-5,680.89	-0.0443

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	106,320.15	-16,348.06	-0.1333
TSLM	239,379.35	-33,916.13	-0.1241
ARIMA_auto	80,917.70	-7,205.53	-0.0818
ARIMA_d0D1	80,917.70	-4,001.37	-0.0471
ARIMA_d1D1	85,924.97	-2,570.91	-0.0291
HWA	88,648.27	3,083.93	0.0360
ETS_auto	91,968.58	9,072.05	0.1094
Prophet	293,633.77	46,779.45	0.1895
Drift_STL	94,862.22	16,501.52	0.2106
SNaive	494,290.74	119,156.50	0.3176

2.1.2.7 Change of RMSSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_slide, tourism_madeira_until2019) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_slide, tourism_madeira_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
Drift_STL	7	0.5670	1	0.3906
ETS_auto	10	0.6518	2	0.4035
ARIMA_auto	2	0.5284	3	0.4065
ARIMA_d1D1	3	0.5332	4	0.4089
HWA	8	0.6217	5	0.4371
ARIMA_auto_log	6	0.5660	6	0.4558
ETS_auto_log	12	0.7280	7	0.5012
HWA_log	11	0.7254	8	0.5080
ARIMA_d0D1	1	0.5215	9	0.5162
Drift_STL_log	9	0.6293	10	0.5324
ARIMA_d0D1_log	4	0.5491	11	0.5504
ARIMA_d1D1_log	5	0.5615	12	0.5617
Naive	18	1.7715	13	0.5922
Naive_log	19	1.7860	14	0.6059
Prophet	16	1.2345	15	1.0030
Prophet_log	15	1.1825	16	1.0578
TSLM	17	1.7050	17	1.2167
TSLM_log	20	1.9015	18	1.3051
SNaive	14	1.1572	19	1.3213
SNaive_log	13	1.1420	20	1.4976

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_madeira_slide, tourism_madeira_until2019) %>%
  filter(.model %in% best_models_fc_madeira_slide) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_madeira_slide, tourism_madeira_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
Drift_STL	4	0.5670	1	0.3906
ETS_auto	6	0.6518	2	0.4035
ARIMA_auto	2	0.5284	3	0.4065
ARIMA_d1D1	3	0.5332	4	0.4089
HWA	5	0.6217	5	0.4371
ARIMA_d0D1	1	0.5215	9	0.5162
Naive	10	1.7715	13	0.5922
Prophet	8	1.2345	15	1.0030
TSLM	9	1.7050	17	1.2167
SNaive	7	1.1572	19	1.3213

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.1.2.8 RMSSE Development by including more Years in Time Series

All Models

# Plot development of RMSSE for period 2010-2022
accuracy_madeira_slide %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_madeira_slide %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_madeira_slide %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

Each Model once

# Plot development of RMSSE for period 2010-2022
accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_madeira_slide %>%
  filter(Model %in% best_models_fc_madeira_slide) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSSE")

2.2 Algarve

2.2.1 Recursive Window Cross-Validation

2.2.1.1 Time series Cross-Validation & Seasonal Strength Test

# Cross-Validation to create Training sets
data_stretch_algarve <- tourism_algarve_until2022 %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Testing for Seasonal Strength
data_stretch_algarve %>%
  features(Overnight_Stays, unitroot_nsdiffs) %>%
  group_by(Region) %>%
  summarise(Mean_nsdiffs = (mean(nsdiffs))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Strength Test</span>", align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Strength Test

Region	Mean_nsdiffs
Algarve	1

2.2.1.2 Fitting Models and one-step ahead Forecasts

# Fit models
fit_algarve_stretch <- data_stretch_algarve %>%
  model(
    SNaive = SNAIVE(Overnight_Stays),
    Drift_STL = decomposition_model(STL(Overnight_Stays),RW(season_adjust ~ drift())),
    Naive = NAIVE(Overnight_Stays),
    TSLM = TSLM(Overnight_Stays ~ trend() + season()),
    ETS_auto = ETS(Overnight_Stays),
    HWA = ETS(Overnight_Stays ~ error("A") + trend("A") + season("A")),
    ARIMA_auto = ARIMA(Overnight_Stays),
        ARIMA_d1D1 = ARIMA(Overnight_Stays ~ pdq(d=1) + PDQ(D=1)),
        ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)),
        Prophet = fable.prophet::prophet(Overnight_Stays ~ season(period = 12)),
        SNaive_log = SNAIVE(log(Overnight_Stays)),
    Drift_STL_log = decomposition_model(STL(log(Overnight_Stays)),RW(season_adjust ~ drift())),
    Naive_log = NAIVE(log(Overnight_Stays)),
    TSLM_log = TSLM(log(Overnight_Stays) ~ trend() + season()),
    ETS_auto_log = ETS(log(Overnight_Stays)),
        HWA_log = ETS(log(Overnight_Stays) ~ error("A") + trend("A") + season("A")),
    ARIMA_auto_log = ARIMA(log(Overnight_Stays)),
    ARIMA_d1D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)),
    Prophet_log = fable.prophet::prophet(log(Overnight_Stays) ~ season(period = 12))
    )

# Perform a one-step ahead Forecast
fc_algarve_stretch <- fit_algarve_stretch %>% forecast(h=1)

2.2.1.3 Forecast Errors

# Calculate forecast error per observation and model
error_fc_algarve_stretch <- merge(tourism_algarve_until2022, fc_algarve_stretch, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# Show table
error_fc_algarve_stretch %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Forecast Error per Observation and Model</span>", digits = 2, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Forecast Error per Observation and Model

Month	Overnight_Stays	Model	Point_Forecast	Forecast_Error
2010 Jan	366,296	ARIMA_auto	383,209.18	-16,913.18
2010 Feb	533,056	ARIMA_auto	554,062.08	-21,006.08
2010 Mar	742,227	ARIMA_auto	773,222.97	-30,995.97
2010 Apr	902,745	ARIMA_auto	966,448.71	-63,703.71
2010 May	1,107,303	ARIMA_auto	1,170,336.36	-63,033.36
2010 Jun	1,464,695	ARIMA_auto	1,457,055.65	7,639.35
2010 Jul	2,050,478	ARIMA_auto	1,907,336.43	143,141.57
2010 Aug	2,468,924	ARIMA_auto	2,344,678.83	124,245.17
2010 Sep	1,696,356	ARIMA_auto	1,641,848.76	54,507.24
2010 Oct	1,104,659	ARIMA_auto	1,125,393.00	-20,734.00
2010 Nov	445,221	ARIMA_auto	537,347.41	-92,126.41
2010 Dec	365,490	ARIMA_auto	402,700.64	-37,210.64
2011 Jan	357,209	ARIMA_auto	396,782.21	-39,573.21
2011 Feb	503,831	ARIMA_auto	554,616.35	-50,785.35
2011 Mar	761,343	ARIMA_auto	756,530.03	4,812.97
2011 Apr	1,177,115	ARIMA_auto	945,394.97	231,720.03
2011 May	1,169,516	ARIMA_auto	1,271,378.50	-101,862.50
2011 Jun	1,576,730	ARIMA_auto	1,515,664.81	61,065.19
2011 Jul	2,208,160	ARIMA_auto	2,033,145.86	175,014.14
2011 Aug	2,572,404	ARIMA_auto	2,492,624.68	79,779.32
2011 Sep	1,731,056	ARIMA_auto	1,750,440.32	-19,384.32
2011 Oct	1,161,751	ARIMA_auto	1,170,406.70	-8,655.70
2011 Nov	427,550	ARIMA_auto	543,689.56	-116,139.56
2011 Dec	333,201	ARIMA_auto	403,246.23	-70,045.23
2012 Jan	359,355	ARIMA_auto	373,878.30	-14,523.30
2012 Feb	531,709	ARIMA_auto	527,779.71	3,929.29
2012 Mar	751,024	ARIMA_auto	765,126.93	-14,102.93
2012 Apr	1,017,976	ARIMA_auto	1,055,233.18	-37,257.18
2012 May	1,194,673	ARIMA_auto	1,152,922.15	41,750.85
2012 Jun	1,678,327	ARIMA_auto	1,531,096.45	147,230.55
2012 Jul	2,296,474	ARIMA_auto	2,144,078.34	152,395.66
2012 Aug	2,622,801	ARIMA_auto	2,596,281.74	26,519.26
2012 Sep	1,829,252	ARIMA_auto	1,786,092.23	43,159.77
2012 Oct	1,244,751	ARIMA_auto	1,192,360.52	52,390.48
2012 Nov	453,958	ARIMA_auto	528,799.41	-74,841.41
2012 Dec	346,474	ARIMA_auto	389,400.59	-42,926.59
2013 Jan	369,969	ARIMA_auto	366,149.66	3,819.34
2013 Feb	520,055	ARIMA_auto	530,911.31	-10,856.31
2013 Mar	840,024	ARIMA_auto	755,926.68	84,097.32
2013 Apr	986,191	ARIMA_auto	1,068,524.68	-82,333.68
2013 May	1,382,234	ARIMA_auto	1,183,969.45	198,264.55
2013 Jun	1,814,108	ARIMA_auto	1,657,758.68	156,349.32
2013 Jul	2,387,304	ARIMA_auto	2,336,442.45	50,861.55
2013 Aug	2,764,686	ARIMA_auto	2,684,143.67	80,542.33
2013 Sep	1,943,037	ARIMA_auto	1,893,125.02	49,911.98
2013 Oct	1,291,360	ARIMA_auto	1,311,315.29	-19,955.29
2013 Nov	455,695	ARIMA_auto	536,026.48	-80,331.48
2013 Dec	358,062	ARIMA_auto	378,930.31	-20,868.31
2014 Jan	377,387	ARIMA_auto	367,216.19	10,170.81
2014 Feb	543,470	ARIMA_auto	523,125.33	20,344.67
2014 Mar	749,773	ARIMA_auto	812,705.32	-62,932.32
2014 Apr	1,337,145	ARIMA_auto	1,000,303.43	336,841.57
2014 May	1,538,342	ARIMA_auto	1,375,468.41	162,873.59
2014 Jun	1,994,167	ARIMA_auto	1,907,176.14	86,990.86
2014 Jul	2,529,246	ARIMA_auto	2,525,257.40	3,988.60
2014 Aug	3,069,865	ARIMA_auto	2,893,182.74	176,682.26
2014 Sep	2,089,656	ARIMA_auto	2,153,621.93	-63,965.93
2014 Oct	1,477,481	ARIMA_auto	1,502,029.80	-24,548.80
2014 Nov	502,473	ARIMA_auto	687,777.94	-185,304.94
2014 Dec	382,543	ARIMA_auto	517,445.84	-134,902.84
2015 Jan	381,607	ARIMA_auto	483,911.20	-102,304.20
2015 Feb	544,777	ARIMA_auto	600,881.81	-56,104.81
2015 Mar	827,071	ARIMA_auto	809,999.29	17,071.71
2015 Apr	1,242,844	ARIMA_auto	1,266,789.15	-23,945.15
2015 May	1,654,526	ARIMA_auto	1,492,977.49	161,548.51
2015 Jun	2,079,484	ARIMA_auto	2,024,823.64	54,660.36
2015 Jul	2,688,710	ARIMA_auto	2,599,869.08	88,840.92
2015 Aug	3,108,357	ARIMA_auto	3,107,524.57	832.43
2015 Sep	2,196,681	ARIMA_auto	2,194,214.96	2,466.04
2015 Oct	1,553,142	ARIMA_auto	1,567,878.91	-14,736.91
2015 Nov	552,778	ARIMA_auto	639,379.21	-86,601.21
2015 Dec	426,419	ARIMA_auto	489,803.17	-63,384.17
2016 Jan	443,150	ARIMA_auto	470,936.87	-27,786.87
2016 Feb	664,278	ARIMA_auto	622,815.26	41,462.74
2016 Mar	1,089,392	ARIMA_auto	897,797.46	191,594.54
2016 Apr	1,335,308	ARIMA_auto	1,445,874.34	-110,566.34
2016 May	1,828,292	ARIMA_auto	1,744,860.80	83,431.20
2016 Jun	2,288,337	ARIMA_auto	2,213,667.08	74,669.92
2016 Jul	2,848,570	ARIMA_auto	2,822,599.08	25,970.92
2016 Aug	3,204,047	ARIMA_auto	3,297,775.39	-93,728.39
2016 Sep	2,378,618	ARIMA_auto	2,331,517.94	47,100.06
2016 Oct	1,793,822	ARIMA_auto	1,713,841.15	79,980.85
2016 Nov	653,514	ARIMA_auto	766,914.98	-113,400.98
2016 Dec	478,510	ARIMA_auto	589,198.69	-110,688.69
2017 Jan	495,629	ARIMA_auto	557,579.76	-61,950.76
2017 Feb	704,532	ARIMA_auto	734,268.83	-29,736.83
2017 Mar	1,015,421	ARIMA_auto	1,092,155.38	-76,734.38
2017 Apr	1,765,170	ARIMA_auto	1,390,503.10	374,666.90
2017 May	1,970,072	ARIMA_auto	1,978,766.49	-8,694.49
2017 Jun	2,417,100	ARIMA_auto	2,473,579.63	-56,479.63
2017 Jul	2,968,641	ARIMA_auto	3,012,325.51	-43,684.51
2017 Aug	3,295,406	ARIMA_auto	3,346,294.86	-50,888.86
2017 Sep	2,470,298	ARIMA_auto	2,446,537.14	23,760.86
2017 Oct	1,911,961	ARIMA_auto	1,850,120.54	61,840.46
2017 Nov	680,373	ARIMA_auto	798,391.69	-118,018.69
2017 Dec	512,548	ARIMA_auto	613,088.67	-100,540.67
2018 Jan	503,908	ARIMA_auto	581,069.67	-77,161.67
2018 Feb	731,090	ARIMA_auto	769,632.42	-38,542.42
2018 Mar	1,151,455	ARIMA_auto	1,122,754.74	28,700.26
2018 Apr	1,575,078	ARIMA_auto	1,666,092.46	-91,014.46
2018 May	2,003,996	ARIMA_auto	1,975,293.25	28,702.75
2018 Jun	2,381,154	ARIMA_auto	2,436,874.68	-55,720.68
2018 Jul	2,981,643	ARIMA_auto	2,977,932.80	3,710.20
2018 Aug	3,371,918	ARIMA_auto	3,309,103.53	62,814.47
2018 Sep	2,499,368	ARIMA_auto	2,510,972.98	-11,604.98
2018 Oct	1,956,693	ARIMA_auto	1,937,270.66	19,422.34
2018 Nov	732,141	ARIMA_auto	740,493.22	-8,352.22
2018 Dec	554,803	ARIMA_auto	562,954.10	-8,151.10
2019 Jan	548,686	ARIMA_auto	564,072.46	-15,386.46
2019 Feb	739,981	ARIMA_auto	784,158.63	-44,177.63
2019 Mar	1,078,918	ARIMA_auto	1,156,197.50	-77,279.50
2019 Apr	1,795,494	ARIMA_auto	1,686,341.32	109,152.68
2019 May	1,990,529	ARIMA_auto	2,060,274.63	-69,745.63
2019 Jun	2,425,834	ARIMA_auto	2,447,621.89	-21,787.89
2019 Jul	2,988,668	ARIMA_auto	3,016,675.97	-28,007.97
2019 Aug	3,439,271	ARIMA_auto	3,349,169.38	90,101.62
2019 Sep	2,573,527	ARIMA_auto	2,546,466.97	27,060.03
2019 Oct	1,930,852	ARIMA_auto	2,014,410.56	-83,558.56
2019 Nov	785,875	ARIMA_auto	736,833.49	49,041.51
2019 Dec	602,860	ARIMA_auto	574,937.69	27,922.31
2020 Jan	560,368	ARIMA_auto	577,421.07	-17,053.07
2020 Feb	844,247	ARIMA_auto	780,262.43	63,984.57
2020 Mar	513,360	ARIMA_auto	1,174,636.90	-661,276.90
2020 Apr	25,614	ARIMA_auto	1,602,113.82	-1,576,499.82
2020 May	40,932	ARIMA_auto	517,816.14	-476,884.14
2020 Jun	330,393	ARIMA_auto	379,977.66	-49,584.66
2020 Jul	1,035,732	ARIMA_auto	994,627.32	41,104.68
2020 Aug	2,090,569	ARIMA_auto	1,685,662.41	404,906.59
2020 Sep	1,418,185	ARIMA_auto	1,602,458.96	-184,273.96
2020 Oct	696,087	ARIMA_auto	1,125,566.22	-429,479.22
2020 Nov	181,873	ARIMA_auto	-316,017.23	497,890.23
2020 Dec	153,351	ARIMA_auto	91,733.32	61,617.68
2021 Jan	105,336	ARIMA_auto	284,376.94	-179,040.94
2021 Feb	66,194	ARIMA_auto	492,755.60	-426,561.60
2021 Mar	84,413	ARIMA_auto	207,636.33	-123,223.33
2021 Apr	138,661	ARIMA_auto	287,723.46	-149,062.46
2021 May	502,057	ARIMA_auto	387,238.74	114,818.26
2021 Jun	1,182,009	ARIMA_auto	997,119.36	184,889.64
2021 Jul	1,551,789	ARIMA_auto	1,939,988.27	-388,199.27
2021 Aug	2,762,537	ARIMA_auto	2,302,104.75	460,432.25
2021 Sep	1,869,194	ARIMA_auto	2,001,978.84	-132,784.84
2021 Oct	1,584,764	ARIMA_auto	1,269,910.65	314,853.35
2021 Nov	651,051	ARIMA_auto	721,433.36	-70,382.36
2021 Dec	376,031	ARIMA_auto	560,303.64	-184,272.64
2022 Jan	344,634	ARIMA_auto	336,432.52	8,201.48
2022 Feb	590,122	ARIMA_auto	415,629.11	174,492.89
2022 Mar	873,841	ARIMA_auto	633,759.17	240,081.83
2022 Apr	1,629,377	ARIMA_auto	1,023,765.80	605,611.20
2022 May	1,867,744	ARIMA_auto	1,906,757.36	-39,013.36
2022 Jun	2,230,207	ARIMA_auto	2,350,104.16	-119,897.16
2010 Jan	366,296	ARIMA_auto_log	410,896.99	-44,600.99
2010 Feb	533,056	ARIMA_auto_log	548,250.46	-15,194.46
2010 Mar	742,227	ARIMA_auto_log	735,503.00	6,724.00
2010 Apr	902,745	ARIMA_auto_log	941,569.72	-38,824.72
2010 May	1,107,303	ARIMA_auto_log	1,120,692.50	-13,389.50
2010 Jun	1,464,695	ARIMA_auto_log	1,383,714.64	80,980.36
2010 Jul	2,050,478	ARIMA_auto_log	1,800,061.59	250,416.41
2010 Aug	2,468,924	ARIMA_auto_log	2,297,571.68	171,352.32
2010 Sep	1,696,356	ARIMA_auto_log	1,662,188.29	34,167.71
2010 Oct	1,104,659	ARIMA_auto_log	1,126,853.68	-22,194.68
2010 Nov	445,221	ARIMA_auto_log	525,636.19	-80,415.19
2010 Dec	365,490	ARIMA_auto_log	395,099.50	-29,609.50
2011 Jan	357,209	ARIMA_auto_log	376,154.67	-18,945.67
2011 Feb	503,831	ARIMA_auto_log	545,492.68	-41,661.68
2011 Mar	761,343	ARIMA_auto_log	723,369.19	37,973.81
2011 Apr	1,177,115	ARIMA_auto_log	811,995.69	365,119.31
2011 May	1,169,516	ARIMA_auto_log	1,214,114.58	-44,598.58
2011 Jun	1,576,730	ARIMA_auto_log	1,521,462.10	55,267.90
2011 Jul	2,208,160	ARIMA_auto_log	2,050,475.12	157,684.88
2011 Aug	2,572,404	ARIMA_auto_log	2,523,972.21	48,431.79
2011 Sep	1,731,056	ARIMA_auto_log	1,732,609.31	-1,553.31
2011 Oct	1,161,751	ARIMA_auto_log	1,139,882.01	21,868.99
2011 Nov	427,550	ARIMA_auto_log	500,875.08	-73,325.08
2011 Dec	333,201	ARIMA_auto_log	381,679.64	-48,478.64
2012 Jan	359,355	ARIMA_auto_log	361,251.04	-1,896.04
2012 Feb	531,709	ARIMA_auto_log	512,947.23	18,761.77
2012 Mar	751,024	ARIMA_auto_log	751,766.58	-742.58
2012 Apr	1,017,976	ARIMA_auto_log	1,047,938.80	-29,962.80
2012 May	1,194,673	ARIMA_auto_log	1,142,165.10	52,507.90
2012 Jun	1,678,327	ARIMA_auto_log	1,529,145.21	149,181.79
2012 Jul	2,296,474	ARIMA_auto_log	2,162,528.07	133,945.93
2012 Aug	2,622,801	ARIMA_auto_log	2,605,878.11	16,922.89
2012 Sep	1,829,252	ARIMA_auto_log	1,762,237.25	67,014.75
2012 Oct	1,244,751	ARIMA_auto_log	1,180,811.13	63,939.87
2012 Nov	453,958	ARIMA_auto_log	476,899.40	-22,941.40
2012 Dec	346,474	ARIMA_auto_log	368,010.62	-21,536.62
2013 Jan	369,969	ARIMA_auto_log	371,729.09	-1,760.09
2013 Feb	520,055	ARIMA_auto_log	537,103.46	-17,048.46
2013 Mar	840,024	ARIMA_auto_log	757,904.09	82,119.91
2013 Apr	986,191	ARIMA_auto_log	1,076,724.73	-90,533.73
2013 May	1,382,234	ARIMA_auto_log	1,184,522.60	197,711.40
2013 Jun	1,814,108	ARIMA_auto_log	1,694,134.12	119,973.88
2013 Jul	2,387,304	ARIMA_auto_log	2,360,686.37	26,617.63
2013 Aug	2,764,686	ARIMA_auto_log	2,727,631.89	37,054.11
2013 Sep	1,943,037	ARIMA_auto_log	1,873,483.79	69,553.21
2013 Oct	1,291,360	ARIMA_auto_log	1,268,397.04	22,962.96
2013 Nov	455,695	ARIMA_auto_log	478,148.29	-22,453.29
2013 Dec	358,062	ARIMA_auto_log	362,707.01	-4,645.01
2014 Jan	377,387	ARIMA_auto_log	379,574.48	-2,187.48
2014 Feb	543,470	ARIMA_auto_log	538,310.73	5,159.27
2014 Mar	749,773	ARIMA_auto_log	824,949.55	-75,176.55
2014 Apr	1,337,145	ARIMA_auto_log	1,005,698.99	331,446.01
2014 May	1,538,342	ARIMA_auto_log	1,381,689.28	156,652.72
2014 Jun	1,994,167	ARIMA_auto_log	1,931,489.52	62,677.48
2014 Jul	2,529,246	ARIMA_auto_log	2,615,791.10	-86,545.10
2014 Aug	3,069,865	ARIMA_auto_log	2,952,447.06	117,417.94
2014 Sep	2,089,656	ARIMA_auto_log	2,071,139.05	18,516.95
2014 Oct	1,477,481	ARIMA_auto_log	1,387,506.11	89,974.89
2014 Nov	502,473	ARIMA_auto_log	499,646.38	2,826.62
2014 Dec	382,543	ARIMA_auto_log	393,637.92	-11,094.92
2015 Jan	381,607	ARIMA_auto_log	417,446.12	-35,839.12
2015 Feb	544,777	ARIMA_auto_log	582,726.98	-37,949.98
2015 Mar	827,071	ARIMA_auto_log	849,032.86	-21,961.86
2015 Apr	1,242,844	ARIMA_auto_log	1,224,835.83	18,008.17
2015 May	1,654,526	ARIMA_auto_log	1,551,966.46	102,559.54
2015 Jun	2,079,484	ARIMA_auto_log	2,081,768.52	-2,284.52
2015 Jul	2,688,710	ARIMA_auto_log	2,694,734.52	-6,024.52
2015 Aug	3,108,357	ARIMA_auto_log	3,181,493.57	-73,136.57
2015 Sep	2,196,681	ARIMA_auto_log	2,192,055.19	4,625.81
2015 Oct	1,553,142	ARIMA_auto_log	1,510,019.81	43,122.19
2015 Nov	552,778	ARIMA_auto_log	525,206.10	27,571.90
2015 Dec	426,419	ARIMA_auto_log	410,531.65	15,887.35
2016 Jan	443,150	ARIMA_auto_log	427,889.91	15,260.09
2016 Feb	664,278	ARIMA_auto_log	618,478.16	45,799.84
2016 Mar	1,089,392	ARIMA_auto_log	930,215.73	159,176.27
2016 Apr	1,335,308	ARIMA_auto_log	1,540,664.54	-205,356.54
2016 May	1,828,292	ARIMA_auto_log	1,868,844.60	-40,552.60
2016 Jun	2,288,337	ARIMA_auto_log	2,373,404.57	-85,067.57
2016 Jul	2,848,570	ARIMA_auto_log	3,013,389.72	-164,819.72
2016 Aug	3,204,047	ARIMA_auto_log	3,499,631.75	-295,584.75
2016 Sep	2,378,618	ARIMA_auto_log	2,376,151.43	2,466.57
2016 Oct	1,793,822	ARIMA_auto_log	1,671,624.12	122,197.88
2016 Nov	653,514	ARIMA_auto_log	594,090.74	59,423.26
2016 Dec	478,510	ARIMA_auto_log	469,615.59	8,894.41
2017 Jan	495,629	ARIMA_auto_log	483,713.83	11,915.17
2017 Feb	704,532	ARIMA_auto_log	713,478.49	-8,946.49
2017 Mar	1,015,421	ARIMA_auto_log	1,109,850.51	-94,429.51
2017 Apr	1,765,170	ARIMA_auto_log	1,513,881.58	251,288.42
2017 May	1,970,072	ARIMA_auto_log	2,119,931.95	-149,859.95
2017 Jun	2,417,100	ARIMA_auto_log	2,598,122.35	-181,022.35
2017 Jul	2,968,641	ARIMA_auto_log	3,216,024.46	-247,383.46
2017 Aug	3,295,406	ARIMA_auto_log	3,620,664.62	-325,258.62
2017 Sep	2,470,298	ARIMA_auto_log	2,536,372.83	-66,074.83
2017 Oct	1,911,961	ARIMA_auto_log	1,839,000.29	72,960.71
2017 Nov	680,373	ARIMA_auto_log	665,337.75	15,035.25
2017 Dec	512,548	ARIMA_auto_log	503,590.66	8,957.34
2018 Jan	503,908	ARIMA_auto_log	521,405.63	-17,497.63
2018 Feb	731,090	ARIMA_auto_log	752,542.28	-21,452.28
2018 Mar	1,151,455	ARIMA_auto_log	1,145,841.28	5,613.72
2018 Apr	1,575,078	ARIMA_auto_log	1,696,726.75	-121,648.75
2018 May	2,003,996	ARIMA_auto_log	2,072,079.00	-68,083.00
2018 Jun	2,381,154	ARIMA_auto_log	2,535,978.47	-154,824.47
2018 Jul	2,981,643	ARIMA_auto_log	3,085,679.43	-104,036.43
2018 Aug	3,371,918	ARIMA_auto_log	3,421,320.53	-49,402.53
2018 Sep	2,499,368	ARIMA_auto_log	2,535,607.73	-36,239.73
2018 Oct	1,956,693	ARIMA_auto_log	1,925,336.96	31,356.04
2018 Nov	732,141	ARIMA_auto_log	698,151.17	33,989.83
2018 Dec	554,803	ARIMA_auto_log	527,595.11	27,207.89
2019 Jan	548,686	ARIMA_auto_log	541,794.52	6,891.48
2019 Feb	739,981	ARIMA_auto_log	786,979.72	-46,998.72
2019 Mar	1,078,918	ARIMA_auto_log	1,182,196.94	-103,278.94
2019 Apr	1,795,494	ARIMA_auto_log	1,716,148.95	79,345.05
2019 May	1,990,529	ARIMA_auto_log	2,103,710.09	-113,181.09
2019 Jun	2,425,834	ARIMA_auto_log	2,500,447.33	-74,613.33
2019 Jul	2,988,668	ARIMA_auto_log	3,067,615.38	-78,947.38
2019 Aug	3,439,271	ARIMA_auto_log	3,393,780.78	45,490.22
2019 Sep	2,573,527	ARIMA_auto_log	2,559,061.93	14,465.07
2019 Oct	1,930,852	ARIMA_auto_log	2,007,790.73	-76,938.73
2019 Nov	785,875	ARIMA_auto_log	728,087.46	57,787.54
2019 Dec	602,860	ARIMA_auto_log	559,446.73	43,413.27
2020 Jan	560,368	ARIMA_auto_log	566,464.37	-6,096.37
2020 Feb	844,247	ARIMA_auto_log	789,719.31	54,527.69
2020 Mar	513,360	ARIMA_auto_log	1,212,663.47	-699,303.47
2020 Apr	25,614	ARIMA_auto_log	1,542,583.82	-1,516,969.82
2020 May	40,932	ARIMA_auto_log	4,885.48	36,046.52
2020 Jun	330,393	ARIMA_auto_log	738,628.03	-408,235.03
2020 Jul	1,035,732	ARIMA_auto_log	983,765.59	51,966.41
2020 Aug	2,090,569	ARIMA_auto_log	1,904,952.51	185,616.49
2020 Sep	1,418,185	ARIMA_auto_log	1,981,878.84	-563,693.84
2020 Oct	696,087	ARIMA_auto_log	1,099,068.94	-402,981.94
2020 Nov	181,873	ARIMA_auto_log	305,395.84	-123,522.84
2020 Dec	153,351	ARIMA_auto_log	177,450.88	-24,099.88
2021 Jan	105,336	ARIMA_auto_log	228,990.40	-123,654.40
2021 Feb	66,194	ARIMA_auto_log	145,299.83	-79,105.83
2021 Mar	84,413	ARIMA_auto_log	95,921.55	-11,508.55
2021 Apr	138,661	ARIMA_auto_log	71,225.49	67,435.51
2021 May	502,057	ARIMA_auto_log	243,195.69	258,861.31
2021 Jun	1,182,009	ARIMA_auto_log	1,428,206.59	-246,197.59
2021 Jul	1,551,789	ARIMA_auto_log	1,816,189.31	-264,400.31
2021 Aug	2,762,537	ARIMA_auto_log	2,155,534.54	607,002.46
2021 Sep	1,869,194	ARIMA_auto_log	2,419,179.64	-549,985.64
2021 Oct	1,584,764	ARIMA_auto_log	1,172,871.01	411,892.99
2021 Nov	651,051	ARIMA_auto_log	664,629.51	-13,578.51
2021 Dec	376,031	ARIMA_auto_log	477,090.21	-101,059.21
2022 Jan	344,634	ARIMA_auto_log	319,502.97	25,131.03
2022 Feb	590,122	ARIMA_auto_log	463,324.64	126,797.36
2022 Mar	873,841	ARIMA_auto_log	806,069.64	67,771.36
2022 Apr	1,629,377	ARIMA_auto_log	734,536.95	894,840.05
2022 May	1,867,744	ARIMA_auto_log	2,627,976.22	-760,232.22
2022 Jun	2,230,207	ARIMA_auto_log	2,128,488.65	101,718.35
2010 Jan	366,296	ARIMA_d0D1	383,209.18	-16,913.18
2010 Feb	533,056	ARIMA_d0D1	554,062.08	-21,006.08
2010 Mar	742,227	ARIMA_d0D1	773,222.97	-30,995.97
2010 Apr	902,745	ARIMA_d0D1	966,448.71	-63,703.71
2010 May	1,107,303	ARIMA_d0D1	1,170,336.36	-63,033.36
2010 Jun	1,464,695	ARIMA_d0D1	1,457,055.65	7,639.35
2010 Jul	2,050,478	ARIMA_d0D1	1,907,336.43	143,141.57
2010 Aug	2,468,924	ARIMA_d0D1	2,344,678.83	124,245.17
2010 Sep	1,696,356	ARIMA_d0D1	1,641,848.76	54,507.24
2010 Oct	1,104,659	ARIMA_d0D1	1,125,393.00	-20,734.00
2010 Nov	445,221	ARIMA_d0D1	537,347.41	-92,126.41
2010 Dec	365,490	ARIMA_d0D1	402,700.64	-37,210.64
2011 Jan	357,209	ARIMA_d0D1	396,782.21	-39,573.21
2011 Feb	503,831	ARIMA_d0D1	554,616.35	-50,785.35
2011 Mar	761,343	ARIMA_d0D1	756,530.03	4,812.97
2011 Apr	1,177,115	ARIMA_d0D1	945,394.97	231,720.03
2011 May	1,169,516	ARIMA_d0D1	1,271,378.50	-101,862.50
2011 Jun	1,576,730	ARIMA_d0D1	1,515,664.81	61,065.19
2011 Jul	2,208,160	ARIMA_d0D1	2,033,145.86	175,014.14
2011 Aug	2,572,404	ARIMA_d0D1	2,492,624.68	79,779.32
2011 Sep	1,731,056	ARIMA_d0D1	1,750,440.32	-19,384.32
2011 Oct	1,161,751	ARIMA_d0D1	1,170,406.70	-8,655.70
2011 Nov	427,550	ARIMA_d0D1	543,689.56	-116,139.56
2011 Dec	333,201	ARIMA_d0D1	403,246.23	-70,045.23
2012 Jan	359,355	ARIMA_d0D1	373,878.30	-14,523.30
2012 Feb	531,709	ARIMA_d0D1	527,779.71	3,929.29
2012 Mar	751,024	ARIMA_d0D1	765,126.93	-14,102.93
2012 Apr	1,017,976	ARIMA_d0D1	1,055,233.18	-37,257.18
2012 May	1,194,673	ARIMA_d0D1	1,152,922.15	41,750.85
2012 Jun	1,678,327	ARIMA_d0D1	1,531,096.45	147,230.55
2012 Jul	2,296,474	ARIMA_d0D1	2,144,078.34	152,395.66
2012 Aug	2,622,801	ARIMA_d0D1	2,596,281.74	26,519.26
2012 Sep	1,829,252	ARIMA_d0D1	1,786,092.23	43,159.77
2012 Oct	1,244,751	ARIMA_d0D1	1,192,360.52	52,390.48
2012 Nov	453,958	ARIMA_d0D1	528,799.41	-74,841.41
2012 Dec	346,474	ARIMA_d0D1	389,400.59	-42,926.59
2013 Jan	369,969	ARIMA_d0D1	366,149.66	3,819.34
2013 Feb	520,055	ARIMA_d0D1	530,911.31	-10,856.31
2013 Mar	840,024	ARIMA_d0D1	755,926.68	84,097.32
2013 Apr	986,191	ARIMA_d0D1	1,068,524.68	-82,333.68
2013 May	1,382,234	ARIMA_d0D1	1,183,969.45	198,264.55
2013 Jun	1,814,108	ARIMA_d0D1	1,657,758.68	156,349.32
2013 Jul	2,387,304	ARIMA_d0D1	2,336,442.45	50,861.55
2013 Aug	2,764,686	ARIMA_d0D1	2,684,143.67	80,542.33
2013 Sep	1,943,037	ARIMA_d0D1	1,893,125.02	49,911.98
2013 Oct	1,291,360	ARIMA_d0D1	1,311,315.29	-19,955.29
2013 Nov	455,695	ARIMA_d0D1	536,026.48	-80,331.48
2013 Dec	358,062	ARIMA_d0D1	378,930.31	-20,868.31
2014 Jan	377,387	ARIMA_d0D1	367,216.19	10,170.81
2014 Feb	543,470	ARIMA_d0D1	523,125.33	20,344.67
2014 Mar	749,773	ARIMA_d0D1	812,705.32	-62,932.32
2014 Apr	1,337,145	ARIMA_d0D1	1,000,303.43	336,841.57
2014 May	1,538,342	ARIMA_d0D1	1,375,468.41	162,873.59
2014 Jun	1,994,167	ARIMA_d0D1	1,907,176.14	86,990.86
2014 Jul	2,529,246	ARIMA_d0D1	2,507,595.47	21,650.53
2014 Aug	3,069,865	ARIMA_d0D1	2,843,024.96	226,840.04
2014 Sep	2,089,656	ARIMA_d0D1	2,083,198.23	6,457.77
2014 Oct	1,477,481	ARIMA_d0D1	1,459,176.13	18,304.87
2014 Nov	502,473	ARIMA_d0D1	620,022.75	-117,549.75
2014 Dec	382,543	ARIMA_d0D1	440,765.78	-58,222.78
2015 Jan	381,607	ARIMA_d0D1	394,464.89	-12,857.89
2015 Feb	544,777	ARIMA_d0D1	534,982.70	9,794.30
2015 Mar	827,071	ARIMA_d0D1	772,172.00	54,899.00
2015 Apr	1,242,844	ARIMA_d0D1	1,232,472.54	10,371.46
2015 May	1,654,526	ARIMA_d0D1	1,480,207.51	174,318.49
2015 Jun	2,079,484	ARIMA_d0D1	1,986,157.69	93,326.31
2015 Jul	2,688,710	ARIMA_d0D1	2,588,707.71	100,002.29
2015 Aug	3,108,357	ARIMA_d0D1	3,093,754.21	14,602.79
2015 Sep	2,196,681	ARIMA_d0D1	2,160,658.12	36,022.88
2015 Oct	1,553,142	ARIMA_d0D1	1,525,538.63	27,603.37
2015 Nov	552,778	ARIMA_d0D1	596,828.11	-44,050.11
2015 Dec	426,419	ARIMA_d0D1	446,688.52	-20,269.52
2016 Jan	443,150	ARIMA_d0D1	417,936.50	25,213.50
2016 Feb	664,278	ARIMA_d0D1	575,872.42	88,405.58
2016 Mar	1,089,392	ARIMA_d0D1	870,874.59	218,517.41
2016 Apr	1,335,308	ARIMA_d0D1	1,386,379.55	-51,071.55
2016 May	1,828,292	ARIMA_d0D1	1,729,661.47	98,630.53
2016 Jun	2,288,337	ARIMA_d0D1	2,159,011.69	129,325.31
2016 Jul	2,848,570	ARIMA_d0D1	2,789,920.81	58,649.19
2016 Aug	3,204,047	ARIMA_d0D1	3,244,853.10	-40,806.10
2016 Sep	2,378,618	ARIMA_d0D1	2,286,692.63	91,925.37
2016 Oct	1,793,822	ARIMA_d0D1	1,648,264.49	145,557.51
2016 Nov	653,514	ARIMA_d0D1	721,539.12	-68,025.12
2016 Dec	478,510	ARIMA_d0D1	566,965.89	-88,455.89
2017 Jan	495,629	ARIMA_d0D1	504,925.99	-9,296.99
2017 Feb	704,532	ARIMA_d0D1	672,941.26	31,590.74
2017 Mar	1,015,421	ARIMA_d0D1	1,052,498.89	-37,077.89
2017 Apr	1,765,170	ARIMA_d0D1	1,337,619.97	427,550.03
2017 May	1,970,072	ARIMA_d0D1	1,979,261.60	-9,189.60
2017 Jun	2,417,100	ARIMA_d0D1	2,401,937.15	15,162.85
2017 Jul	2,968,641	ARIMA_d0D1	2,969,671.49	-1,030.49
2017 Aug	3,295,406	ARIMA_d0D1	3,357,862.86	-62,456.86
2017 Sep	2,470,298	ARIMA_d0D1	2,439,759.24	30,538.76
2017 Oct	1,911,961	ARIMA_d0D1	1,832,721.49	79,239.51
2017 Nov	680,373	ARIMA_d0D1	759,538.64	-79,165.64
2017 Dec	512,548	ARIMA_d0D1	561,210.15	-48,662.15
2018 Jan	503,908	ARIMA_d0D1	548,967.27	-45,059.27
2018 Feb	731,090	ARIMA_d0D1	741,019.09	-9,929.09
2018 Mar	1,151,455	ARIMA_d0D1	1,099,123.48	52,331.52
2018 Apr	1,575,078	ARIMA_d0D1	1,646,331.91	-71,253.91
2018 May	2,003,996	ARIMA_d0D1	1,958,371.65	45,624.35
2018 Jun	2,381,154	ARIMA_d0D1	2,424,536.59	-43,382.59
2018 Jul	2,981,643	ARIMA_d0D1	2,965,631.28	16,011.72
2018 Aug	3,371,918	ARIMA_d0D1	3,300,897.84	71,020.16
2018 Sep	2,499,368	ARIMA_d0D1	2,503,558.49	-4,190.49
2018 Oct	1,956,693	ARIMA_d0D1	1,927,448.81	29,244.19
2018 Nov	732,141	ARIMA_d0D1	732,218.33	-77.33
2018 Dec	554,803	ARIMA_d0D1	553,522.94	1,280.06
2019 Jan	548,686	ARIMA_d0D1	554,120.37	-5,434.37
2019 Feb	739,981	ARIMA_d0D1	773,782.85	-33,801.85
2019 Mar	1,078,918	ARIMA_d0D1	1,145,357.34	-66,439.34
2019 Apr	1,795,494	ARIMA_d0D1	1,674,992.82	120,501.18
2019 May	1,990,529	ARIMA_d0D1	2,056,487.23	-65,958.23
2019 Jun	2,425,834	ARIMA_d0D1	2,441,464.88	-15,630.88
2019 Jul	2,988,668	ARIMA_d0D1	3,011,451.36	-22,783.36
2019 Aug	3,439,271	ARIMA_d0D1	3,344,870.84	94,400.16
2019 Sep	2,573,527	ARIMA_d0D1	2,545,693.22	27,833.78
2019 Oct	1,930,852	ARIMA_d0D1	2,011,834.89	-80,982.89
2019 Nov	785,875	ARIMA_d0D1	730,532.38	55,342.62
2019 Dec	602,860	ARIMA_d0D1	571,224.77	31,635.23
2020 Jan	560,368	ARIMA_d0D1	573,582.11	-13,214.11
2020 Feb	844,247	ARIMA_d0D1	774,983.05	69,263.95
2020 Mar	513,360	ARIMA_d0D1	1,170,735.59	-657,375.59
2020 Apr	25,614	ARIMA_d0D1	1,620,872.43	-1,595,258.43
2020 May	40,932	ARIMA_d0D1	517,816.14	-476,884.14
2020 Jun	330,393	ARIMA_d0D1	379,977.66	-49,584.66
2020 Jul	1,035,732	ARIMA_d0D1	994,627.32	41,104.68
2020 Aug	2,090,569	ARIMA_d0D1	1,685,662.41	404,906.59
2020 Sep	1,418,185	ARIMA_d0D1	1,602,458.96	-184,273.96
2020 Oct	696,087	ARIMA_d0D1	1,125,566.22	-429,479.22
2020 Nov	181,873	ARIMA_d0D1	-316,017.23	497,890.23
2020 Dec	153,351	ARIMA_d0D1	91,733.32	61,617.68
2021 Jan	105,336	ARIMA_d0D1	284,376.94	-179,040.94
2021 Feb	66,194	ARIMA_d0D1	492,755.60	-426,561.60
2021 Mar	84,413	ARIMA_d0D1	207,636.33	-123,223.33
2021 Apr	138,661	ARIMA_d0D1	287,723.46	-149,062.46
2021 May	502,057	ARIMA_d0D1	387,238.74	114,818.26
2021 Jun	1,182,009	ARIMA_d0D1	997,119.36	184,889.64
2021 Jul	1,551,789	ARIMA_d0D1	1,939,988.27	-388,199.27
2021 Aug	2,762,537	ARIMA_d0D1	2,302,104.75	460,432.25
2021 Sep	1,869,194	ARIMA_d0D1	2,001,978.84	-132,784.84
2021 Oct	1,584,764	ARIMA_d0D1	1,269,910.65	314,853.35
2021 Nov	651,051	ARIMA_d0D1	721,433.36	-70,382.36
2021 Dec	376,031	ARIMA_d0D1	560,303.64	-184,272.64
2022 Jan	344,634	ARIMA_d0D1	336,432.52	8,201.48
2022 Feb	590,122	ARIMA_d0D1	415,629.11	174,492.89
2022 Mar	873,841	ARIMA_d0D1	633,759.17	240,081.83
2022 Apr	1,629,377	ARIMA_d0D1	1,023,765.80	605,611.20
2022 May	1,867,744	ARIMA_d0D1	1,906,757.36	-39,013.36
2022 Jun	2,230,207	ARIMA_d0D1	2,350,104.16	-119,897.16
2010 Jan	366,296	ARIMA_d0D1_log	410,896.99	-44,600.99
2010 Feb	533,056	ARIMA_d0D1_log	548,250.46	-15,194.46
2010 Mar	742,227	ARIMA_d0D1_log	735,503.00	6,724.00
2010 Apr	902,745	ARIMA_d0D1_log	941,569.72	-38,824.72
2010 May	1,107,303	ARIMA_d0D1_log	1,120,692.50	-13,389.50
2010 Jun	1,464,695	ARIMA_d0D1_log	1,383,714.64	80,980.36
2010 Jul	2,050,478	ARIMA_d0D1_log	1,800,061.59	250,416.41
2010 Aug	2,468,924	ARIMA_d0D1_log	2,297,571.68	171,352.32
2010 Sep	1,696,356	ARIMA_d0D1_log	1,662,188.29	34,167.71
2010 Oct	1,104,659	ARIMA_d0D1_log	1,126,853.68	-22,194.68
2010 Nov	445,221	ARIMA_d0D1_log	525,636.19	-80,415.19
2010 Dec	365,490	ARIMA_d0D1_log	395,099.50	-29,609.50
2011 Jan	357,209	ARIMA_d0D1_log	376,154.67	-18,945.67
2011 Feb	503,831	ARIMA_d0D1_log	545,492.68	-41,661.68
2011 Mar	761,343	ARIMA_d0D1_log	723,369.19	37,973.81
2011 Apr	1,177,115	ARIMA_d0D1_log	811,995.69	365,119.31
2011 May	1,169,516	ARIMA_d0D1_log	1,214,114.58	-44,598.58
2011 Jun	1,576,730	ARIMA_d0D1_log	1,521,462.10	55,267.90
2011 Jul	2,208,160	ARIMA_d0D1_log	2,050,475.12	157,684.88
2011 Aug	2,572,404	ARIMA_d0D1_log	2,523,972.21	48,431.79
2011 Sep	1,731,056	ARIMA_d0D1_log	1,732,609.31	-1,553.31
2011 Oct	1,161,751	ARIMA_d0D1_log	1,139,882.01	21,868.99
2011 Nov	427,550	ARIMA_d0D1_log	500,875.08	-73,325.08
2011 Dec	333,201	ARIMA_d0D1_log	381,679.64	-48,478.64
2012 Jan	359,355	ARIMA_d0D1_log	361,251.04	-1,896.04
2012 Feb	531,709	ARIMA_d0D1_log	512,947.23	18,761.77
2012 Mar	751,024	ARIMA_d0D1_log	751,766.58	-742.58
2012 Apr	1,017,976	ARIMA_d0D1_log	1,047,938.80	-29,962.80
2012 May	1,194,673	ARIMA_d0D1_log	1,142,165.10	52,507.90
2012 Jun	1,678,327	ARIMA_d0D1_log	1,529,145.21	149,181.79
2012 Jul	2,296,474	ARIMA_d0D1_log	2,162,528.07	133,945.93
2012 Aug	2,622,801	ARIMA_d0D1_log	2,605,878.11	16,922.89
2012 Sep	1,829,252	ARIMA_d0D1_log	1,762,237.25	67,014.75
2012 Oct	1,244,751	ARIMA_d0D1_log	1,180,811.13	63,939.87
2012 Nov	453,958	ARIMA_d0D1_log	476,899.40	-22,941.40
2012 Dec	346,474	ARIMA_d0D1_log	368,010.62	-21,536.62
2013 Jan	369,969	ARIMA_d0D1_log	371,729.09	-1,760.09
2013 Feb	520,055	ARIMA_d0D1_log	537,103.46	-17,048.46
2013 Mar	840,024	ARIMA_d0D1_log	757,904.09	82,119.91
2013 Apr	986,191	ARIMA_d0D1_log	1,076,724.73	-90,533.73
2013 May	1,382,234	ARIMA_d0D1_log	1,184,522.60	197,711.40
2013 Jun	1,814,108	ARIMA_d0D1_log	1,694,134.12	119,973.88
2013 Jul	2,387,304	ARIMA_d0D1_log	2,360,686.37	26,617.63
2013 Aug	2,764,686	ARIMA_d0D1_log	2,727,631.89	37,054.11
2013 Sep	1,943,037	ARIMA_d0D1_log	1,873,483.79	69,553.21
2013 Oct	1,291,360	ARIMA_d0D1_log	1,268,397.04	22,962.96
2013 Nov	455,695	ARIMA_d0D1_log	478,148.29	-22,453.29
2013 Dec	358,062	ARIMA_d0D1_log	362,707.01	-4,645.01
2014 Jan	377,387	ARIMA_d0D1_log	379,574.48	-2,187.48
2014 Feb	543,470	ARIMA_d0D1_log	538,310.73	5,159.27
2014 Mar	749,773	ARIMA_d0D1_log	824,949.55	-75,176.55
2014 Apr	1,337,145	ARIMA_d0D1_log	1,005,698.99	331,446.01
2014 May	1,538,342	ARIMA_d0D1_log	1,381,689.28	156,652.72
2014 Jun	1,994,167	ARIMA_d0D1_log	1,931,489.52	62,677.48
2014 Jul	2,529,246	ARIMA_d0D1_log	2,615,791.10	-86,545.10
2014 Aug	3,069,865	ARIMA_d0D1_log	2,952,447.06	117,417.94
2014 Sep	2,089,656	ARIMA_d0D1_log	2,071,139.05	18,516.95
2014 Oct	1,477,481	ARIMA_d0D1_log	1,387,506.11	89,974.89
2014 Nov	502,473	ARIMA_d0D1_log	499,646.38	2,826.62
2014 Dec	382,543	ARIMA_d0D1_log	385,484.58	-2,941.58
2015 Jan	381,607	ARIMA_d0D1_log	407,885.29	-26,278.29
2015 Feb	544,777	ARIMA_d0D1_log	568,474.68	-23,697.68
2015 Mar	827,071	ARIMA_d0D1_log	827,169.14	-98.14
2015 Apr	1,242,844	ARIMA_d0D1_log	1,201,425.02	41,418.98
2015 May	1,654,526	ARIMA_d0D1_log	1,519,811.67	134,714.33
2015 Jun	2,079,484	ARIMA_d0D1_log	2,047,753.12	31,730.88
2015 Jul	2,688,710	ARIMA_d0D1_log	2,651,267.69	37,442.31
2015 Aug	3,108,357	ARIMA_d0D1_log	3,131,376.89	-23,019.89
2015 Sep	2,196,681	ARIMA_d0D1_log	2,155,636.63	41,044.37
2015 Oct	1,553,142	ARIMA_d0D1_log	1,485,972.50	67,169.50
2015 Nov	552,778	ARIMA_d0D1_log	517,302.39	35,475.61
2015 Dec	426,419	ARIMA_d0D1_log	404,358.98	22,060.02
2016 Jan	443,150	ARIMA_d0D1_log	420,973.54	22,176.46
2016 Feb	664,278	ARIMA_d0D1_log	608,236.27	56,041.73
2016 Mar	1,089,392	ARIMA_d0D1_log	914,965.28	174,426.72
2016 Apr	1,335,308	ARIMA_d0D1_log	1,515,510.97	-180,202.97
2016 May	1,828,292	ARIMA_d0D1_log	1,826,045.76	2,246.24
2016 Jun	2,288,337	ARIMA_d0D1_log	2,319,365.40	-31,028.40
2016 Jul	2,848,570	ARIMA_d0D1_log	2,942,067.53	-93,497.53
2016 Aug	3,204,047	ARIMA_d0D1_log	3,413,750.91	-209,703.91
2016 Sep	2,378,618	ARIMA_d0D1_log	2,314,330.65	64,287.35
2016 Oct	1,793,822	ARIMA_d0D1_log	1,634,843.63	158,978.37
2016 Nov	653,514	ARIMA_d0D1_log	583,428.48	70,085.52
2016 Dec	478,510	ARIMA_d0D1_log	462,256.05	16,253.95
2017 Jan	495,629	ARIMA_d0D1_log	475,636.39	19,992.61
2017 Feb	704,532	ARIMA_d0D1_log	701,434.26	3,097.74
2017 Mar	1,015,421	ARIMA_d0D1_log	1,090,070.68	-74,649.68
2017 Apr	1,765,170	ARIMA_d0D1_log	1,479,109.96	286,060.04
2017 May	1,970,072	ARIMA_d0D1_log	2,089,635.80	-119,563.80
2017 Jun	2,417,100	ARIMA_d0D1_log	2,551,912.82	-134,812.82
2017 Jul	2,968,641	ARIMA_d0D1_log	3,150,286.97	-181,645.97
2017 Aug	3,295,406	ARIMA_d0D1_log	3,542,380.63	-246,974.63
2017 Sep	2,470,298	ARIMA_d0D1_log	2,478,200.87	-7,902.87
2017 Oct	1,911,961	ARIMA_d0D1_log	1,802,676.66	109,284.34
2017 Nov	680,373	ARIMA_d0D1_log	654,742.32	25,630.68
2017 Dec	512,548	ARIMA_d0D1_log	496,386.79	16,161.21
2018 Jan	503,908	ARIMA_d0D1_log	514,053.54	-10,145.54
2018 Feb	731,090	ARIMA_d0D1_log	741,866.15	-10,776.15
2018 Mar	1,151,455	ARIMA_d0D1_log	1,130,600.68	20,854.32
2018 Apr	1,575,078	ARIMA_d0D1_log	1,671,462.62	-96,384.62
2018 May	2,003,996	ARIMA_d0D1_log	2,042,477.18	-38,481.18
2018 Jun	2,381,154	ARIMA_d0D1_log	2,501,410.93	-120,256.93
2018 Jul	2,981,643	ARIMA_d0D1_log	3,046,220.54	-64,577.54
2018 Aug	3,371,918	ARIMA_d0D1_log	3,383,071.11	-11,153.11
2018 Sep	2,499,368	ARIMA_d0D1_log	2,512,721.88	-13,353.88
2018 Oct	1,956,693	ARIMA_d0D1_log	1,910,963.11	45,729.89
2018 Nov	732,141	ARIMA_d0D1_log	694,028.63	38,112.37
2018 Dec	554,803	ARIMA_d0D1_log	524,597.28	30,205.72
2019 Jan	548,686	ARIMA_d0D1_log	538,699.61	9,986.39
2019 Feb	739,981	ARIMA_d0D1_log	781,701.65	-41,720.65
2019 Mar	1,078,918	ARIMA_d0D1_log	1,172,475.58	-93,557.58
2019 Apr	1,795,494	ARIMA_d0D1_log	1,701,930.61	93,563.39
2019 May	1,990,529	ARIMA_d0D1_log	2,087,277.93	-96,748.93
2019 Jun	2,425,834	ARIMA_d0D1_log	2,482,076.99	-56,242.99
2019 Jul	2,988,668	ARIMA_d0D1_log	3,048,108.30	-59,440.30
2019 Aug	3,439,271	ARIMA_d0D1_log	3,374,943.73	64,327.27
2019 Sep	2,573,527	ARIMA_d0D1_log	2,549,287.15	24,239.85
2019 Oct	1,930,852	ARIMA_d0D1_log	2,002,141.29	-71,289.29
2019 Nov	785,875	ARIMA_d0D1_log	726,018.99	59,856.01
2019 Dec	602,860	ARIMA_d0D1_log	558,229.57	44,630.43
2020 Jan	560,368	ARIMA_d0D1_log	564,903.36	-4,535.36
2020 Feb	844,247	ARIMA_d0D1_log	786,320.99	57,926.01
2020 Mar	513,360	ARIMA_d0D1_log	1,206,809.38	-693,449.38
2020 Apr	25,614	ARIMA_d0D1_log	1,542,836.33	-1,517,222.33
2020 May	40,932	ARIMA_d0D1_log	4,885.48	36,046.52
2020 Jun	330,393	ARIMA_d0D1_log	738,628.03	-408,235.03
2020 Jul	1,035,732	ARIMA_d0D1_log	983,765.59	51,966.41
2020 Aug	2,090,569	ARIMA_d0D1_log	1,904,952.51	185,616.49
2020 Sep	1,418,185	ARIMA_d0D1_log	1,981,878.84	-563,693.84
2020 Oct	696,087	ARIMA_d0D1_log	1,099,068.94	-402,981.94
2020 Nov	181,873	ARIMA_d0D1_log	305,395.84	-123,522.84
2020 Dec	153,351	ARIMA_d0D1_log	177,450.88	-24,099.88
2021 Jan	105,336	ARIMA_d0D1_log	228,990.40	-123,654.40
2021 Feb	66,194	ARIMA_d0D1_log	175,397.30	-109,203.30
2021 Mar	84,413	ARIMA_d0D1_log	121,107.25	-36,694.25
2021 Apr	138,661	ARIMA_d0D1_log	149,934.27	-11,273.27
2021 May	502,057	ARIMA_d0D1_log	322,389.44	179,667.56
2021 Jun	1,182,009	ARIMA_d0D1_log	1,428,206.59	-246,197.59
2021 Jul	1,551,789	ARIMA_d0D1_log	1,816,189.31	-264,400.31
2021 Aug	2,762,537	ARIMA_d0D1_log	2,155,534.54	607,002.46
2021 Sep	1,869,194	ARIMA_d0D1_log	2,419,179.64	-549,985.64
2021 Oct	1,584,764	ARIMA_d0D1_log	1,172,871.01	411,892.99
2021 Nov	651,051	ARIMA_d0D1_log	664,629.51	-13,578.51
2021 Dec	376,031	ARIMA_d0D1_log	477,090.21	-101,059.21
2022 Jan	344,634	ARIMA_d0D1_log	319,502.97	25,131.03
2022 Feb	590,122	ARIMA_d0D1_log	463,324.64	126,797.36
2022 Mar	873,841	ARIMA_d0D1_log	806,069.64	67,771.36
2022 Apr	1,629,377	ARIMA_d0D1_log	734,536.95	894,840.05
2022 May	1,867,744	ARIMA_d0D1_log	2,627,976.22	-760,232.22
2022 Jun	2,230,207	ARIMA_d0D1_log	2,128,488.65	101,718.35
2010 Jan	366,296	ARIMA_d1D1	353,423.74	12,872.26
2010 Feb	533,056	ARIMA_d1D1	526,454.33	6,601.67
2010 Mar	742,227	ARIMA_d1D1	747,810.54	-5,583.54
2010 Apr	902,745	ARIMA_d1D1	943,051.55	-40,306.55
2010 May	1,107,303	ARIMA_d1D1	1,148,754.67	-41,451.67
2010 Jun	1,464,695	ARIMA_d1D1	1,435,346.88	29,348.12
2010 Jul	2,050,478	ARIMA_d1D1	1,867,307.33	183,170.67
2010 Aug	2,468,924	ARIMA_d1D1	2,313,875.87	155,048.13
2010 Sep	1,696,356	ARIMA_d1D1	1,622,567.10	73,788.90
2010 Oct	1,104,659	ARIMA_d1D1	1,117,437.70	-12,778.70
2010 Nov	445,221	ARIMA_d1D1	536,134.24	-90,913.24
2010 Dec	365,490	ARIMA_d1D1	401,611.36	-36,121.36
2011 Jan	357,209	ARIMA_d1D1	366,569.95	-9,360.95
2011 Feb	503,831	ARIMA_d1D1	556,662.26	-52,831.26
2011 Mar	761,343	ARIMA_d1D1	786,604.70	-25,261.70
2011 Apr	1,177,115	ARIMA_d1D1	816,787.30	360,327.70
2011 May	1,169,516	ARIMA_d1D1	1,243,286.82	-73,770.82
2011 Jun	1,576,730	ARIMA_d1D1	1,511,120.39	65,609.61
2011 Jul	2,208,160	ARIMA_d1D1	2,044,000.96	164,159.04
2011 Aug	2,572,404	ARIMA_d1D1	2,518,723.83	53,680.17
2011 Sep	1,731,056	ARIMA_d1D1	1,773,177.33	-42,121.33
2011 Oct	1,161,751	ARIMA_d1D1	1,173,966.41	-12,215.41
2011 Nov	427,550	ARIMA_d1D1	564,031.32	-136,481.32
2011 Dec	333,201	ARIMA_d1D1	432,392.64	-99,191.64
2012 Jan	359,355	ARIMA_d1D1	396,551.84	-37,196.84
2012 Feb	531,709	ARIMA_d1D1	540,123.50	-8,414.50
2012 Mar	751,024	ARIMA_d1D1	771,429.93	-20,405.93
2012 Apr	1,017,976	ARIMA_d1D1	1,061,267.53	-43,291.53
2012 May	1,194,673	ARIMA_d1D1	1,150,048.79	44,624.21
2012 Jun	1,678,327	ARIMA_d1D1	1,528,033.68	150,293.32
2012 Jul	2,296,474	ARIMA_d1D1	2,145,707.62	150,766.38
2012 Aug	2,622,801	ARIMA_d1D1	2,599,667.94	23,133.06
2012 Sep	1,829,252	ARIMA_d1D1	1,810,138.23	19,113.77
2012 Oct	1,244,751	ARIMA_d1D1	1,233,383.83	11,367.17
2012 Nov	453,958	ARIMA_d1D1	578,001.40	-124,043.40
2012 Dec	346,474	ARIMA_d1D1	439,464.85	-92,990.85
2013 Jan	369,969	ARIMA_d1D1	398,772.69	-28,803.69
2013 Feb	520,055	ARIMA_d1D1	540,908.30	-20,853.30
2013 Mar	840,024	ARIMA_d1D1	762,940.54	77,083.46
2013 Apr	986,191	ARIMA_d1D1	1,097,151.46	-110,960.46
2013 May	1,382,234	ARIMA_d1D1	1,186,490.16	195,743.84
2013 Jun	1,814,108	ARIMA_d1D1	1,686,409.19	127,698.81
2013 Jul	2,387,304	ARIMA_d1D1	2,336,583.51	50,720.49
2013 Aug	2,764,686	ARIMA_d1D1	2,707,906.70	56,779.30
2013 Sep	1,943,037	ARIMA_d1D1	1,929,488.85	13,548.15
2013 Oct	1,291,360	ARIMA_d1D1	1,356,731.77	-65,371.77
2013 Nov	455,695	ARIMA_d1D1	585,354.25	-129,659.25
2013 Dec	358,062	ARIMA_d1D1	436,284.34	-78,222.34
2014 Jan	377,387	ARIMA_d1D1	426,990.94	-49,603.94
2014 Feb	543,470	ARIMA_d1D1	563,914.20	-20,444.20
2014 Mar	749,773	ARIMA_d1D1	839,603.44	-89,830.44
2014 Apr	1,337,145	ARIMA_d1D1	1,007,059.66	330,085.34
2014 May	1,538,342	ARIMA_d1D1	1,411,807.36	126,534.64
2014 Jun	1,994,167	ARIMA_d1D1	1,916,004.81	78,162.19
2014 Jul	2,529,246	ARIMA_d1D1	2,525,257.40	3,988.60
2014 Aug	3,069,865	ARIMA_d1D1	2,893,182.74	176,682.26
2014 Sep	2,089,656	ARIMA_d1D1	2,153,621.93	-63,965.93
2014 Oct	1,477,481	ARIMA_d1D1	1,502,029.80	-24,548.80
2014 Nov	502,473	ARIMA_d1D1	687,777.94	-185,304.94
2014 Dec	382,543	ARIMA_d1D1	517,445.84	-134,902.84
2015 Jan	381,607	ARIMA_d1D1	483,911.20	-102,304.20
2015 Feb	544,777	ARIMA_d1D1	600,881.81	-56,104.81
2015 Mar	827,071	ARIMA_d1D1	809,999.29	17,071.71
2015 Apr	1,242,844	ARIMA_d1D1	1,266,789.15	-23,945.15
2015 May	1,654,526	ARIMA_d1D1	1,492,977.49	161,548.51
2015 Jun	2,079,484	ARIMA_d1D1	2,024,823.64	54,660.36
2015 Jul	2,688,710	ARIMA_d1D1	2,599,869.08	88,840.92
2015 Aug	3,108,357	ARIMA_d1D1	3,107,524.57	832.43
2015 Sep	2,196,681	ARIMA_d1D1	2,194,214.96	2,466.04
2015 Oct	1,553,142	ARIMA_d1D1	1,567,878.91	-14,736.91
2015 Nov	552,778	ARIMA_d1D1	639,379.21	-86,601.21
2015 Dec	426,419	ARIMA_d1D1	489,803.17	-63,384.17
2016 Jan	443,150	ARIMA_d1D1	470,936.87	-27,786.87
2016 Feb	664,278	ARIMA_d1D1	622,815.26	41,462.74
2016 Mar	1,089,392	ARIMA_d1D1	897,797.46	191,594.54
2016 Apr	1,335,308	ARIMA_d1D1	1,445,874.34	-110,566.34
2016 May	1,828,292	ARIMA_d1D1	1,744,860.80	83,431.20
2016 Jun	2,288,337	ARIMA_d1D1	2,213,667.08	74,669.92
2016 Jul	2,848,570	ARIMA_d1D1	2,822,599.08	25,970.92
2016 Aug	3,204,047	ARIMA_d1D1	3,297,775.39	-93,728.39
2016 Sep	2,378,618	ARIMA_d1D1	2,331,517.94	47,100.06
2016 Oct	1,793,822	ARIMA_d1D1	1,713,841.15	79,980.85
2016 Nov	653,514	ARIMA_d1D1	766,914.98	-113,400.98
2016 Dec	478,510	ARIMA_d1D1	589,198.69	-110,688.69
2017 Jan	495,629	ARIMA_d1D1	557,579.76	-61,950.76
2017 Feb	704,532	ARIMA_d1D1	734,268.83	-29,736.83
2017 Mar	1,015,421	ARIMA_d1D1	1,092,155.38	-76,734.38
2017 Apr	1,765,170	ARIMA_d1D1	1,390,503.10	374,666.90
2017 May	1,970,072	ARIMA_d1D1	1,978,766.49	-8,694.49
2017 Jun	2,417,100	ARIMA_d1D1	2,473,579.63	-56,479.63
2017 Jul	2,968,641	ARIMA_d1D1	3,012,325.51	-43,684.51
2017 Aug	3,295,406	ARIMA_d1D1	3,346,294.86	-50,888.86
2017 Sep	2,470,298	ARIMA_d1D1	2,446,537.14	23,760.86
2017 Oct	1,911,961	ARIMA_d1D1	1,850,120.54	61,840.46
2017 Nov	680,373	ARIMA_d1D1	798,391.69	-118,018.69
2017 Dec	512,548	ARIMA_d1D1	613,088.67	-100,540.67
2018 Jan	503,908	ARIMA_d1D1	581,069.67	-77,161.67
2018 Feb	731,090	ARIMA_d1D1	769,632.42	-38,542.42
2018 Mar	1,151,455	ARIMA_d1D1	1,122,754.74	28,700.26
2018 Apr	1,575,078	ARIMA_d1D1	1,666,092.46	-91,014.46
2018 May	2,003,996	ARIMA_d1D1	1,975,293.25	28,702.75
2018 Jun	2,381,154	ARIMA_d1D1	2,436,874.68	-55,720.68
2018 Jul	2,981,643	ARIMA_d1D1	2,977,932.80	3,710.20
2018 Aug	3,371,918	ARIMA_d1D1	3,309,103.53	62,814.47
2018 Sep	2,499,368	ARIMA_d1D1	2,510,972.98	-11,604.98
2018 Oct	1,956,693	ARIMA_d1D1	1,937,270.66	19,422.34
2018 Nov	732,141	ARIMA_d1D1	740,493.22	-8,352.22
2018 Dec	554,803	ARIMA_d1D1	562,954.10	-8,151.10
2019 Jan	548,686	ARIMA_d1D1	564,072.46	-15,386.46
2019 Feb	739,981	ARIMA_d1D1	784,158.63	-44,177.63
2019 Mar	1,078,918	ARIMA_d1D1	1,156,197.50	-77,279.50
2019 Apr	1,795,494	ARIMA_d1D1	1,686,341.32	109,152.68
2019 May	1,990,529	ARIMA_d1D1	2,060,274.63	-69,745.63
2019 Jun	2,425,834	ARIMA_d1D1	2,447,621.89	-21,787.89
2019 Jul	2,988,668	ARIMA_d1D1	3,016,675.97	-28,007.97
2019 Aug	3,439,271	ARIMA_d1D1	3,349,169.38	90,101.62
2019 Sep	2,573,527	ARIMA_d1D1	2,546,466.97	27,060.03
2019 Oct	1,930,852	ARIMA_d1D1	2,014,410.56	-83,558.56
2019 Nov	785,875	ARIMA_d1D1	736,833.49	49,041.51
2019 Dec	602,860	ARIMA_d1D1	574,937.69	27,922.31
2020 Jan	560,368	ARIMA_d1D1	577,421.07	-17,053.07
2020 Feb	844,247	ARIMA_d1D1	780,262.43	63,984.57
2020 Mar	513,360	ARIMA_d1D1	1,174,636.90	-661,276.90
2020 Apr	25,614	ARIMA_d1D1	1,602,113.82	-1,576,499.82
2020 May	40,932	ARIMA_d1D1	342,097.50	-301,165.50
2020 Jun	330,393	ARIMA_d1D1	458,387.49	-127,994.49
2020 Jul	1,035,732	ARIMA_d1D1	905,714.63	130,017.37
2020 Aug	2,090,569	ARIMA_d1D1	1,430,530.18	660,038.82
2020 Sep	1,418,185	ARIMA_d1D1	1,231,120.70	187,064.30
2020 Oct	696,087	ARIMA_d1D1	930,904.67	-234,817.67
2020 Nov	181,873	ARIMA_d1D1	-502,729.36	684,602.36
2020 Dec	153,351	ARIMA_d1D1	13,080.60	140,270.40
2021 Jan	105,336	ARIMA_d1D1	137,917.05	-32,581.05
2021 Feb	66,194	ARIMA_d1D1	337,706.85	-271,512.85
2021 Mar	84,413	ARIMA_d1D1	161,545.55	-77,132.55
2021 Apr	138,661	ARIMA_d1D1	259,711.34	-121,050.34
2021 May	502,057	ARIMA_d1D1	317,812.71	184,244.29
2021 Jun	1,182,009	ARIMA_d1D1	873,491.61	308,517.39
2021 Jul	1,551,789	ARIMA_d1D1	1,829,150.10	-277,361.10
2021 Aug	2,762,537	ARIMA_d1D1	2,201,979.54	560,557.46
2021 Sep	1,869,194	ARIMA_d1D1	1,988,390.82	-119,196.82
2021 Oct	1,584,764	ARIMA_d1D1	1,212,867.11	371,896.89
2021 Nov	651,051	ARIMA_d1D1	715,645.03	-64,594.03
2021 Dec	376,031	ARIMA_d1D1	541,882.23	-165,851.23
2022 Jan	344,634	ARIMA_d1D1	344,651.96	-17.96
2022 Feb	590,122	ARIMA_d1D1	461,851.13	128,270.87
2022 Mar	873,841	ARIMA_d1D1	632,038.97	241,802.03
2022 Apr	1,629,377	ARIMA_d1D1	977,312.00	652,065.00
2022 May	1,867,744	ARIMA_d1D1	1,885,011.13	-17,267.13
2022 Jun	2,230,207	ARIMA_d1D1	2,349,366.99	-119,159.99
2010 Jan	366,296	ARIMA_d1D1_log	403,467.67	-37,171.67
2010 Feb	533,056	ARIMA_d1D1_log	539,719.78	-6,663.78
2010 Mar	742,227	ARIMA_d1D1_log	724,447.31	17,779.69
2010 Apr	902,745	ARIMA_d1D1_log	917,578.61	-14,833.61
2010 May	1,107,303	ARIMA_d1D1_log	1,092,909.29	14,393.71
2010 Jun	1,464,695	ARIMA_d1D1_log	1,348,409.08	116,285.92
2010 Jul	2,050,478	ARIMA_d1D1_log	1,764,727.20	285,750.80
2010 Aug	2,468,924	ARIMA_d1D1_log	2,213,606.16	255,317.84
2010 Sep	1,696,356	ARIMA_d1D1_log	1,579,393.64	116,962.36
2010 Oct	1,104,659	ARIMA_d1D1_log	1,093,309.29	11,349.71
2010 Nov	445,221	ARIMA_d1D1_log	518,135.99	-72,914.99
2010 Dec	365,490	ARIMA_d1D1_log	391,727.59	-26,237.59
2011 Jan	357,209	ARIMA_d1D1_log	387,555.85	-30,346.85
2011 Feb	503,831	ARIMA_d1D1_log	531,872.08	-28,041.08
2011 Mar	761,343	ARIMA_d1D1_log	714,069.45	47,273.55
2011 Apr	1,177,115	ARIMA_d1D1_log	899,794.56	277,320.44
2011 May	1,169,516	ARIMA_d1D1_log	1,181,898.66	-12,382.66
2011 Jun	1,576,730	ARIMA_d1D1_log	1,502,465.41	74,264.59
2011 Jul	2,208,160	ARIMA_d1D1_log	2,038,752.35	169,407.65
2011 Aug	2,572,404	ARIMA_d1D1_log	2,527,165.41	45,238.59
2011 Sep	1,731,056	ARIMA_d1D1_log	1,742,881.10	-11,825.10
2011 Oct	1,161,751	ARIMA_d1D1_log	1,149,133.90	12,617.10
2011 Nov	427,550	ARIMA_d1D1_log	504,350.81	-76,800.81
2011 Dec	333,201	ARIMA_d1D1_log	385,963.09	-52,762.09
2012 Jan	359,355	ARIMA_d1D1_log	364,393.72	-5,038.72
2012 Feb	531,709	ARIMA_d1D1_log	512,805.00	18,904.00
2012 Mar	751,024	ARIMA_d1D1_log	748,987.83	2,036.17
2012 Apr	1,017,976	ARIMA_d1D1_log	1,046,790.51	-28,814.51
2012 May	1,194,673	ARIMA_d1D1_log	1,133,182.21	61,490.79
2012 Jun	1,678,327	ARIMA_d1D1_log	1,517,597.53	160,729.47
2012 Jul	2,296,474	ARIMA_d1D1_log	2,150,811.32	145,662.68
2012 Aug	2,622,801	ARIMA_d1D1_log	2,653,949.22	-31,148.22
2012 Sep	1,829,252	ARIMA_d1D1_log	1,789,522.93	39,729.07
2012 Oct	1,244,751	ARIMA_d1D1_log	1,191,007.26	53,743.74
2012 Nov	453,958	ARIMA_d1D1_log	473,497.69	-19,539.69
2012 Dec	346,474	ARIMA_d1D1_log	370,246.94	-23,772.94
2013 Jan	369,969	ARIMA_d1D1_log	372,114.60	-2,145.60
2013 Feb	520,055	ARIMA_d1D1_log	539,794.17	-19,739.17
2013 Mar	840,024	ARIMA_d1D1_log	775,495.22	64,528.78
2013 Apr	986,191	ARIMA_d1D1_log	1,143,696.39	-157,505.39
2013 May	1,382,234	ARIMA_d1D1_log	1,199,071.07	183,162.93
2013 Jun	1,814,108	ARIMA_d1D1_log	1,711,449.83	102,658.17
2013 Jul	2,387,304	ARIMA_d1D1_log	2,392,100.66	-4,796.66
2013 Aug	2,764,686	ARIMA_d1D1_log	2,771,276.95	-6,590.95
2013 Sep	1,943,037	ARIMA_d1D1_log	1,909,776.61	33,260.39
2013 Oct	1,291,360	ARIMA_d1D1_log	1,294,730.00	-3,370.00
2013 Nov	455,695	ARIMA_d1D1_log	486,546.73	-30,851.73
2013 Dec	358,062	ARIMA_d1D1_log	369,860.82	-11,798.82
2014 Jan	377,387	ARIMA_d1D1_log	386,062.47	-8,675.47
2014 Feb	543,470	ARIMA_d1D1_log	550,656.74	-7,186.74
2014 Mar	749,773	ARIMA_d1D1_log	840,191.07	-90,418.07
2014 Apr	1,337,145	ARIMA_d1D1_log	1,037,947.53	299,197.47
2014 May	1,538,342	ARIMA_d1D1_log	1,399,807.64	138,534.36
2014 Jun	1,994,167	ARIMA_d1D1_log	1,964,104.09	30,062.91
2014 Jul	2,529,246	ARIMA_d1D1_log	2,669,423.00	-140,177.00
2014 Aug	3,069,865	ARIMA_d1D1_log	3,018,114.22	51,750.78
2014 Sep	2,089,656	ARIMA_d1D1_log	2,118,243.45	-28,587.45
2014 Oct	1,477,481	ARIMA_d1D1_log	1,420,965.30	56,515.70
2014 Nov	502,473	ARIMA_d1D1_log	509,871.67	-7,398.67
2014 Dec	382,543	ARIMA_d1D1_log	393,637.92	-11,094.92
2015 Jan	381,607	ARIMA_d1D1_log	417,446.12	-35,839.12
2015 Feb	544,777	ARIMA_d1D1_log	582,726.98	-37,949.98
2015 Mar	827,071	ARIMA_d1D1_log	849,032.86	-21,961.86
2015 Apr	1,242,844	ARIMA_d1D1_log	1,224,835.83	18,008.17
2015 May	1,654,526	ARIMA_d1D1_log	1,551,966.46	102,559.54
2015 Jun	2,079,484	ARIMA_d1D1_log	2,081,768.52	-2,284.52
2015 Jul	2,688,710	ARIMA_d1D1_log	2,694,734.52	-6,024.52
2015 Aug	3,108,357	ARIMA_d1D1_log	3,181,493.57	-73,136.57
2015 Sep	2,196,681	ARIMA_d1D1_log	2,192,055.19	4,625.81
2015 Oct	1,553,142	ARIMA_d1D1_log	1,510,019.81	43,122.19
2015 Nov	552,778	ARIMA_d1D1_log	525,206.10	27,571.90
2015 Dec	426,419	ARIMA_d1D1_log	410,531.65	15,887.35
2016 Jan	443,150	ARIMA_d1D1_log	427,889.91	15,260.09
2016 Feb	664,278	ARIMA_d1D1_log	618,478.16	45,799.84
2016 Mar	1,089,392	ARIMA_d1D1_log	930,215.73	159,176.27
2016 Apr	1,335,308	ARIMA_d1D1_log	1,540,664.54	-205,356.54
2016 May	1,828,292	ARIMA_d1D1_log	1,868,844.60	-40,552.60
2016 Jun	2,288,337	ARIMA_d1D1_log	2,373,404.57	-85,067.57
2016 Jul	2,848,570	ARIMA_d1D1_log	3,013,389.72	-164,819.72
2016 Aug	3,204,047	ARIMA_d1D1_log	3,499,631.75	-295,584.75
2016 Sep	2,378,618	ARIMA_d1D1_log	2,376,151.43	2,466.57
2016 Oct	1,793,822	ARIMA_d1D1_log	1,671,624.12	122,197.88
2016 Nov	653,514	ARIMA_d1D1_log	594,090.74	59,423.26
2016 Dec	478,510	ARIMA_d1D1_log	469,615.59	8,894.41
2017 Jan	495,629	ARIMA_d1D1_log	483,713.83	11,915.17
2017 Feb	704,532	ARIMA_d1D1_log	713,478.49	-8,946.49
2017 Mar	1,015,421	ARIMA_d1D1_log	1,109,850.51	-94,429.51
2017 Apr	1,765,170	ARIMA_d1D1_log	1,513,881.58	251,288.42
2017 May	1,970,072	ARIMA_d1D1_log	2,119,931.95	-149,859.95
2017 Jun	2,417,100	ARIMA_d1D1_log	2,598,122.35	-181,022.35
2017 Jul	2,968,641	ARIMA_d1D1_log	3,216,024.46	-247,383.46
2017 Aug	3,295,406	ARIMA_d1D1_log	3,620,664.62	-325,258.62
2017 Sep	2,470,298	ARIMA_d1D1_log	2,536,372.83	-66,074.83
2017 Oct	1,911,961	ARIMA_d1D1_log	1,839,000.29	72,960.71
2017 Nov	680,373	ARIMA_d1D1_log	665,337.75	15,035.25
2017 Dec	512,548	ARIMA_d1D1_log	503,590.66	8,957.34
2018 Jan	503,908	ARIMA_d1D1_log	521,405.63	-17,497.63
2018 Feb	731,090	ARIMA_d1D1_log	752,542.28	-21,452.28
2018 Mar	1,151,455	ARIMA_d1D1_log	1,145,841.28	5,613.72
2018 Apr	1,575,078	ARIMA_d1D1_log	1,696,726.75	-121,648.75
2018 May	2,003,996	ARIMA_d1D1_log	2,072,079.00	-68,083.00
2018 Jun	2,381,154	ARIMA_d1D1_log	2,535,978.47	-154,824.47
2018 Jul	2,981,643	ARIMA_d1D1_log	3,085,679.43	-104,036.43
2018 Aug	3,371,918	ARIMA_d1D1_log	3,421,320.53	-49,402.53
2018 Sep	2,499,368	ARIMA_d1D1_log	2,535,607.73	-36,239.73
2018 Oct	1,956,693	ARIMA_d1D1_log	1,925,336.96	31,356.04
2018 Nov	732,141	ARIMA_d1D1_log	698,151.17	33,989.83
2018 Dec	554,803	ARIMA_d1D1_log	527,595.11	27,207.89
2019 Jan	548,686	ARIMA_d1D1_log	541,794.52	6,891.48
2019 Feb	739,981	ARIMA_d1D1_log	786,979.72	-46,998.72
2019 Mar	1,078,918	ARIMA_d1D1_log	1,182,196.94	-103,278.94
2019 Apr	1,795,494	ARIMA_d1D1_log	1,716,148.95	79,345.05
2019 May	1,990,529	ARIMA_d1D1_log	2,103,710.09	-113,181.09
2019 Jun	2,425,834	ARIMA_d1D1_log	2,500,447.33	-74,613.33
2019 Jul	2,988,668	ARIMA_d1D1_log	3,067,615.38	-78,947.38
2019 Aug	3,439,271	ARIMA_d1D1_log	3,393,780.78	45,490.22
2019 Sep	2,573,527	ARIMA_d1D1_log	2,559,061.93	14,465.07
2019 Oct	1,930,852	ARIMA_d1D1_log	2,007,790.73	-76,938.73
2019 Nov	785,875	ARIMA_d1D1_log	728,087.46	57,787.54
2019 Dec	602,860	ARIMA_d1D1_log	559,446.73	43,413.27
2020 Jan	560,368	ARIMA_d1D1_log	566,464.37	-6,096.37
2020 Feb	844,247	ARIMA_d1D1_log	789,719.31	54,527.69
2020 Mar	513,360	ARIMA_d1D1_log	1,212,663.47	-699,303.47
2020 Apr	25,614	ARIMA_d1D1_log	1,542,583.82	-1,516,969.82
2020 May	40,932	ARIMA_d1D1_log	1,404.25	39,527.75
2020 Jun	330,393	ARIMA_d1D1_log	340,105.61	-9,712.61
2020 Jul	1,035,732	ARIMA_d1D1_log	921,879.62	113,852.38
2020 Aug	2,090,569	ARIMA_d1D1_log	1,036,791.81	1,053,777.19
2020 Sep	1,418,185	ARIMA_d1D1_log	1,564,446.33	-146,261.33
2020 Oct	696,087	ARIMA_d1D1_log	990,705.24	-294,618.24
2020 Nov	181,873	ARIMA_d1D1_log	233,947.37	-52,074.37
2020 Dec	153,351	ARIMA_d1D1_log	147,461.84	5,889.16
2021 Jan	105,336	ARIMA_d1D1_log	189,167.42	-83,831.42
2021 Feb	66,194	ARIMA_d1D1_log	145,299.83	-79,105.83
2021 Mar	84,413	ARIMA_d1D1_log	95,921.55	-11,508.55
2021 Apr	138,661	ARIMA_d1D1_log	71,225.49	67,435.51
2021 May	502,057	ARIMA_d1D1_log	243,195.69	258,861.31
2021 Jun	1,182,009	ARIMA_d1D1_log	1,095,894.55	86,114.45
2021 Jul	1,551,789	ARIMA_d1D1_log	1,317,042.47	234,746.53
2021 Aug	2,762,537	ARIMA_d1D1_log	1,495,135.44	1,267,401.56
2021 Sep	1,869,194	ARIMA_d1D1_log	1,904,840.38	-35,646.38
2021 Oct	1,584,764	ARIMA_d1D1_log	931,362.40	653,401.60
2021 Nov	651,051	ARIMA_d1D1_log	567,794.64	83,256.36
2021 Dec	376,031	ARIMA_d1D1_log	412,518.91	-36,487.91
2022 Jan	344,634	ARIMA_d1D1_log	280,859.89	63,774.11
2022 Feb	590,122	ARIMA_d1D1_log	411,951.88	178,170.12
2022 Mar	873,841	ARIMA_d1D1_log	633,956.73	239,884.27
2022 Apr	1,629,377	ARIMA_d1D1_log	488,391.56	1,140,985.44
2022 May	1,867,744	ARIMA_d1D1_log	2,504,495.91	-636,751.91
2022 Jun	2,230,207	ARIMA_d1D1_log	2,012,171.82	218,035.18
2010 Jan	366,296	Drift_STL	388,925.98	-22,629.98
2010 Feb	533,056	Drift_STL	546,090.82	-13,034.82
2010 Mar	742,227	Drift_STL	761,586.89	-19,359.89
2010 Apr	902,745	Drift_STL	932,461.55	-29,716.55
2010 May	1,107,303	Drift_STL	1,131,972.81	-24,669.81
2010 Jun	1,464,695	Drift_STL	1,389,406.04	75,288.96
2010 Jul	2,050,478	Drift_STL	1,888,599.69	161,878.31
2010 Aug	2,468,924	Drift_STL	2,421,399.69	47,524.31
2010 Sep	1,696,356	Drift_STL	1,717,648.09	-21,292.09
2010 Oct	1,104,659	Drift_STL	1,168,175.21	-63,516.21
2010 Nov	445,221	Drift_STL	518,264.52	-73,043.52
2010 Dec	365,490	Drift_STL	358,117.01	7,372.99
2011 Jan	357,209	Drift_STL	392,652.89	-35,443.89
2011 Feb	503,831	Drift_STL	546,048.91	-42,217.91
2011 Mar	761,343	Drift_STL	743,601.32	17,741.68
2011 Apr	1,177,115	Drift_STL	953,346.79	223,768.21
2011 May	1,169,516	Drift_STL	1,376,806.96	-207,290.96
2011 Jun	1,576,730	Drift_STL	1,470,231.14	106,498.86
2011 Jul	2,208,160	Drift_STL	2,026,326.66	181,833.34
2011 Aug	2,572,404	Drift_STL	2,572,984.35	-580.35
2011 Sep	1,731,056	Drift_STL	1,809,940.45	-78,884.45
2011 Oct	1,161,751	Drift_STL	1,195,832.91	-34,081.91
2011 Nov	427,550	Drift_STL	567,840.03	-140,290.03
2011 Dec	333,201	Drift_STL	355,169.41	-21,968.41
2012 Jan	359,355	Drift_STL	362,740.08	-3,385.08
2012 Feb	531,709	Drift_STL	543,576.12	-11,867.12
2012 Mar	751,024	Drift_STL	774,278.03	-23,254.03
2012 Apr	1,017,976	Drift_STL	983,070.12	34,905.88
2012 May	1,194,673	Drift_STL	1,199,157.07	-4,484.07
2012 Jun	1,678,327	Drift_STL	1,506,430.26	171,896.74
2012 Jul	2,296,474	Drift_STL	2,145,556.24	150,917.76
2012 Aug	2,622,801	Drift_STL	2,645,214.10	-22,413.10
2012 Sep	1,829,252	Drift_STL	1,835,622.77	-6,370.77
2012 Oct	1,244,751	Drift_STL	1,272,085.69	-27,334.69
2012 Nov	453,958	Drift_STL	621,166.39	-167,208.39
2012 Dec	346,474	Drift_STL	385,831.84	-39,357.84
2013 Jan	369,969	Drift_STL	380,839.65	-10,870.65
2013 Feb	520,055	Drift_STL	556,762.49	-36,707.49
2013 Mar	840,024	Drift_STL	768,409.31	71,614.69
2013 Apr	986,191	Drift_STL	1,078,926.68	-92,735.68
2013 May	1,382,234	Drift_STL	1,171,732.99	210,501.01
2013 Jun	1,814,108	Drift_STL	1,710,292.55	103,815.45
2013 Jul	2,387,304	Drift_STL	2,305,521.02	81,782.98
2013 Aug	2,764,686	Drift_STL	2,727,506.08	37,179.92
2013 Sep	1,943,037	Drift_STL	1,962,868.10	-19,831.10
2013 Oct	1,291,360	Drift_STL	1,373,006.25	-81,646.25
2013 Nov	455,695	Drift_STL	642,191.89	-186,496.89
2013 Dec	358,062	Drift_STL	394,800.63	-36,738.63
2014 Jan	377,387	Drift_STL	398,834.87	-21,447.87
2014 Feb	543,470	Drift_STL	564,530.33	-21,060.33
2014 Mar	749,773	Drift_STL	807,351.88	-57,578.88
2014 Apr	1,337,145	Drift_STL	994,828.83	342,316.17
2014 May	1,538,342	Drift_STL	1,510,924.89	27,417.11
2014 Jun	1,994,167	Drift_STL	1,881,853.87	112,313.13
2014 Jul	2,529,246	Drift_STL	2,497,070.95	32,175.05
2014 Aug	3,069,865	Drift_STL	2,868,107.12	201,757.88
2014 Sep	2,089,656	Drift_STL	2,235,847.60	-146,191.60
2014 Oct	1,477,481	Drift_STL	1,504,090.39	-26,609.39
2014 Nov	502,473	Drift_STL	788,605.88	-286,132.88
2014 Dec	382,543	Drift_STL	456,527.56	-73,984.56
2015 Jan	381,607	Drift_STL	440,091.27	-58,484.27
2015 Feb	544,777	Drift_STL	582,803.52	-38,026.52
2015 Mar	827,071	Drift_STL	815,371.63	11,699.37
2015 Apr	1,242,844	Drift_STL	1,132,572.23	110,271.77
2015 May	1,654,526	Drift_STL	1,434,409.40	220,116.60
2015 Jun	2,079,484	Drift_STL	2,008,354.36	71,129.64
2015 Jul	2,688,710	Drift_STL	2,582,499.69	106,210.31
2015 Aug	3,108,357	Drift_STL	3,037,384.75	70,972.25
2015 Sep	2,196,681	Drift_STL	2,237,045.18	-40,364.18
2015 Oct	1,553,142	Drift_STL	1,588,641.30	-35,499.30
2015 Nov	552,778	Drift_STL	798,619.16	-245,841.16
2015 Dec	426,419	Drift_STL	498,574.11	-72,155.11
2016 Jan	443,150	Drift_STL	481,259.84	-38,109.84
2016 Feb	664,278	Drift_STL	641,503.01	22,774.99
2016 Mar	1,089,392	Drift_STL	935,392.86	153,999.14
2016 Apr	1,335,308	Drift_STL	1,406,727.92	-71,419.92
2016 May	1,828,292	Drift_STL	1,567,936.56	260,355.44
2016 Jun	2,288,337	Drift_STL	2,194,956.51	93,380.49
2016 Jul	2,848,570	Drift_STL	2,804,479.68	44,090.32
2016 Aug	3,204,047	Drift_STL	3,207,992.98	-3,945.98
2016 Sep	2,378,618	Drift_STL	2,320,737.91	57,880.09
2016 Oct	1,793,822	Drift_STL	1,752,722.32	41,099.68
2016 Nov	653,514	Drift_STL	968,662.77	-315,148.77
2016 Dec	478,510	Drift_STL	598,804.58	-120,294.58
2017 Jan	495,629	Drift_STL	544,545.48	-48,916.48
2017 Feb	704,532	Drift_STL	710,656.12	-6,124.12
2017 Mar	1,015,421	Drift_STL	1,012,046.79	3,374.21
2017 Apr	1,765,170	Drift_STL	1,351,754.85	413,415.15
2017 May	1,970,072	Drift_STL	2,000,141.75	-30,069.75
2017 Jun	2,417,100	Drift_STL	2,352,237.38	64,862.62
2017 Jul	2,968,641	Drift_STL	2,941,095.92	27,545.08
2017 Aug	3,295,406	Drift_STL	3,328,001.15	-32,595.15
2017 Sep	2,470,298	Drift_STL	2,412,721.11	57,576.89
2017 Oct	1,911,961	Drift_STL	1,843,290.04	68,670.96
2017 Nov	680,373	Drift_STL	1,005,589.38	-325,216.38
2017 Dec	512,548	Drift_STL	613,740.26	-101,192.26
2018 Jan	503,908	Drift_STL	579,081.05	-75,173.05
2018 Feb	731,090	Drift_STL	728,856.90	2,233.10
2018 Mar	1,151,455	Drift_STL	1,049,399.37	102,055.63
2018 Apr	1,575,078	Drift_STL	1,551,958.71	23,119.29
2018 May	2,003,996	Drift_STL	1,843,073.19	160,922.81
2018 Jun	2,381,154	Drift_STL	2,391,629.84	-10,475.84
2018 Jul	2,981,643	Drift_STL	2,911,326.73	70,316.27
2018 Aug	3,371,918	Drift_STL	3,330,876.87	41,041.13
2018 Sep	2,499,368	Drift_STL	2,477,915.11	21,452.89
2018 Oct	1,956,693	Drift_STL	1,871,128.81	85,564.19
2018 Nov	732,141	Drift_STL	959,338.42	-227,197.42
2018 Dec	554,803	Drift_STL	639,524.94	-84,721.94
2019 Jan	548,686	Drift_STL	607,996.29	-59,310.29
2019 Feb	739,981	Drift_STL	776,574.26	-36,593.26
2019 Mar	1,078,918	Drift_STL	1,086,715.00	-7,797.00
2019 Apr	1,795,494	Drift_STL	1,511,759.04	283,734.96
2019 May	1,990,529	Drift_STL	2,078,699.06	-88,170.06
2019 Jun	2,425,834	Drift_STL	2,389,440.16	36,393.84
2019 Jul	2,988,668	Drift_STL	2,970,223.14	18,444.86
2019 Aug	3,439,271	Drift_STL	3,351,974.56	87,296.44
2019 Sep	2,573,527	Drift_STL	2,542,960.49	30,566.51
2019 Oct	1,930,852	Drift_STL	1,953,497.93	-22,645.93
2019 Nov	785,875	Drift_STL	872,143.02	-86,268.02
2019 Dec	602,860	Drift_STL	668,699.36	-65,839.36
2020 Jan	560,368	Drift_STL	642,178.54	-81,810.54
2020 Feb	844,247	Drift_STL	788,236.62	56,010.38
2020 Mar	513,360	Drift_STL	1,189,686.20	-676,326.20
2020 Apr	25,614	Drift_STL	1,079,497.46	-1,053,883.46
2020 May	40,932	Drift_STL	502,368.23	-461,436.23
2020 Jun	330,393	Drift_STL	609,875.81	-279,482.81
2020 Jul	1,035,732	Drift_STL	1,002,247.44	33,484.56
2020 Aug	2,090,569	Drift_STL	1,477,386.09	613,182.91
2020 Sep	1,418,185	Drift_STL	1,146,450.80	271,734.20
2020 Oct	696,087	Drift_STL	708,986.76	-12,899.76
2020 Nov	181,873	Drift_STL	-472,204.66	654,077.66
2020 Dec	153,351	Drift_STL	-94,403.55	247,754.55
2021 Jan	105,336	Drift_STL	44,190.91	61,145.09
2021 Feb	66,194	Drift_STL	241,713.25	-175,519.25
2021 Mar	84,413	Drift_STL	278,764.40	-194,351.40
2021 Apr	138,661	Drift_STL	463,076.47	-324,415.47
2021 May	502,057	Drift_STL	488,241.43	13,815.57
2021 Jun	1,182,009	Drift_STL	980,909.95	201,099.05
2021 Jul	1,551,789	Drift_STL	1,814,135.42	-262,346.42
2021 Aug	2,762,537	Drift_STL	2,119,869.83	642,667.17
2021 Sep	1,869,194	Drift_STL	1,882,196.12	-13,002.12
2021 Oct	1,584,764	Drift_STL	1,219,375.02	365,388.98
2021 Nov	651,051	Drift_STL	503,067.49	147,983.51
2021 Dec	376,031	Drift_STL	457,728.98	-81,697.98
2022 Jan	344,634	Drift_STL	342,800.04	1,833.96
2022 Feb	590,122	Drift_STL	509,744.30	80,377.70
2022 Mar	873,841	Drift_STL	770,051.02	103,789.98
2022 Apr	1,629,377	Drift_STL	1,173,081.91	456,295.09
2022 May	1,867,744	Drift_STL	1,891,159.11	-23,415.11
2022 Jun	2,230,207	Drift_STL	2,333,252.76	-103,045.76
2010 Jan	366,296	Drift_STL_log	394,378.62	-28,082.62
2010 Feb	533,056	Drift_STL_log	516,396.96	16,659.04
2010 Mar	742,227	Drift_STL_log	723,315.52	18,911.48
2010 Apr	902,745	Drift_STL_log	904,478.35	-1,733.35
2010 May	1,107,303	Drift_STL_log	1,097,128.55	10,174.45
2010 Jun	1,464,695	Drift_STL_log	1,347,374.49	117,320.51
2010 Jul	2,050,478	Drift_STL_log	1,849,551.68	200,926.32
2010 Aug	2,468,924	Drift_STL_log	2,414,793.09	54,130.91
2010 Sep	1,696,356	Drift_STL_log	1,683,742.24	12,613.76
2010 Oct	1,104,659	Drift_STL_log	1,150,206.83	-45,547.83
2010 Nov	445,221	Drift_STL_log	523,287.01	-78,066.01
2010 Dec	365,490	Drift_STL_log	368,557.91	-3,067.91
2011 Jan	357,209	Drift_STL_log	387,690.54	-30,481.54
2011 Feb	503,831	Drift_STL_log	512,404.55	-8,573.55
2011 Mar	761,343	Drift_STL_log	698,702.56	62,640.44
2011 Apr	1,177,115	Drift_STL_log	931,119.21	245,995.79
2011 May	1,169,516	Drift_STL_log	1,394,379.47	-224,863.47
2011 Jun	1,576,730	Drift_STL_log	1,449,028.64	127,701.36
2011 Jul	2,208,160	Drift_STL_log	2,025,531.46	182,628.54
2011 Aug	2,572,404	Drift_STL_log	2,598,085.89	-25,681.89
2011 Sep	1,731,056	Drift_STL_log	1,754,853.06	-23,797.06
2011 Oct	1,161,751	Drift_STL_log	1,166,746.23	-4,995.23
2011 Nov	427,550	Drift_STL_log	535,885.10	-108,335.10
2011 Dec	333,201	Drift_STL_log	358,706.21	-25,505.21
2012 Jan	359,355	Drift_STL_log	352,335.86	7,019.14
2012 Feb	531,709	Drift_STL_log	514,800.97	16,908.03
2012 Mar	751,024	Drift_STL_log	746,035.66	4,988.34
2012 Apr	1,017,976	Drift_STL_log	958,266.21	59,709.79
2012 May	1,194,673	Drift_STL_log	1,187,162.27	7,510.73
2012 Jun	1,678,327	Drift_STL_log	1,491,391.57	186,935.43
2012 Jul	2,296,474	Drift_STL_log	2,163,787.63	132,686.37
2012 Aug	2,622,801	Drift_STL_log	2,669,183.27	-46,382.27
2012 Sep	1,829,252	Drift_STL_log	1,773,639.41	55,612.59
2012 Oct	1,244,751	Drift_STL_log	1,216,733.09	28,017.91
2012 Nov	453,958	Drift_STL_log	546,676.47	-92,718.47
2012 Dec	346,474	Drift_STL_log	377,435.56	-30,961.56
2013 Jan	369,969	Drift_STL_log	367,539.85	2,429.15
2013 Feb	520,055	Drift_STL_log	536,209.70	-16,154.70
2013 Mar	840,024	Drift_STL_log	742,006.53	98,017.47
2013 Apr	986,191	Drift_STL_log	1,082,843.18	-96,652.18
2013 May	1,382,234	Drift_STL_log	1,159,169.01	223,064.99
2013 Jun	1,814,108	Drift_STL_log	1,746,906.10	67,201.90
2013 Jul	2,387,304	Drift_STL_log	2,366,072.16	21,231.84
2013 Aug	2,764,686	Drift_STL_log	2,768,628.90	-3,942.90
2013 Sep	1,943,037	Drift_STL_log	1,875,995.52	67,041.48
2013 Oct	1,291,360	Drift_STL_log	1,289,538.40	1,821.60
2013 Nov	455,695	Drift_STL_log	544,995.20	-89,300.20
2013 Dec	358,062	Drift_STL_log	375,872.00	-17,810.00
2014 Jan	377,387	Drift_STL_log	380,438.97	-3,051.97
2014 Feb	543,470	Drift_STL_log	547,646.80	-4,176.80
2014 Mar	749,773	Drift_STL_log	794,366.52	-44,593.52
2014 Apr	1,337,145	Drift_STL_log	976,034.66	361,110.34
2014 May	1,538,342	Drift_STL_log	1,553,906.33	-15,564.33
2014 Jun	1,994,167	Drift_STL_log	1,958,823.92	35,343.08
2014 Jul	2,529,246	Drift_STL_log	2,609,753.05	-80,507.05
2014 Aug	3,069,865	Drift_STL_log	2,935,989.66	133,875.34
2014 Sep	2,089,656	Drift_STL_log	2,086,623.79	3,032.21
2014 Oct	1,477,481	Drift_STL_log	1,385,524.84	91,956.16
2014 Nov	502,473	Drift_STL_log	593,003.57	-90,530.57
2014 Dec	382,543	Drift_STL_log	410,911.97	-28,368.97
2015 Jan	381,607	Drift_STL_log	408,798.69	-27,191.69
2015 Feb	544,777	Drift_STL_log	561,369.35	-16,592.35
2015 Mar	827,071	Drift_STL_log	802,502.73	24,568.27
2015 Apr	1,242,844	Drift_STL_log	1,136,065.49	106,778.51
2015 May	1,654,526	Drift_STL_log	1,459,325.90	195,200.10
2015 Jun	2,079,484	Drift_STL_log	2,107,560.48	-28,076.48
2015 Jul	2,688,710	Drift_STL_log	2,704,598.81	-15,888.81
2015 Aug	3,108,357	Drift_STL_log	3,122,510.59	-14,153.59
2015 Sep	2,196,681	Drift_STL_log	2,112,647.11	84,033.89
2015 Oct	1,553,142	Drift_STL_log	1,461,346.53	91,795.47
2015 Nov	552,778	Drift_STL_log	591,888.84	-39,110.84
2015 Dec	426,419	Drift_STL_log	441,044.20	-14,625.20
2016 Jan	443,150	Drift_STL_log	448,073.34	-4,923.34
2016 Feb	664,278	Drift_STL_log	644,242.76	20,035.24
2016 Mar	1,089,392	Drift_STL_log	977,310.21	112,081.79
2016 Apr	1,335,308	Drift_STL_log	1,513,111.83	-177,803.83
2016 May	1,828,292	Drift_STL_log	1,619,170.75	209,121.25
2016 Jun	2,288,337	Drift_STL_log	2,349,505.45	-61,168.45
2016 Jul	2,848,570	Drift_STL_log	2,998,667.02	-150,097.02
2016 Aug	3,204,047	Drift_STL_log	3,342,217.97	-138,170.97
2016 Sep	2,378,618	Drift_STL_log	2,218,553.89	160,064.11
2016 Oct	1,793,822	Drift_STL_log	1,602,641.75	191,180.25
2016 Nov	653,514	Drift_STL_log	657,319.70	-3,805.70
2016 Dec	478,510	Drift_STL_log	510,332.97	-31,822.97
2017 Jan	495,629	Drift_STL_log	500,587.56	-4,958.56
2017 Feb	704,532	Drift_STL_log	722,648.18	-18,116.18
2017 Mar	1,015,421	Drift_STL_log	1,062,158.50	-46,737.50
2017 Apr	1,765,170	Drift_STL_log	1,421,128.50	344,041.50
2017 May	1,970,072	Drift_STL_log	2,130,563.65	-160,491.65
2017 Jun	2,417,100	Drift_STL_log	2,527,179.88	-110,079.88
2017 Jul	2,968,641	Drift_STL_log	3,153,967.51	-185,326.51
2017 Aug	3,295,406	Drift_STL_log	3,482,539.98	-187,133.98
2017 Sep	2,470,298	Drift_STL_log	2,329,962.01	140,335.99
2017 Oct	1,911,961	Drift_STL_log	1,705,174.36	206,786.64
2017 Nov	680,373	Drift_STL_log	685,027.47	-4,654.47
2017 Dec	512,548	Drift_STL_log	521,188.24	-8,640.24
2018 Jan	503,908	Drift_STL_log	531,469.02	-27,561.02
2018 Feb	731,090	Drift_STL_log	732,113.46	-1,023.46
2018 Mar	1,151,455	Drift_STL_log	1,097,136.05	54,318.95
2018 Apr	1,575,078	Drift_STL_log	1,658,352.81	-83,274.81
2018 May	2,003,996	Drift_STL_log	1,923,489.25	80,506.75
2018 Jun	2,381,154	Drift_STL_log	2,542,423.02	-161,269.02
2018 Jul	2,981,643	Drift_STL_log	3,077,528.35	-95,885.35
2018 Aug	3,371,918	Drift_STL_log	3,467,851.80	-95,933.80
2018 Sep	2,499,368	Drift_STL_log	2,414,695.88	84,672.12
2018 Oct	1,956,693	Drift_STL_log	1,767,179.97	189,513.03
2018 Nov	732,141	Drift_STL_log	689,006.76	43,134.24
2018 Dec	554,803	Drift_STL_log	549,633.37	5,169.63
2019 Jan	548,686	Drift_STL_log	564,060.32	-15,374.32
2019 Feb	739,981	Drift_STL_log	790,718.97	-50,737.97
2019 Mar	1,078,918	Drift_STL_log	1,126,671.00	-47,753.00
2019 Apr	1,795,494	Drift_STL_log	1,571,625.36	223,868.64
2019 May	1,990,529	Drift_STL_log	2,193,342.72	-202,813.72
2019 Jun	2,425,834	Drift_STL_log	2,508,367.37	-82,533.37
2019 Jul	2,988,668	Drift_STL_log	3,119,153.13	-130,485.13
2019 Aug	3,439,271	Drift_STL_log	3,477,127.78	-37,856.78
2019 Sep	2,573,527	Drift_STL_log	2,498,630.98	74,896.02
2019 Oct	1,930,852	Drift_STL_log	1,867,627.62	63,224.38
2019 Nov	785,875	Drift_STL_log	685,009.12	100,865.88
2019 Dec	602,860	Drift_STL_log	581,524.02	21,335.98
2020 Jan	560,368	Drift_STL_log	601,641.22	-41,273.22
2020 Feb	844,247	Drift_STL_log	798,071.44	46,175.56
2020 Mar	513,360	Drift_STL_log	1,263,882.25	-750,522.25
2020 Apr	25,614	Drift_STL_log	845,619.25	-820,005.25
2020 May	40,932	Drift_STL_log	51,465.43	-10,533.43
2020 Jun	330,393	Drift_STL_log	70,860.34	259,532.66
2020 Jul	1,035,732	Drift_STL_log	419,085.01	616,646.99
2020 Aug	2,090,569	Drift_STL_log	1,057,790.88	1,032,778.12
2020 Sep	1,418,185	Drift_STL_log	1,270,943.31	147,241.69
2020 Oct	696,087	Drift_STL_log	903,346.53	-207,259.53
2020 Nov	181,873	Drift_STL_log	238,461.61	-56,588.61
2020 Dec	153,351	Drift_STL_log	136,354.84	16,996.16
2021 Jan	105,336	Drift_STL_log	151,079.52	-45,743.52
2021 Feb	66,194	Drift_STL_log	156,886.09	-90,692.09
2021 Mar	84,413	Drift_STL_log	99,216.67	-14,803.67
2021 Apr	138,661	Drift_STL_log	84,260.45	54,400.55
2021 May	502,057	Drift_STL_log	199,069.96	302,987.04
2021 Jun	1,182,009	Drift_STL_log	832,263.71	349,745.29
2021 Jul	1,551,789	Drift_STL_log	1,614,251.93	-62,462.93
2021 Aug	2,762,537	Drift_STL_log	1,878,838.76	883,698.24
2021 Sep	1,869,194	Drift_STL_log	1,873,231.97	-4,037.97
2021 Oct	1,584,764	Drift_STL_log	1,265,567.04	319,196.96
2021 Nov	651,051	Drift_STL_log	534,030.91	117,020.09
2021 Dec	376,031	Drift_STL_log	490,474.96	-114,443.96
2022 Jan	344,634	Drift_STL_log	366,581.24	-21,947.24
2022 Feb	590,122	Drift_STL_log	461,428.25	128,693.75
2022 Mar	873,841	Drift_STL_log	793,950.57	79,890.43
2022 Apr	1,629,377	Drift_STL_log	837,995.85	791,381.15
2022 May	1,867,744	Drift_STL_log	2,629,349.56	-761,605.56
2022 Jun	2,230,207	Drift_STL_log	3,797,942.51	-1,567,735.51
2010 Jan	366,296	ETS_auto	417,493.58	-51,197.58
2010 Feb	533,056	ETS_auto	557,663.47	-24,607.47
2010 Mar	742,227	ETS_auto	749,301.96	-7,074.96
2010 Apr	902,745	ETS_auto	904,007.37	-1,262.37
2010 May	1,107,303	ETS_auto	1,084,183.10	23,119.90
2010 Jun	1,464,695	ETS_auto	1,327,204.36	137,490.64
2010 Jul	2,050,478	ETS_auto	1,711,799.52	338,678.48
2010 Aug	2,468,924	ETS_auto	2,150,911.80	318,012.20
2010 Sep	1,696,356	ETS_auto	1,647,820.22	48,535.78
2010 Oct	1,104,659	ETS_auto	1,170,628.73	-65,969.73
2010 Nov	445,221	ETS_auto	542,816.33	-97,595.33
2010 Dec	365,490	ETS_auto	398,359.67	-32,869.67
2011 Jan	357,209	ETS_auto	408,555.68	-51,346.68
2011 Feb	503,831	ETS_auto	544,295.40	-40,464.40
2011 Mar	761,343	ETS_auto	710,683.89	50,659.11
2011 Apr	1,177,115	ETS_auto	895,250.28	281,864.72
2011 May	1,169,516	ETS_auto	1,200,849.32	-31,333.32
2011 Jun	1,576,730	ETS_auto	1,511,815.77	64,914.23
2011 Jul	2,208,160	ETS_auto	1,927,808.36	280,351.64
2011 Aug	2,572,404	ETS_auto	2,431,638.31	140,765.69
2011 Sep	1,731,056	ETS_auto	1,756,490.02	-25,434.02
2011 Oct	1,161,751	ETS_auto	1,210,715.49	-48,964.49
2011 Nov	427,550	ETS_auto	559,354.62	-131,804.62
2011 Dec	333,201	ETS_auto	383,841.42	-50,640.42
2012 Jan	359,355	ETS_auto	375,295.11	-15,940.11
2012 Feb	531,709	ETS_auto	519,463.94	12,245.06
2012 Mar	751,024	ETS_auto	717,132.79	33,891.21
2012 Apr	1,017,976	ETS_auto	918,561.92	99,414.08
2012 May	1,194,673	ETS_auto	1,151,367.30	43,305.70
2012 Jun	1,678,327	ETS_auto	1,450,355.43	227,971.57
2012 Jul	2,296,474	ETS_auto	2,035,764.39	260,709.61
2012 Aug	2,622,801	ETS_auto	2,579,227.73	43,573.27
2012 Sep	1,829,252	ETS_auto	1,685,280.89	143,971.11
2012 Oct	1,244,751	ETS_auto	1,265,518.95	-20,767.95
2012 Nov	453,958	ETS_auto	580,619.85	-126,661.85
2012 Dec	346,474	ETS_auto	361,138.55	-14,664.55
2013 Jan	369,969	ETS_auto	378,586.36	-8,617.36
2013 Feb	520,055	ETS_auto	549,806.47	-29,751.47
2013 Mar	840,024	ETS_auto	784,114.50	55,909.50
2013 Apr	986,191	ETS_auto	1,092,758.38	-106,567.38
2013 May	1,382,234	ETS_auto	1,210,730.24	171,503.76
2013 Jun	1,814,108	ETS_auto	1,687,126.25	126,981.75
2013 Jul	2,387,304	ETS_auto	2,325,703.69	61,600.31
2013 Aug	2,764,686	ETS_auto	2,674,038.22	90,647.78
2013 Sep	1,943,037	ETS_auto	1,829,121.81	113,915.19
2013 Oct	1,291,360	ETS_auto	1,236,838.98	54,521.02
2013 Nov	455,695	ETS_auto	464,982.22	-9,287.22
2013 Dec	358,062	ETS_auto	362,998.03	-4,936.03
2014 Jan	377,387	ETS_auto	389,364.56	-11,977.56
2014 Feb	543,470	ETS_auto	551,718.93	-8,248.93
2014 Mar	749,773	ETS_auto	848,081.27	-98,308.27
2014 Apr	1,337,145	ETS_auto	1,044,938.62	292,206.38
2014 May	1,538,342	ETS_auto	1,398,107.58	140,234.42
2014 Jun	1,994,167	ETS_auto	1,863,512.33	130,654.67
2014 Jul	2,529,246	ETS_auto	2,521,994.82	7,251.18
2014 Aug	3,069,865	ETS_auto	2,896,732.33	173,132.67
2014 Sep	2,089,656	ETS_auto	2,024,917.26	64,738.74
2014 Oct	1,477,481	ETS_auto	1,348,330.40	129,150.60
2014 Nov	502,473	ETS_auto	494,960.26	7,512.74
2014 Dec	382,543	ETS_auto	389,976.48	-7,433.48
2015 Jan	381,607	ETS_auto	411,057.09	-29,450.09
2015 Feb	544,777	ETS_auto	586,314.34	-41,537.34
2015 Mar	827,071	ETS_auto	841,139.83	-14,068.83
2015 Apr	1,242,844	ETS_auto	1,303,842.18	-60,998.18
2015 May	1,654,526	ETS_auto	1,515,270.38	139,255.62
2015 Jun	2,079,484	ETS_auto	1,985,726.46	93,757.54
2015 Jul	2,688,710	ETS_auto	2,575,822.01	112,887.99
2015 Aug	3,108,357	ETS_auto	3,075,393.96	32,963.04
2015 Sep	2,196,681	ETS_auto	2,099,938.26	96,742.74
2015 Oct	1,553,142	ETS_auto	1,447,084.45	106,057.55
2015 Nov	552,778	ETS_auto	506,894.25	45,883.75
2015 Dec	426,419	ETS_auto	398,051.17	28,367.83
2016 Jan	443,150	ETS_auto	410,496.72	32,653.28
2016 Feb	664,278	ETS_auto	602,167.49	62,110.51
2016 Mar	1,089,392	ETS_auto	932,535.86	156,856.14
2016 Apr	1,335,308	ETS_auto	1,487,201.31	-151,893.31
2016 May	1,828,292	ETS_auto	1,816,918.58	11,373.42
2016 Jun	2,288,337	ETS_auto	2,291,845.36	-3,508.36
2016 Jul	2,848,570	ETS_auto	2,939,909.83	-91,339.83
2016 Aug	3,204,047	ETS_auto	3,396,258.07	-192,211.07
2016 Sep	2,378,618	ETS_auto	2,330,553.51	48,064.49
2016 Oct	1,793,822	ETS_auto	1,621,754.04	172,067.96
2016 Nov	653,514	ETS_auto	577,330.44	76,183.56
2016 Dec	478,510	ETS_auto	452,799.19	25,710.81
2017 Jan	495,629	ETS_auto	469,866.05	25,762.95
2017 Feb	704,532	ETS_auto	696,734.23	7,797.77
2017 Mar	1,015,421	ETS_auto	1,091,427.50	-76,006.50
2017 Apr	1,765,170	ETS_auto	1,428,010.42	337,159.58
2017 May	1,970,072	ETS_auto	1,994,466.98	-24,394.98
2017 Jun	2,417,100	ETS_auto	2,488,506.71	-71,406.71
2017 Jul	2,968,641	ETS_auto	3,132,244.38	-163,603.38
2017 Aug	3,295,406	ETS_auto	3,556,303.31	-260,897.31
2017 Sep	2,470,298	ETS_auto	2,518,038.95	-47,740.95
2017 Oct	1,911,961	ETS_auto	1,811,005.09	100,955.91
2017 Nov	680,373	ETS_auto	649,312.68	31,060.32
2017 Dec	512,548	ETS_auto	482,773.07	29,774.93
2018 Jan	503,908	ETS_auto	501,759.48	2,148.52
2018 Feb	731,090	ETS_auto	720,409.70	10,680.30
2018 Mar	1,151,455	ETS_auto	1,083,333.80	68,121.20
2018 Apr	1,575,078	ETS_auto	1,695,637.94	-120,559.94
2018 May	2,003,996	ETS_auto	1,975,549.13	28,446.87
2018 Jun	2,381,154	ETS_auto	2,455,827.02	-74,673.02
2018 Jul	2,981,643	ETS_auto	3,048,890.95	-67,247.95
2018 Aug	3,371,918	ETS_auto	3,449,927.03	-78,009.03
2018 Sep	2,499,368	ETS_auto	2,544,075.12	-44,707.12
2018 Oct	1,956,693	ETS_auto	1,896,284.16	60,408.84
2018 Nov	732,141	ETS_auto	673,969.19	58,171.81
2018 Dec	554,803	ETS_auto	508,499.00	46,304.00
2019 Jan	548,686	ETS_auto	516,096.24	32,589.76
2019 Feb	739,981	ETS_auto	752,890.99	-12,909.99
2019 Mar	1,078,918	ETS_auto	1,153,690.51	-74,772.51
2019 Apr	1,795,494	ETS_auto	1,644,208.55	151,285.45
2019 May	1,990,529	ETS_auto	2,062,763.53	-72,234.53
2019 Jun	2,425,834	ETS_auto	2,485,587.01	-59,753.01
2019 Jul	2,988,668	ETS_auto	3,096,670.92	-108,002.92
2019 Aug	3,439,271	ETS_auto	3,496,283.42	-57,012.42
2019 Sep	2,573,527	ETS_auto	2,590,948.73	-17,421.73
2019 Oct	1,930,852	ETS_auto	1,988,597.86	-57,745.86
2019 Nov	785,875	ETS_auto	715,243.96	70,631.04
2019 Dec	602,860	ETS_auto	543,759.73	59,100.27
2020 Jan	560,368	ETS_auto	546,562.03	13,805.97
2020 Feb	844,247	ETS_auto	758,462.88	85,784.12
2020 Mar	513,360	ETS_auto	1,159,257.46	-645,897.46
2020 Apr	25,614	ETS_auto	1,635,853.49	-1,610,239.49
2020 May	40,932	ETS_auto	1,566,371.32	-1,525,439.32
2020 Jun	330,393	ETS_auto	1,554,346.57	-1,223,953.57
2020 Jul	1,035,732	ETS_auto	403,909.72	631,822.28
2020 Aug	2,090,569	ETS_auto	1,127,828.20	962,740.80
2020 Sep	1,418,185	ETS_auto	1,274,002.65	144,182.35
2020 Oct	696,087	ETS_auto	1,002,543.02	-306,456.02
2020 Nov	181,873	ETS_auto	359,301.55	-177,428.55
2020 Dec	153,351	ETS_auto	233,518.87	-80,167.87
2021 Jan	105,336	ETS_auto	176,435.05	-71,099.05
2021 Feb	66,194	ETS_auto	108,480.22	-42,286.22
2021 Mar	84,413	ETS_auto	23,076.12	61,336.88
2021 Apr	138,661	ETS_auto	31,875.45	106,785.55
2021 May	502,057	ETS_auto	377,196.43	124,860.57
2021 Jun	1,182,009	ETS_auto	860,635.09	321,373.91
2021 Jul	1,551,789	ETS_auto	1,684,594.20	-132,805.20
2021 Aug	2,762,537	ETS_auto	1,956,644.94	805,892.06
2021 Sep	1,869,194	ETS_auto	2,013,861.06	-144,667.06
2021 Oct	1,584,764	ETS_auto	1,317,893.71	266,870.29
2021 Nov	651,051	ETS_auto	817,938.59	-166,887.59
2021 Dec	376,031	ETS_auto	531,858.66	-155,827.66
2022 Jan	344,634	ETS_auto	389,993.94	-45,359.94
2022 Feb	590,122	ETS_auto	533,049.53	57,072.47
2022 Mar	873,841	ETS_auto	817,437.35	56,403.65
2022 Apr	1,629,377	ETS_auto	1,116,843.57	512,533.43
2022 May	1,867,744	ETS_auto	1,863,539.41	4,204.59
2022 Jun	2,230,207	ETS_auto	2,240,316.15	-10,109.15
2010 Jan	366,296	ETS_auto_log	417,048.27	-50,752.27
2010 Feb	533,056	ETS_auto_log	580,819.69	-47,763.69
2010 Mar	742,227	ETS_auto_log	755,624.26	-13,397.26
2010 Apr	902,745	ETS_auto_log	911,391.15	-8,646.15
2010 May	1,107,303	ETS_auto_log	1,076,654.26	30,648.74
2010 Jun	1,464,695	ETS_auto_log	1,339,156.89	125,538.11
2010 Jul	2,050,478	ETS_auto_log	1,726,541.41	323,936.59
2010 Aug	2,468,924	ETS_auto_log	2,092,336.26	376,587.74
2010 Sep	1,696,356	ETS_auto_log	1,596,362.93	99,993.07
2010 Oct	1,104,659	ETS_auto_log	1,108,471.74	-3,812.74
2010 Nov	445,221	ETS_auto_log	532,309.89	-87,088.89
2010 Dec	365,490	ETS_auto_log	397,600.19	-32,110.19
2011 Jan	357,209	ETS_auto_log	409,446.09	-52,237.09
2011 Feb	503,831	ETS_auto_log	556,049.25	-52,218.25
2011 Mar	761,343	ETS_auto_log	725,248.89	36,094.11
2011 Apr	1,177,115	ETS_auto_log	910,410.41	266,704.59
2011 May	1,169,516	ETS_auto_log	1,185,121.54	-15,605.54
2011 Jun	1,576,730	ETS_auto_log	1,507,698.33	69,031.67
2011 Jul	2,208,160	ETS_auto_log	1,971,817.12	236,342.88
2011 Aug	2,572,404	ETS_auto_log	2,424,570.63	147,833.37
2011 Sep	1,731,056	ETS_auto_log	1,676,402.04	54,653.96
2011 Oct	1,161,751	ETS_auto_log	1,112,179.14	49,571.86
2011 Nov	427,550	ETS_auto_log	497,278.71	-69,728.71
2011 Dec	333,201	ETS_auto_log	384,272.52	-51,071.52
2012 Jan	359,355	ETS_auto_log	378,547.54	-19,192.54
2012 Feb	531,709	ETS_auto_log	536,596.32	-4,887.32
2012 Mar	751,024	ETS_auto_log	774,228.51	-23,204.51
2012 Apr	1,017,976	ETS_auto_log	1,064,404.50	-46,428.50
2012 May	1,194,673	ETS_auto_log	1,140,343.80	54,329.20
2012 Jun	1,678,327	ETS_auto_log	1,519,812.19	158,514.81
2012 Jul	2,296,474	ETS_auto_log	2,104,668.73	191,805.27
2012 Aug	2,622,801	ETS_auto_log	2,492,244.02	130,556.98
2012 Sep	1,829,252	ETS_auto_log	1,696,250.97	133,001.03
2012 Oct	1,244,751	ETS_auto_log	1,133,915.89	110,835.11
2012 Nov	453,958	ETS_auto_log	462,825.23	-8,867.23
2012 Dec	346,474	ETS_auto_log	369,184.56	-22,710.56
2013 Jan	369,969	ETS_auto_log	385,933.73	-15,964.73
2013 Feb	520,055	ETS_auto_log	555,697.02	-35,642.02
2013 Mar	840,024	ETS_auto_log	789,327.07	50,696.93
2013 Apr	986,191	ETS_auto_log	1,101,076.51	-114,885.51
2013 May	1,382,234	ETS_auto_log	1,220,270.42	161,963.58
2013 Jun	1,814,108	ETS_auto_log	1,690,758.68	123,349.32
2013 Jul	2,387,304	ETS_auto_log	2,332,358.00	54,946.00
2013 Aug	2,764,686	ETS_auto_log	2,681,009.06	83,676.94
2013 Sep	1,943,037	ETS_auto_log	1,837,501.70	105,535.30
2013 Oct	1,291,360	ETS_auto_log	1,239,361.12	51,998.88
2013 Nov	455,695	ETS_auto_log	466,714.60	-11,019.60
2013 Dec	358,062	ETS_auto_log	362,779.16	-4,717.16
2014 Jan	377,387	ETS_auto_log	385,844.92	-8,457.92
2014 Feb	543,470	ETS_auto_log	554,412.61	-10,942.61
2014 Mar	749,773	ETS_auto_log	851,027.96	-101,254.96
2014 Apr	1,337,145	ETS_auto_log	1,043,315.91	293,829.09
2014 May	1,538,342	ETS_auto_log	1,397,943.57	140,398.43
2014 Jun	1,994,167	ETS_auto_log	1,878,880.16	115,286.84
2014 Jul	2,529,246	ETS_auto_log	2,518,303.73	10,942.27
2014 Aug	3,069,865	ETS_auto_log	2,903,562.14	166,302.86
2014 Sep	2,089,656	ETS_auto_log	2,021,245.50	68,410.50
2014 Oct	1,477,481	ETS_auto_log	1,350,822.00	126,659.00
2014 Nov	502,473	ETS_auto_log	500,094.19	2,378.81
2014 Dec	382,543	ETS_auto_log	388,730.46	-6,187.46
2015 Jan	381,607	ETS_auto_log	410,892.50	-29,285.50
2015 Feb	544,777	ETS_auto_log	584,129.59	-39,352.59
2015 Mar	827,071	ETS_auto_log	838,146.40	-11,075.40
2015 Apr	1,242,844	ETS_auto_log	1,293,419.65	-50,575.65
2015 May	1,654,526	ETS_auto_log	1,523,111.72	131,414.28
2015 Jun	2,079,484	ETS_auto_log	1,998,526.43	80,957.57
2015 Jul	2,688,710	ETS_auto_log	2,585,870.10	102,839.90
2015 Aug	3,108,357	ETS_auto_log	3,088,878.78	19,478.22
2015 Sep	2,196,681	ETS_auto_log	2,109,503.43	87,177.57
2015 Oct	1,553,142	ETS_auto_log	1,456,193.82	96,948.18
2015 Nov	552,778	ETS_auto_log	507,586.71	45,191.29
2015 Dec	426,419	ETS_auto_log	398,145.95	28,273.05
2016 Jan	443,150	ETS_auto_log	415,726.58	27,423.42
2016 Feb	664,278	ETS_auto_log	609,364.22	54,913.78
2016 Mar	1,089,392	ETS_auto_log	927,370.94	162,021.06
2016 Apr	1,335,308	ETS_auto_log	1,447,592.96	-112,284.96
2016 May	1,828,292	ETS_auto_log	1,843,051.19	-14,759.19
2016 Jun	2,288,337	ETS_auto_log	2,345,264.76	-56,927.76
2016 Jul	2,848,570	ETS_auto_log	2,995,750.57	-147,180.57
2016 Aug	3,204,047	ETS_auto_log	3,408,432.99	-204,385.99
2016 Sep	2,378,618	ETS_auto_log	2,337,428.74	41,189.26
2016 Oct	1,793,822	ETS_auto_log	1,638,512.37	155,309.63
2016 Nov	653,514	ETS_auto_log	585,573.44	67,940.56
2016 Dec	478,510	ETS_auto_log	461,015.92	17,494.08
2017 Jan	495,629	ETS_auto_log	475,421.92	20,207.08
2017 Feb	704,532	ETS_auto_log	697,358.20	7,173.80
2017 Mar	1,015,421	ETS_auto_log	1,090,746.03	-75,325.03
2017 Apr	1,765,170	ETS_auto_log	1,455,422.82	309,747.18
2017 May	1,970,072	ETS_auto_log	2,024,682.50	-54,610.50
2017 Jun	2,417,100	ETS_auto_log	2,495,254.75	-78,154.75
2017 Jul	2,968,641	ETS_auto_log	3,136,707.11	-168,066.11
2017 Aug	3,295,406	ETS_auto_log	3,629,920.96	-334,514.96
2017 Sep	2,470,298	ETS_auto_log	2,607,466.67	-137,168.67
2017 Oct	1,911,961	ETS_auto_log	1,868,389.14	43,571.86
2017 Nov	680,373	ETS_auto_log	668,278.36	12,094.64
2017 Dec	512,548	ETS_auto_log	498,064.35	14,483.65
2018 Jan	503,908	ETS_auto_log	515,447.03	-11,539.03
2018 Feb	731,090	ETS_auto_log	737,407.97	-6,317.97
2018 Mar	1,151,455	ETS_auto_log	1,103,669.38	47,785.62
2018 Apr	1,575,078	ETS_auto_log	1,698,055.12	-122,977.12
2018 May	2,003,996	ETS_auto_log	2,026,719.33	-22,723.33
2018 Jun	2,381,154	ETS_auto_log	2,512,866.95	-131,712.95
2018 Jul	2,981,643	ETS_auto_log	3,108,944.54	-127,301.54
2018 Aug	3,371,918	ETS_auto_log	3,502,873.62	-130,955.62
2018 Sep	2,499,368	ETS_auto_log	2,554,009.62	-54,641.62
2018 Oct	1,956,693	ETS_auto_log	1,916,087.85	40,605.15
2018 Nov	732,141	ETS_auto_log	678,250.92	53,890.08
2018 Dec	554,803	ETS_auto_log	520,979.52	33,823.48
2019 Jan	548,686	ETS_auto_log	526,575.93	22,110.07
2019 Feb	739,981	ETS_auto_log	767,865.56	-27,884.56
2019 Mar	1,078,918	ETS_auto_log	1,164,770.79	-85,852.79
2019 Apr	1,795,494	ETS_auto_log	1,666,710.73	128,783.27
2019 May	1,990,529	ETS_auto_log	2,104,691.21	-114,162.21
2019 Jun	2,425,834	ETS_auto_log	2,526,335.67	-100,501.67
2019 Jul	2,988,668	ETS_auto_log	3,119,100.22	-130,432.22
2019 Aug	3,439,271	ETS_auto_log	3,510,678.12	-71,407.12
2019 Sep	2,573,527	ETS_auto_log	2,594,203.98	-20,676.98
2019 Oct	1,930,852	ETS_auto_log	1,999,961.74	-69,109.74
2019 Nov	785,875	ETS_auto_log	725,835.59	60,039.41
2019 Dec	602,860	ETS_auto_log	554,838.87	48,021.13
2020 Jan	560,368	ETS_auto_log	552,312.88	8,055.12
2020 Feb	844,247	ETS_auto_log	770,880.45	73,366.55
2020 Mar	513,360	ETS_auto_log	1,160,071.18	-646,711.18
2020 Apr	25,614	ETS_auto_log	1,633,482.02	-1,607,868.02
2020 May	40,932	ETS_auto_log	18,695.94	22,236.06
2020 Jun	330,393	ETS_auto_log	41,906.06	288,486.94
2020 Jul	1,035,732	ETS_auto_log	327,439.00	708,293.00
2020 Aug	2,090,569	ETS_auto_log	1,228,655.20	861,913.80
2020 Sep	1,418,185	ETS_auto_log	1,597,187.60	-179,002.60
2020 Oct	696,087	ETS_auto_log	1,044,294.93	-348,207.93
2020 Nov	181,873	ETS_auto_log	304,387.67	-122,514.67
2020 Dec	153,351	ETS_auto_log	150,212.43	3,138.57
2021 Jan	105,336	ETS_auto_log	165,287.80	-59,951.80
2021 Feb	66,194	ETS_auto_log	158,685.74	-92,491.74
2021 Mar	84,413	ETS_auto_log	93,140.39	-8,727.39
2021 Apr	138,661	ETS_auto_log	95,430.79	43,230.21
2021 May	502,057	ETS_auto_log	168,175.91	333,881.09
2021 Jun	1,182,009	ETS_auto_log	685,151.50	496,857.50
2021 Jul	1,551,789	ETS_auto_log	1,662,767.27	-110,978.27
2021 Aug	2,762,537	ETS_auto_log	1,810,101.50	952,435.50
2021 Sep	1,869,194	ETS_auto_log	2,002,202.06	-133,008.06
2021 Oct	1,584,764	ETS_auto_log	1,324,703.32	260,060.68
2021 Nov	651,051	ETS_auto_log	684,557.69	-33,506.69
2021 Dec	376,031	ETS_auto_log	542,062.76	-166,031.76
2022 Jan	344,634	ETS_auto_log	404,698.49	-60,064.49
2022 Feb	590,122	ETS_auto_log	477,918.86	112,203.14
2022 Mar	873,841	ETS_auto_log	880,293.11	-6,452.11
2022 Apr	1,629,377	ETS_auto_log	1,046,572.04	582,804.96
2022 May	1,867,744	ETS_auto_log	2,273,900.43	-406,156.43
2022 Jun	2,230,207	ETS_auto_log	2,789,856.69	-559,649.69
2010 Jan	366,296	HWA	379,162.29	-12,866.29
2010 Feb	533,056	HWA	575,889.99	-42,833.99
2010 Mar	742,227	HWA	790,723.48	-48,496.48
2010 Apr	902,745	HWA	959,389.39	-56,644.39
2010 May	1,107,303	HWA	1,166,099.39	-58,796.39
2010 Jun	1,464,695	HWA	1,433,876.12	30,818.88
2010 Jul	2,050,478	HWA	1,836,849.91	213,628.09
2010 Aug	2,468,924	HWA	2,228,340.41	240,583.59
2010 Sep	1,696,356	HWA	1,644,148.32	52,207.68
2010 Oct	1,104,659	HWA	1,170,088.74	-65,429.74
2010 Nov	445,221	HWA	548,576.48	-103,355.48
2010 Dec	365,490	HWA	395,188.10	-29,698.10
2011 Jan	357,209	HWA	407,866.05	-50,657.05
2011 Feb	503,831	HWA	596,923.20	-93,092.20
2011 Mar	761,343	HWA	789,213.74	-27,870.74
2011 Apr	1,177,115	HWA	958,803.18	218,311.82
2011 May	1,169,516	HWA	1,226,576.31	-57,060.31
2011 Jun	1,576,730	HWA	1,501,840.47	74,889.53
2011 Jul	2,208,160	HWA	1,938,761.30	269,398.70
2011 Aug	2,572,404	HWA	2,363,049.38	209,354.62
2011 Sep	1,731,056	HWA	1,711,537.26	19,518.74
2011 Oct	1,161,751	HWA	1,155,181.75	6,569.25
2011 Nov	427,550	HWA	548,498.19	-120,948.19
2011 Dec	333,201	HWA	430,402.26	-97,201.26
2012 Jan	359,355	HWA	412,094.03	-52,739.03
2012 Feb	531,709	HWA	565,893.12	-34,184.12
2012 Mar	751,024	HWA	798,252.99	-47,228.99
2012 Apr	1,017,976	HWA	1,067,598.33	-49,622.33
2012 May	1,194,673	HWA	1,170,532.58	24,140.42
2012 Jun	1,678,327	HWA	1,534,404.83	143,922.17
2012 Jul	2,296,474	HWA	2,105,595.38	190,878.62
2012 Aug	2,622,801	HWA	2,519,903.95	102,897.05
2012 Sep	1,829,252	HWA	1,730,777.98	98,474.02
2012 Oct	1,244,751	HWA	1,183,978.86	60,772.14
2012 Nov	453,958	HWA	533,023.24	-79,065.24
2012 Dec	346,474	HWA	431,958.18	-85,484.18
2013 Jan	369,969	HWA	432,481.12	-62,512.12
2013 Feb	520,055	HWA	589,837.17	-69,782.17
2013 Mar	840,024	HWA	808,303.66	31,720.34
2013 Apr	986,191	HWA	1,100,757.67	-114,566.67
2013 May	1,382,234	HWA	1,215,122.14	167,111.86
2013 Jun	1,814,108	HWA	1,666,651.60	147,456.40
2013 Jul	2,387,304	HWA	2,273,829.18	113,474.82
2013 Aug	2,764,686	HWA	2,630,331.60	134,354.40
2013 Sep	1,943,037	HWA	1,842,772.35	100,264.65
2013 Oct	1,291,360	HWA	1,275,036.29	16,323.71
2013 Nov	455,695	HWA	534,728.33	-79,033.33
2013 Dec	358,062	HWA	427,387.65	-69,325.65
2014 Jan	377,387	HWA	442,346.73	-64,959.73
2014 Feb	543,470	HWA	593,542.84	-50,072.84
2014 Mar	749,773	HWA	870,487.62	-120,714.62
2014 Apr	1,337,145	HWA	1,055,960.77	281,184.23
2014 May	1,538,342	HWA	1,393,823.18	144,518.82
2014 Jun	1,994,167	HWA	1,840,574.20	153,592.80
2014 Jul	2,529,246	HWA	2,439,011.26	90,234.74
2014 Aug	3,069,865	HWA	2,803,667.06	266,197.94
2014 Sep	2,089,656	HWA	2,028,101.45	61,554.55
2014 Oct	1,477,481	HWA	1,409,401.10	68,079.90
2014 Nov	502,473	HWA	623,374.23	-120,901.23
2014 Dec	382,543	HWA	501,576.70	-119,033.70
2015 Jan	381,607	HWA	506,244.51	-124,637.51
2015 Feb	544,777	HWA	652,381.69	-107,604.69
2015 Mar	827,071	HWA	874,665.14	-47,594.14
2015 Apr	1,242,844	HWA	1,329,587.11	-86,743.11
2015 May	1,654,526	HWA	1,521,836.80	132,689.20
2015 Jun	2,079,484	HWA	1,976,781.32	102,702.68
2015 Jul	2,688,710	HWA	2,526,629.25	162,080.75
2015 Aug	3,108,357	HWA	3,023,286.35	85,070.65
2015 Sep	2,196,681	HWA	2,079,077.09	117,603.91
2015 Oct	1,553,142	HWA	1,468,713.10	84,428.90
2015 Nov	552,778	HWA	559,014.44	-6,236.44
2015 Dec	426,419	HWA	455,820.27	-29,401.27
2016 Jan	443,150	HWA	469,312.94	-26,162.94
2016 Feb	664,278	HWA	642,245.11	22,032.89
2016 Mar	1,089,392	HWA	926,228.75	163,163.25
2016 Apr	1,335,308	HWA	1,397,015.86	-61,707.86
2016 May	1,828,292	HWA	1,748,891.67	79,400.33
2016 Jun	2,288,337	HWA	2,182,833.38	105,503.62
2016 Jul	2,848,570	HWA	2,781,833.77	66,736.23
2016 Aug	3,204,047	HWA	3,218,902.66	-14,855.66
2016 Sep	2,378,618	HWA	2,286,858.14	91,759.86
2016 Oct	1,793,822	HWA	1,656,036.23	137,785.77
2016 Nov	653,514	HWA	690,788.25	-37,274.25
2016 Dec	478,510	HWA	568,672.20	-90,162.20
2017 Jan	495,629	HWA	576,507.76	-80,878.76
2017 Feb	704,532	HWA	776,986.25	-72,454.25
2017 Mar	1,015,421	HWA	1,151,498.42	-136,077.42
2017 Apr	1,765,170	HWA	1,412,795.46	352,374.54
2017 May	1,970,072	HWA	1,932,079.55	37,992.45
2017 Jun	2,417,100	HWA	2,381,660.39	35,439.61
2017 Jul	2,968,641	HWA	2,946,123.23	22,517.77
2017 Aug	3,295,406	HWA	3,321,195.08	-25,789.08
2017 Sep	2,470,298	HWA	2,465,456.14	4,841.86
2017 Oct	1,911,961	HWA	1,857,383.50	54,577.50
2017 Nov	680,373	HWA	757,017.54	-76,644.54
2017 Dec	512,548	HWA	590,958.15	-78,410.15
2018 Jan	503,908	HWA	605,908.33	-102,000.33
2018 Feb	731,090	HWA	808,601.04	-77,511.04
2018 Mar	1,151,455	HWA	1,135,134.28	16,320.72
2018 Apr	1,575,078	HWA	1,776,530.24	-201,452.24
2018 May	2,003,996	HWA	1,986,792.97	17,203.03
2018 Jun	2,381,154	HWA	2,430,752.54	-49,598.54
2018 Jul	2,981,643	HWA	2,970,378.66	11,264.34
2018 Aug	3,371,918	HWA	3,307,671.45	64,246.55
2018 Sep	2,499,368	HWA	2,484,714.59	14,653.41
2018 Oct	1,956,693	HWA	1,911,239.38	45,453.62
2018 Nov	732,141	HWA	714,461.45	17,679.55
2018 Dec	554,803	HWA	557,693.34	-2,890.34
2019 Jan	548,686	HWA	564,270.74	-15,584.74
2019 Feb	739,981	HWA	794,492.56	-54,511.56
2019 Mar	1,078,918	HWA	1,190,478.20	-111,560.20
2019 Apr	1,795,494	HWA	1,655,904.38	139,589.62
2019 May	1,990,529	HWA	2,068,293.93	-77,764.93
2019 Jun	2,425,834	HWA	2,452,720.00	-26,886.00
2019 Jul	2,988,668	HWA	3,039,623.84	-50,955.84
2019 Aug	3,439,271	HWA	3,407,000.35	32,270.65
2019 Sep	2,573,527	HWA	2,544,604.22	28,922.78
2019 Oct	1,930,852	HWA	1,995,263.83	-64,411.83
2019 Nov	785,875	HWA	763,981.52	21,893.48
2019 Dec	602,860	HWA	592,408.44	10,451.56
2020 Jan	560,368	HWA	590,840.35	-30,472.35
2020 Feb	844,247	HWA	790,479.49	53,767.51
2020 Mar	513,360	HWA	1,158,387.07	-645,027.07
2020 Apr	25,614	HWA	1,738,457.39	-1,712,843.39
2020 May	40,932	HWA	1,506,570.38	-1,465,638.38
2020 Jun	330,393	HWA	935,006.65	-604,613.65
2020 Jul	1,035,732	HWA	912,362.50	123,369.50
2020 Aug	2,090,569	HWA	1,219,992.20	870,576.80
2020 Sep	1,418,185	HWA	663,411.50	754,773.50
2020 Oct	696,087	HWA	358,648.46	337,438.54
2020 Nov	181,873	HWA	-74,593.86	256,466.86
2020 Dec	153,351	HWA	60,722.25	92,628.75
2021 Jan	105,336	HWA	177,808.80	-72,472.80
2021 Feb	66,194	HWA	313,898.18	-247,704.18
2021 Mar	84,413	HWA	311,574.21	-227,161.21
2021 Apr	138,661	HWA	350,644.43	-211,983.43
2021 May	502,057	HWA	377,196.43	124,860.57
2021 Jun	1,182,009	HWA	860,635.09	321,373.91
2021 Jul	1,551,789	HWA	1,684,594.20	-132,805.20
2021 Aug	2,762,537	HWA	1,956,644.94	805,892.06
2021 Sep	1,869,194	HWA	2,013,861.06	-144,667.06
2021 Oct	1,584,764	HWA	1,317,893.71	266,870.29
2021 Nov	651,051	HWA	817,938.59	-166,887.59
2021 Dec	376,031	HWA	531,858.66	-155,827.66
2022 Jan	344,634	HWA	389,993.94	-45,359.94
2022 Feb	590,122	HWA	533,049.53	57,072.47
2022 Mar	873,841	HWA	817,437.35	56,403.65
2022 Apr	1,629,377	HWA	1,116,843.57	512,533.43
2022 May	1,867,744	HWA	1,863,539.41	4,204.59
2022 Jun	2,230,207	HWA	2,240,316.15	-10,109.15
2010 Jan	366,296	HWA_log	409,254.18	-42,958.18
2010 Feb	533,056	HWA_log	553,467.64	-20,411.64
2010 Mar	742,227	HWA_log	744,440.51	-2,213.51
2010 Apr	902,745	HWA_log	918,388.04	-15,643.04
2010 May	1,107,303	HWA_log	1,114,487.98	-7,184.98
2010 Jun	1,464,695	HWA_log	1,364,741.93	99,953.07
2010 Jul	2,050,478	HWA_log	1,704,575.68	345,902.32
2010 Aug	2,468,924	HWA_log	2,178,598.36	290,325.64
2010 Sep	1,696,356	HWA_log	1,537,054.29	159,301.71
2010 Oct	1,104,659	HWA_log	1,058,259.60	46,399.40
2010 Nov	445,221	HWA_log	515,911.85	-70,690.85
2010 Dec	365,490	HWA_log	395,194.85	-29,704.85
2011 Jan	357,209	HWA_log	396,645.83	-39,436.83
2011 Feb	503,831	HWA_log	551,417.69	-47,586.69
2011 Mar	761,343	HWA_log	744,988.88	16,354.12
2011 Apr	1,177,115	HWA_log	926,040.91	251,074.09
2011 May	1,169,516	HWA_log	1,180,603.03	-11,087.03
2011 Jun	1,576,730	HWA_log	1,494,072.17	82,657.83
2011 Jul	2,208,160	HWA_log	1,984,517.95	223,642.05
2011 Aug	2,572,404	HWA_log	2,467,081.90	105,322.10
2011 Sep	1,731,056	HWA_log	1,669,966.91	61,089.09
2011 Oct	1,161,751	HWA_log	1,102,347.26	59,403.74
2011 Nov	427,550	HWA_log	497,278.71	-69,728.71
2011 Dec	333,201	HWA_log	384,272.52	-51,071.52
2012 Jan	359,355	HWA_log	373,911.09	-14,556.09
2012 Feb	531,709	HWA_log	533,731.25	-2,022.25
2012 Mar	751,024	HWA_log	774,228.51	-23,204.51
2012 Apr	1,017,976	HWA_log	1,074,088.61	-56,112.61
2012 May	1,194,673	HWA_log	1,146,685.22	47,987.78
2012 Jun	1,678,327	HWA_log	1,524,159.41	154,167.59
2012 Jul	2,296,474	HWA_log	2,107,042.28	189,431.72
2012 Aug	2,622,801	HWA_log	2,505,072.92	117,728.08
2012 Sep	1,829,252	HWA_log	1,692,749.94	136,502.06
2012 Oct	1,244,751	HWA_log	1,130,896.01	113,854.99
2012 Nov	453,958	HWA_log	451,127.03	2,830.97
2012 Dec	346,474	HWA_log	359,563.42	-13,089.42
2013 Jan	369,969	HWA_log	377,432.97	-7,463.97
2013 Feb	520,055	HWA_log	547,806.38	-27,751.38
2013 Mar	840,024	HWA_log	779,457.35	60,566.65
2013 Apr	986,191	HWA_log	1,084,211.98	-98,020.98
2013 May	1,382,234	HWA_log	1,215,156.76	167,077.24
2013 Jun	1,814,108	HWA_log	1,682,702.34	131,405.66
2013 Jul	2,387,304	HWA_log	2,321,854.18	65,449.82
2013 Aug	2,764,686	HWA_log	2,665,597.32	99,088.68
2013 Sep	1,943,037	HWA_log	1,831,383.08	111,653.92
2013 Oct	1,291,360	HWA_log	1,237,577.21	53,782.79
2013 Nov	455,695	HWA_log	465,234.78	-9,539.78
2013 Dec	358,062	HWA_log	362,507.04	-4,445.04
2014 Jan	377,387	HWA_log	385,958.33	-8,571.33
2014 Feb	543,470	HWA_log	550,292.87	-6,822.87
2014 Mar	749,773	HWA_log	845,190.59	-95,417.59
2014 Apr	1,337,145	HWA_log	1,042,419.90	294,725.10
2014 May	1,538,342	HWA_log	1,397,943.57	140,398.43
2014 Jun	1,994,167	HWA_log	1,872,528.68	121,638.32
2014 Jul	2,529,246	HWA_log	2,519,108.66	10,137.34
2014 Aug	3,069,865	HWA_log	2,890,512.17	179,352.83
2014 Sep	2,089,656	HWA_log	2,035,489.48	54,166.52
2014 Oct	1,477,481	HWA_log	1,346,950.62	130,530.38
2014 Nov	502,473	HWA_log	494,881.94	7,591.06
2014 Dec	382,543	HWA_log	388,730.46	-6,187.46
2015 Jan	381,607	HWA_log	412,118.67	-30,511.67
2015 Feb	544,777	HWA_log	585,632.35	-40,855.35
2015 Mar	827,071	HWA_log	837,393.44	-10,322.44
2015 Apr	1,242,844	HWA_log	1,296,465.02	-53,621.02
2015 May	1,654,526	HWA_log	1,526,082.48	128,443.52
2015 Jun	2,079,484	HWA_log	1,999,616.19	79,867.81
2015 Jul	2,688,710	HWA_log	2,589,718.29	98,991.71
2015 Aug	3,108,357	HWA_log	3,091,842.53	16,514.47
2015 Sep	2,196,681	HWA_log	2,140,223.47	56,457.53
2015 Oct	1,553,142	HWA_log	1,454,846.41	98,295.59
2015 Nov	552,778	HWA_log	512,844.35	39,933.65
2015 Dec	426,419	HWA_log	398,145.95	28,273.05
2016 Jan	443,150	HWA_log	415,726.58	27,423.42
2016 Feb	664,278	HWA_log	609,624.45	54,653.55
2016 Mar	1,089,392	HWA_log	935,122.17	154,269.83
2016 Apr	1,335,308	HWA_log	1,500,300.60	-164,992.60
2016 May	1,828,292	HWA_log	1,843,051.19	-14,759.19
2016 Jun	2,288,337	HWA_log	2,345,264.76	-56,927.76
2016 Jul	2,848,570	HWA_log	2,995,750.57	-147,180.57
2016 Aug	3,204,047	HWA_log	3,469,485.27	-265,438.27
2016 Sep	2,378,618	HWA_log	2,349,615.35	29,002.65
2016 Oct	1,793,822	HWA_log	1,638,512.37	155,309.63
2016 Nov	653,514	HWA_log	585,573.44	67,940.56
2016 Dec	478,510	HWA_log	461,015.92	17,494.08
2017 Jan	495,629	HWA_log	479,706.79	15,922.21
2017 Feb	704,532	HWA_log	715,628.28	-11,096.28
2017 Mar	1,015,421	HWA_log	1,119,471.78	-104,050.78
2017 Apr	1,765,170	HWA_log	1,455,422.82	309,747.18
2017 May	1,970,072	HWA_log	2,031,056.15	-60,984.15
2017 Jun	2,417,100	HWA_log	2,548,451.93	-131,351.93
2017 Jul	2,968,641	HWA_log	3,213,100.83	-244,459.83
2017 Aug	3,295,406	HWA_log	3,629,920.96	-334,514.96
2017 Sep	2,470,298	HWA_log	2,607,466.67	-137,168.67
2017 Oct	1,911,961	HWA_log	1,868,389.14	43,571.86
2017 Nov	680,373	HWA_log	668,278.36	12,094.64
2017 Dec	512,548	HWA_log	498,064.35	14,483.65
2018 Jan	503,908	HWA_log	515,447.03	-11,539.03
2018 Feb	731,090	HWA_log	737,407.97	-6,317.97
2018 Mar	1,151,455	HWA_log	1,103,669.38	47,785.62
2018 Apr	1,575,078	HWA_log	1,727,952.19	-152,874.19
2018 May	2,003,996	HWA_log	2,026,719.33	-22,723.33
2018 Jun	2,381,154	HWA_log	2,512,866.95	-131,712.95
2018 Jul	2,981,643	HWA_log	3,108,944.54	-127,301.54
2018 Aug	3,371,918	HWA_log	3,502,873.62	-130,955.62
2018 Sep	2,499,368	HWA_log	2,591,898.67	-92,530.67
2018 Oct	1,956,693	HWA_log	1,944,154.51	12,538.49
2018 Nov	732,141	HWA_log	692,206.82	39,934.18
2018 Dec	554,803	HWA_log	520,979.52	33,823.48
2019 Jan	548,686	HWA_log	526,575.93	22,110.07
2019 Feb	739,981	HWA_log	767,865.56	-27,884.56
2019 Mar	1,078,918	HWA_log	1,177,478.71	-98,560.71
2019 Apr	1,795,494	HWA_log	1,666,710.73	128,783.27
2019 May	1,990,529	HWA_log	2,104,691.21	-114,162.21
2019 Jun	2,425,834	HWA_log	2,526,335.67	-100,501.67
2019 Jul	2,988,668	HWA_log	3,152,926.46	-164,258.46
2019 Aug	3,439,271	HWA_log	3,553,419.74	-114,148.74
2019 Sep	2,573,527	HWA_log	2,638,938.63	-65,411.63
2019 Oct	1,930,852	HWA_log	2,026,331.20	-95,479.20
2019 Nov	785,875	HWA_log	724,158.90	61,716.10
2019 Dec	602,860	HWA_log	554,838.87	48,021.13
2020 Jan	560,368	HWA_log	557,545.23	2,822.77
2020 Feb	844,247	HWA_log	770,880.45	73,366.55
2020 Mar	513,360	HWA_log	1,176,657.71	-663,297.71
2020 Apr	25,614	HWA_log	1,584,308.65	-1,558,694.65
2020 May	40,932	HWA_log	29,072.34	11,859.66
2020 Jun	330,393	HWA_log	40,603.15	289,789.85
2020 Jul	1,035,732	HWA_log	326,932.46	708,799.54
2020 Aug	2,090,569	HWA_log	1,153,940.60	936,628.40
2020 Sep	1,418,185	HWA_log	1,441,246.48	-23,061.48
2020 Oct	696,087	HWA_log	980,037.46	-283,950.46
2020 Nov	181,873	HWA_log	296,992.59	-115,119.59
2020 Dec	153,351	HWA_log	144,025.42	9,325.58
2021 Jan	105,336	HWA_log	172,849.69	-67,513.69
2021 Feb	66,194	HWA_log	158,685.74	-92,491.74
2021 Mar	84,413	HWA_log	95,108.27	-10,695.27
2021 Apr	138,661	HWA_log	90,313.37	48,347.63
2021 May	502,057	HWA_log	169,427.73	332,629.27
2021 Jun	1,182,009	HWA_log	692,821.40	489,187.60
2021 Jul	1,551,789	HWA_log	1,662,767.27	-110,978.27
2021 Aug	2,762,537	HWA_log	1,906,645.17	855,891.83
2021 Sep	1,869,194	HWA_log	2,094,418.40	-225,224.40
2021 Oct	1,584,764	HWA_log	1,330,042.34	254,721.66
2021 Nov	651,051	HWA_log	675,650.15	-24,599.15
2021 Dec	376,031	HWA_log	536,422.59	-160,391.59
2022 Jan	344,634	HWA_log	400,664.00	-56,030.00
2022 Feb	590,122	HWA_log	535,230.71	54,891.29
2022 Mar	873,841	HWA_log	880,293.11	-6,452.11
2022 Apr	1,629,377	HWA_log	1,046,572.04	582,804.96
2022 May	1,867,744	HWA_log	2,218,633.12	-350,889.12
2022 Jun	2,230,207	HWA_log	2,792,298.54	-562,091.54
2010 Jan	366,296	Naive	370,417.00	-4,121.00
2010 Feb	533,056	Naive	366,296.00	166,760.00
2010 Mar	742,227	Naive	533,056.00	209,171.00
2010 Apr	902,745	Naive	742,227.00	160,518.00
2010 May	1,107,303	Naive	902,745.00	204,558.00
2010 Jun	1,464,695	Naive	1,107,303.00	357,392.00
2010 Jul	2,050,478	Naive	1,464,695.00	585,783.00
2010 Aug	2,468,924	Naive	2,050,478.00	418,446.00
2010 Sep	1,696,356	Naive	2,468,924.00	-772,568.00
2010 Oct	1,104,659	Naive	1,696,356.00	-591,697.00
2010 Nov	445,221	Naive	1,104,659.00	-659,438.00
2010 Dec	365,490	Naive	445,221.00	-79,731.00
2011 Jan	357,209	Naive	365,490.00	-8,281.00
2011 Feb	503,831	Naive	357,209.00	146,622.00
2011 Mar	761,343	Naive	503,831.00	257,512.00
2011 Apr	1,177,115	Naive	761,343.00	415,772.00
2011 May	1,169,516	Naive	1,177,115.00	-7,599.00
2011 Jun	1,576,730	Naive	1,169,516.00	407,214.00
2011 Jul	2,208,160	Naive	1,576,730.00	631,430.00
2011 Aug	2,572,404	Naive	2,208,160.00	364,244.00
2011 Sep	1,731,056	Naive	2,572,404.00	-841,348.00
2011 Oct	1,161,751	Naive	1,731,056.00	-569,305.00
2011 Nov	427,550	Naive	1,161,751.00	-734,201.00
2011 Dec	333,201	Naive	427,550.00	-94,349.00
2012 Jan	359,355	Naive	333,201.00	26,154.00
2012 Feb	531,709	Naive	359,355.00	172,354.00
2012 Mar	751,024	Naive	531,709.00	219,315.00
2012 Apr	1,017,976	Naive	751,024.00	266,952.00
2012 May	1,194,673	Naive	1,017,976.00	176,697.00
2012 Jun	1,678,327	Naive	1,194,673.00	483,654.00
2012 Jul	2,296,474	Naive	1,678,327.00	618,147.00
2012 Aug	2,622,801	Naive	2,296,474.00	326,327.00
2012 Sep	1,829,252	Naive	2,622,801.00	-793,549.00
2012 Oct	1,244,751	Naive	1,829,252.00	-584,501.00
2012 Nov	453,958	Naive	1,244,751.00	-790,793.00
2012 Dec	346,474	Naive	453,958.00	-107,484.00
2013 Jan	369,969	Naive	346,474.00	23,495.00
2013 Feb	520,055	Naive	369,969.00	150,086.00
2013 Mar	840,024	Naive	520,055.00	319,969.00
2013 Apr	986,191	Naive	840,024.00	146,167.00
2013 May	1,382,234	Naive	986,191.00	396,043.00
2013 Jun	1,814,108	Naive	1,382,234.00	431,874.00
2013 Jul	2,387,304	Naive	1,814,108.00	573,196.00
2013 Aug	2,764,686	Naive	2,387,304.00	377,382.00
2013 Sep	1,943,037	Naive	2,764,686.00	-821,649.00
2013 Oct	1,291,360	Naive	1,943,037.00	-651,677.00
2013 Nov	455,695	Naive	1,291,360.00	-835,665.00
2013 Dec	358,062	Naive	455,695.00	-97,633.00
2014 Jan	377,387	Naive	358,062.00	19,325.00
2014 Feb	543,470	Naive	377,387.00	166,083.00
2014 Mar	749,773	Naive	543,470.00	206,303.00
2014 Apr	1,337,145	Naive	749,773.00	587,372.00
2014 May	1,538,342	Naive	1,337,145.00	201,197.00
2014 Jun	1,994,167	Naive	1,538,342.00	455,825.00
2014 Jul	2,529,246	Naive	1,994,167.00	535,079.00
2014 Aug	3,069,865	Naive	2,529,246.00	540,619.00
2014 Sep	2,089,656	Naive	3,069,865.00	-980,209.00
2014 Oct	1,477,481	Naive	2,089,656.00	-612,175.00
2014 Nov	502,473	Naive	1,477,481.00	-975,008.00
2014 Dec	382,543	Naive	502,473.00	-119,930.00
2015 Jan	381,607	Naive	382,543.00	-936.00
2015 Feb	544,777	Naive	381,607.00	163,170.00
2015 Mar	827,071	Naive	544,777.00	282,294.00
2015 Apr	1,242,844	Naive	827,071.00	415,773.00
2015 May	1,654,526	Naive	1,242,844.00	411,682.00
2015 Jun	2,079,484	Naive	1,654,526.00	424,958.00
2015 Jul	2,688,710	Naive	2,079,484.00	609,226.00
2015 Aug	3,108,357	Naive	2,688,710.00	419,647.00
2015 Sep	2,196,681	Naive	3,108,357.00	-911,676.00
2015 Oct	1,553,142	Naive	2,196,681.00	-643,539.00
2015 Nov	552,778	Naive	1,553,142.00	-1,000,364.00
2015 Dec	426,419	Naive	552,778.00	-126,359.00
2016 Jan	443,150	Naive	426,419.00	16,731.00
2016 Feb	664,278	Naive	443,150.00	221,128.00
2016 Mar	1,089,392	Naive	664,278.00	425,114.00
2016 Apr	1,335,308	Naive	1,089,392.00	245,916.00
2016 May	1,828,292	Naive	1,335,308.00	492,984.00
2016 Jun	2,288,337	Naive	1,828,292.00	460,045.00
2016 Jul	2,848,570	Naive	2,288,337.00	560,233.00
2016 Aug	3,204,047	Naive	2,848,570.00	355,477.00
2016 Sep	2,378,618	Naive	3,204,047.00	-825,429.00
2016 Oct	1,793,822	Naive	2,378,618.00	-584,796.00
2016 Nov	653,514	Naive	1,793,822.00	-1,140,308.00
2016 Dec	478,510	Naive	653,514.00	-175,004.00
2017 Jan	495,629	Naive	478,510.00	17,119.00
2017 Feb	704,532	Naive	495,629.00	208,903.00
2017 Mar	1,015,421	Naive	704,532.00	310,889.00
2017 Apr	1,765,170	Naive	1,015,421.00	749,749.00
2017 May	1,970,072	Naive	1,765,170.00	204,902.00
2017 Jun	2,417,100	Naive	1,970,072.00	447,028.00
2017 Jul	2,968,641	Naive	2,417,100.00	551,541.00
2017 Aug	3,295,406	Naive	2,968,641.00	326,765.00
2017 Sep	2,470,298	Naive	3,295,406.00	-825,108.00
2017 Oct	1,911,961	Naive	2,470,298.00	-558,337.00
2017 Nov	680,373	Naive	1,911,961.00	-1,231,588.00
2017 Dec	512,548	Naive	680,373.00	-167,825.00
2018 Jan	503,908	Naive	512,548.00	-8,640.00
2018 Feb	731,090	Naive	503,908.00	227,182.00
2018 Mar	1,151,455	Naive	731,090.00	420,365.00
2018 Apr	1,575,078	Naive	1,151,455.00	423,623.00
2018 May	2,003,996	Naive	1,575,078.00	428,918.00
2018 Jun	2,381,154	Naive	2,003,996.00	377,158.00
2018 Jul	2,981,643	Naive	2,381,154.00	600,489.00
2018 Aug	3,371,918	Naive	2,981,643.00	390,275.00
2018 Sep	2,499,368	Naive	3,371,918.00	-872,550.00
2018 Oct	1,956,693	Naive	2,499,368.00	-542,675.00
2018 Nov	732,141	Naive	1,956,693.00	-1,224,552.00
2018 Dec	554,803	Naive	732,141.00	-177,338.00
2019 Jan	548,686	Naive	554,803.00	-6,117.00
2019 Feb	739,981	Naive	548,686.00	191,295.00
2019 Mar	1,078,918	Naive	739,981.00	338,937.00
2019 Apr	1,795,494	Naive	1,078,918.00	716,576.00
2019 May	1,990,529	Naive	1,795,494.00	195,035.00
2019 Jun	2,425,834	Naive	1,990,529.00	435,305.00
2019 Jul	2,988,668	Naive	2,425,834.00	562,834.00
2019 Aug	3,439,271	Naive	2,988,668.00	450,603.00
2019 Sep	2,573,527	Naive	3,439,271.00	-865,744.00
2019 Oct	1,930,852	Naive	2,573,527.00	-642,675.00
2019 Nov	785,875	Naive	1,930,852.00	-1,144,977.00
2019 Dec	602,860	Naive	785,875.00	-183,015.00
2020 Jan	560,368	Naive	602,860.00	-42,492.00
2020 Feb	844,247	Naive	560,368.00	283,879.00
2020 Mar	513,360	Naive	844,247.00	-330,887.00
2020 Apr	25,614	Naive	513,360.00	-487,746.00
2020 May	40,932	Naive	25,614.00	15,318.00
2020 Jun	330,393	Naive	40,932.00	289,461.00
2020 Jul	1,035,732	Naive	330,393.00	705,339.00
2020 Aug	2,090,569	Naive	1,035,732.00	1,054,837.00
2020 Sep	1,418,185	Naive	2,090,569.00	-672,384.00
2020 Oct	696,087	Naive	1,418,185.00	-722,098.00
2020 Nov	181,873	Naive	696,087.00	-514,214.00
2020 Dec	153,351	Naive	181,873.00	-28,522.00
2021 Jan	105,336	Naive	153,351.00	-48,015.00
2021 Feb	66,194	Naive	105,336.00	-39,142.00
2021 Mar	84,413	Naive	66,194.00	18,219.00
2021 Apr	138,661	Naive	84,413.00	54,248.00
2021 May	502,057	Naive	138,661.00	363,396.00
2021 Jun	1,182,009	Naive	502,057.00	679,952.00
2021 Jul	1,551,789	Naive	1,182,009.00	369,780.00
2021 Aug	2,762,537	Naive	1,551,789.00	1,210,748.00
2021 Sep	1,869,194	Naive	2,762,537.00	-893,343.00
2021 Oct	1,584,764	Naive	1,869,194.00	-284,430.00
2021 Nov	651,051	Naive	1,584,764.00	-933,713.00
2021 Dec	376,031	Naive	651,051.00	-275,020.00
2022 Jan	344,634	Naive	376,031.00	-31,397.00
2022 Feb	590,122	Naive	344,634.00	245,488.00
2022 Mar	873,841	Naive	590,122.00	283,719.00
2022 Apr	1,629,377	Naive	873,841.00	755,536.00
2022 May	1,867,744	Naive	1,629,377.00	238,367.00
2022 Jun	2,230,207	Naive	1,867,744.00	362,463.00
2010 Jan	366,296	Naive_log	390,892.35	-24,596.35
2010 Feb	533,056	Naive_log	386,375.02	146,680.98
2010 Mar	742,227	Naive_log	562,344.77	179,882.23
2010 Apr	902,745	Naive_log	783,007.73	119,737.27
2010 May	1,107,303	Naive_log	952,082.60	155,220.40
2010 Jun	1,464,695	Naive_log	1,167,518.49	297,176.51
2010 Jul	2,050,478	Naive_log	1,544,166.79	506,311.21
2010 Aug	2,468,924	Naive_log	2,161,771.31	307,152.69
2010 Sep	1,696,356	Naive_log	2,602,209.28	-905,853.28
2010 Oct	1,104,659	Naive_log	1,788,151.94	-683,492.94
2010 Nov	445,221	Naive_log	1,164,760.49	-719,539.49
2010 Dec	365,490	Naive_log	470,671.98	-105,181.98
2011 Jan	357,209	Naive_log	386,278.00	-29,069.00
2011 Feb	503,831	Naive_log	377,372.79	126,458.21
2011 Mar	761,343	Naive_log	532,281.54	229,061.46
2011 Apr	1,177,115	Naive_log	804,498.18	372,616.82
2011 May	1,169,516	Naive_log	1,244,170.90	-74,654.90
2011 Jun	1,576,730	Naive_log	1,235,649.32	341,080.68
2011 Jul	2,208,160	Naive_log	1,665,753.13	542,406.87
2011 Aug	2,572,404	Naive_log	2,332,838.19	239,565.81
2011 Sep	1,731,056	Naive_log	2,716,819.09	-985,763.09
2011 Oct	1,161,751	Naive_log	1,828,513.58	-666,762.58
2011 Nov	427,550	Naive_log	1,227,348.33	-799,798.33
2011 Dec	333,201	Naive_log	453,025.55	-119,824.55
2012 Jan	359,355	Naive_log	352,988.35	6,366.65
2012 Feb	531,709	Naive_log	380,554.45	151,154.55
2012 Mar	751,024	Naive_log	563,141.25	187,882.75
2012 Apr	1,017,976	Naive_log	795,423.81	222,552.19
2012 May	1,194,673	Naive_log	1,078,068.63	116,604.37
2012 Jun	1,678,327	Naive_log	1,264,823.20	413,503.80
2012 Jul	2,296,474	Naive_log	1,776,866.32	519,607.68
2012 Aug	2,622,801	Naive_log	2,431,160.30	191,640.70
2012 Sep	1,829,252	Naive_log	2,775,760.72	-946,508.72
2012 Oct	1,244,751	Naive_log	1,936,012.01	-691,261.01
2012 Nov	453,958	Naive_log	1,317,526.02	-863,568.02
2012 Dec	346,474	Naive_log	481,826.16	-135,352.16
2013 Jan	369,969	Naive_log	367,688.16	2,280.84
2013 Feb	520,055	Naive_log	392,481.63	127,573.37
2013 Mar	840,024	Naive_log	551,690.84	288,333.16
2013 Apr	986,191	Naive_log	891,411.88	94,779.12
2013 May	1,382,234	Naive_log	1,046,220.92	336,013.08
2013 Jun	1,814,108	Naive_log	1,466,337.71	347,770.29
2013 Jul	2,387,304	Naive_log	1,924,220.50	463,083.50
2013 Aug	2,764,686	Naive_log	2,531,869.29	232,816.71
2013 Sep	1,943,037	Naive_log	2,931,259.55	-988,222.55
2013 Oct	1,291,360	Naive_log	2,060,128.81	-768,768.81
2013 Nov	455,695	Naive_log	1,369,361.83	-913,666.83
2013 Dec	358,062	Naive_log	484,543.69	-126,481.69
2014 Jan	377,387	Naive_log	380,656.43	-3,269.43
2014 Feb	543,470	Naive_log	401,062.23	142,407.77
2014 Mar	749,773	Naive_log	577,576.50	172,196.50
2014 Apr	1,337,145	Naive_log	796,778.01	540,366.99
2014 May	1,538,342	Naive_log	1,421,792.06	116,549.94
2014 Jun	1,994,167	Naive_log	1,635,247.37	358,919.63
2014 Jul	2,529,246	Naive_log	2,119,448.39	409,797.61
2014 Aug	3,069,865	Naive_log	2,687,640.58	382,224.42
2014 Sep	2,089,656	Naive_log	3,261,346.51	-1,171,690.51
2014 Oct	1,477,481	Naive_log	2,220,135.09	-742,654.09
2014 Nov	502,473	Naive_log	1,569,715.95	-1,067,242.95
2014 Dec	382,543	Naive_log	535,306.63	-152,763.63
2015 Jan	381,607	Naive_log	407,479.74	-25,872.74
2015 Feb	544,777	Naive_log	406,344.53	138,432.47
2015 Mar	827,071	Naive_log	580,087.56	246,983.44
2015 Apr	1,242,844	Naive_log	880,780.41	362,063.59
2015 May	1,654,526	Naive_log	1,323,675.63	330,850.37
2015 Jun	2,079,484	Naive_log	1,761,915.68	317,568.32
2015 Jul	2,688,710	Naive_log	2,214,020.40	474,689.60
2015 Aug	3,108,357	Naive_log	2,862,203.44	246,153.56
2015 Sep	2,196,681	Naive_log	3,308,031.10	-1,111,350.10
2015 Oct	1,553,142	Naive_log	2,337,744.48	-784,602.48
2015 Nov	552,778	Naive_log	1,652,845.65	-1,100,067.65
2015 Dec	426,419	Naive_log	589,629.22	-163,210.22
2016 Jan	443,150	Naive_log	454,772.79	-11,622.79
2016 Feb	664,278	Naive_log	472,464.52	191,813.48
2016 Mar	1,089,392	Naive_log	708,274.52	381,117.48
2016 Apr	1,335,308	Naive_log	1,161,859.83	173,448.17
2016 May	1,828,292	Naive_log	1,423,820.83	404,471.17
2016 Jun	2,288,337	Naive_log	1,949,325.17	339,011.83
2016 Jul	2,848,570	Naive_log	2,439,348.80	409,221.20
2016 Aug	3,204,047	Naive_log	3,035,948.23	168,098.77
2016 Sep	2,378,618	Naive_log	3,413,860.65	-1,035,242.65
2016 Oct	1,793,822	Naive_log	2,534,128.20	-740,306.20
2016 Nov	653,514	Naive_log	1,910,871.00	-1,257,357.00
2016 Dec	478,510	Naive_log	697,594.73	-219,084.73
2017 Jan	495,629	Naive_log	510,741.89	-15,112.89
2017 Feb	704,532	Naive_log	528,851.85	175,680.15
2017 Mar	1,015,421	Naive_log	751,740.16	263,680.84
2017 Apr	1,765,170	Naive_log	1,083,459.72	681,710.28
2017 May	1,970,072	Naive_log	1,884,178.21	85,893.79
2017 Jun	2,417,100	Naive_log	2,102,313.30	314,786.70
2017 Jul	2,968,641	Naive_log	2,578,813.62	389,827.38
2017 Aug	3,295,406	Naive_log	3,166,607.73	128,798.27
2017 Sep	2,470,298	Naive_log	3,514,207.02	-1,043,909.02
2017 Oct	1,911,961	Naive_log	2,634,025.56	-722,064.56
2017 Nov	680,373	Naive_log	2,038,382.52	-1,358,009.52
2017 Dec	512,548	Naive_log	726,847.09	-214,299.09
2018 Jan	503,908	Naive_log	547,491.30	-43,583.30
2018 Feb	731,090	Naive_log	538,103.55	192,986.45
2018 Mar	1,151,455	Naive_log	780,706.94	370,748.06
2018 Apr	1,575,078	Naive_log	1,229,787.35	345,290.65
2018 May	2,003,996	Naive_log	1,682,092.66	321,903.34
2018 Jun	2,381,154	Naive_log	2,139,797.69	241,356.31
2018 Jul	2,981,643	Naive_log	2,541,944.03	439,698.97
2018 Aug	3,371,918	Naive_log	3,182,414.41	189,503.59
2018 Sep	2,499,368	Naive_log	3,598,065.13	-1,098,697.13
2018 Oct	1,956,693	Naive_log	2,666,747.03	-710,054.03
2018 Nov	732,141	Naive_log	2,087,408.03	-1,355,267.03
2018 Dec	554,803	Naive_log	782,399.87	-227,596.87
2019 Jan	548,686	Naive_log	592,814.48	-44,128.48
2019 Feb	739,981	Naive_log	586,113.65	153,867.35
2019 Mar	1,078,918	Naive_log	790,381.62	288,536.38
2019 Apr	1,795,494	Naive_log	1,152,417.87	643,076.13
2019 May	1,990,529	Naive_log	1,918,288.32	72,240.68
2019 Jun	2,425,834	Naive_log	2,126,120.65	299,713.35
2019 Jul	2,988,668	Naive_log	2,590,572.35	398,095.65
2019 Aug	3,439,271	Naive_log	3,191,039.07	248,231.93
2019 Sep	2,573,527	Naive_log	3,671,306.98	-1,097,779.98
2019 Oct	1,930,852	Naive_log	2,746,876.94	-816,024.94
2019 Nov	785,875	Naive_log	2,060,699.56	-1,274,824.56
2019 Dec	602,860	Naive_log	839,836.22	-236,976.22
2020 Jan	560,368	Naive_log	644,170.15	-83,802.15
2020 Feb	844,247	Naive_log	598,612.69	245,634.31
2020 Mar	513,360	Naive_log	901,921.35	-388,561.35
2020 Apr	25,614	Naive_log	548,547.52	-522,933.52
2020 May	40,932	Naive_log	27,836.10	13,095.90
2020 Jun	330,393	Naive_log	44,486.87	285,906.13
2020 Jul	1,035,732	Naive_log	361,910.58	673,821.42
2020 Aug	2,090,569	Naive_log	1,136,881.44	953,687.56
2020 Sep	1,418,185	Naive_log	2,295,994.55	-877,809.55
2020 Oct	696,087	Naive_log	1,557,408.75	-861,321.75
2020 Nov	181,873	Naive_log	764,855.59	-582,982.59
2020 Dec	153,351	Naive_log	200,424.18	-47,073.18
2021 Jan	105,336	Naive_log	168,939.49	-63,603.49
2021 Feb	66,194	Naive_log	116,030.64	-49,836.64
2021 Mar	84,413	Naive_log	72,916.27	11,496.73
2021 Apr	138,661	Naive_log	92,961.55	45,699.45
2021 May	502,057	Naive_log	152,715.19	349,341.81
2021 Jun	1,182,009	Naive_log	554,368.33	627,640.67
2021 Jul	1,551,789	Naive_log	1,306,374.07	245,414.93
2021 Aug	2,762,537	Naive_log	1,714,650.45	1,047,886.55
2021 Sep	1,869,194	Naive_log	3,053,121.91	-1,183,927.91
2021 Oct	1,584,764	Naive_log	2,065,602.54	-480,838.54
2021 Nov	651,051	Naive_log	1,750,730.32	-1,099,679.32
2021 Dec	376,031	Naive_log	719,956.14	-343,925.14
2022 Jan	344,634	Naive_log	415,892.99	-71,258.99
2022 Feb	590,122	Naive_log	381,034.26	209,087.74
2022 Mar	873,841	Naive_log	652,537.60	221,303.40
2022 Apr	1,629,377	Naive_log	966,170.47	663,206.53
2022 May	1,867,744	Naive_log	1,802,075.61	65,668.39
2022 Jun	2,230,207	Naive_log	2,065,033.55	165,173.45
2010 Jan	366,296	Prophet	375,701.90	-9,405.90
2010 Feb	533,056	Prophet	575,081.38	-42,025.38
2010 Mar	742,227	Prophet	784,087.47	-41,860.47
2010 Apr	902,745	Prophet	967,453.86	-64,708.86
2010 May	1,107,303	Prophet	1,154,987.16	-47,684.16
2010 Jun	1,464,695	Prophet	1,439,964.95	24,730.05
2010 Jul	2,050,478	Prophet	1,845,706.59	204,771.41
2010 Aug	2,468,924	Prophet	2,204,685.25	264,238.75
2010 Sep	1,696,356	Prophet	1,544,396.50	151,959.50
2010 Oct	1,104,659	Prophet	1,057,028.24	47,630.76
2010 Nov	445,221	Prophet	475,192.93	-29,971.93
2010 Dec	365,490	Prophet	356,952.04	8,537.96
2011 Jan	357,209	Prophet	378,326.17	-21,117.17
2011 Feb	503,831	Prophet	569,266.30	-65,435.30
2011 Mar	761,343	Prophet	769,143.55	-7,800.55
2011 Apr	1,177,115	Prophet	963,873.12	213,241.88
2011 May	1,169,516	Prophet	1,143,777.79	25,738.21
2011 Jun	1,576,730	Prophet	1,475,411.98	101,318.02
2011 Jul	2,208,160	Prophet	1,917,512.67	290,647.33
2011 Aug	2,572,404	Prophet	2,289,875.71	282,528.29
2011 Sep	1,731,056	Prophet	1,581,077.36	149,978.64
2011 Oct	1,161,751	Prophet	1,062,736.52	99,014.48
2011 Nov	427,550	Prophet	505,344.00	-77,794.00
2011 Dec	333,201	Prophet	411,735.12	-78,534.12
2012 Jan	359,355	Prophet	438,277.09	-78,922.09
2012 Feb	531,709	Prophet	616,043.38	-84,334.38
2012 Mar	751,024	Prophet	845,508.19	-94,484.19
2012 Apr	1,017,976	Prophet	1,008,885.82	9,090.18
2012 May	1,194,673	Prophet	1,263,386.14	-68,713.14
2012 Jun	1,678,327	Prophet	1,529,010.23	149,316.77
2012 Jul	2,296,474	Prophet	1,912,110.70	384,363.30
2012 Aug	2,622,801	Prophet	2,269,068.89	353,732.11
2012 Sep	1,829,252	Prophet	1,658,356.26	170,895.74
2012 Oct	1,244,751	Prophet	1,180,195.42	64,555.58
2012 Nov	453,958	Prophet	566,585.53	-112,627.53
2012 Dec	346,474	Prophet	426,508.11	-80,034.11
2013 Jan	369,969	Prophet	455,798.96	-85,829.96
2013 Feb	520,055	Prophet	646,463.13	-126,408.13
2013 Mar	840,024	Prophet	867,920.68	-27,896.68
2013 Apr	986,191	Prophet	1,063,534.90	-77,343.90
2013 May	1,382,234	Prophet	1,262,351.18	119,882.82
2013 Jun	1,814,108	Prophet	1,574,727.15	239,380.85
2013 Jul	2,387,304	Prophet	2,035,884.24	351,419.76
2013 Aug	2,764,686	Prophet	2,403,361.53	361,324.47
2013 Sep	1,943,037	Prophet	1,759,212.83	183,824.17
2013 Oct	1,291,360	Prophet	1,254,566.76	36,793.24
2013 Nov	455,695	Prophet	629,760.14	-174,065.14
2013 Dec	358,062	Prophet	495,337.86	-137,275.86
2014 Jan	377,387	Prophet	523,259.99	-145,872.99
2014 Feb	543,470	Prophet	696,777.84	-153,307.84
2014 Mar	749,773	Prophet	918,047.94	-168,274.94
2014 Apr	1,337,145	Prophet	1,115,295.37	221,849.63
2014 May	1,538,342	Prophet	1,321,755.67	216,586.33
2014 Jun	1,994,167	Prophet	1,667,658.17	326,508.83
2014 Jul	2,529,246	Prophet	2,157,025.22	372,220.78
2014 Aug	3,069,865	Prophet	2,540,617.73	529,247.27
2014 Sep	2,089,656	Prophet	1,861,275.67	228,380.33
2014 Oct	1,477,481	Prophet	1,351,700.47	125,780.53
2014 Nov	502,473	Prophet	738,565.05	-236,092.05
2014 Dec	382,543	Prophet	621,898.67	-239,355.67
2015 Jan	381,607	Prophet	640,520.32	-258,913.32
2015 Feb	544,777	Prophet	805,282.87	-260,505.87
2015 Mar	827,071	Prophet	987,585.27	-160,514.27
2015 Apr	1,242,844	Prophet	1,244,484.08	-1,640.08
2015 May	1,654,526	Prophet	1,413,216.29	241,309.71
2015 Jun	2,079,484	Prophet	1,768,766.76	310,717.24
2015 Jul	2,688,710	Prophet	2,273,681.09	415,028.91
2015 Aug	3,108,357	Prophet	2,685,725.78	422,631.22
2015 Sep	2,196,681	Prophet	1,946,926.01	249,754.99
2015 Oct	1,553,142	Prophet	1,426,870.96	126,271.04
2015 Nov	552,778	Prophet	804,234.88	-251,456.88
2015 Dec	426,419	Prophet	707,287.08	-280,868.08
2016 Jan	443,150	Prophet	727,809.15	-284,659.15
2016 Feb	664,278	Prophet	902,522.38	-238,244.38
2016 Mar	1,089,392	Prophet	1,124,951.27	-35,559.27
2016 Apr	1,335,308	Prophet	1,326,844.94	8,463.06
2016 May	1,828,292	Prophet	1,591,506.84	236,785.16
2016 Jun	2,288,337	Prophet	1,920,422.58	367,914.42
2016 Jul	2,848,570	Prophet	2,378,647.88	469,922.12
2016 Aug	3,204,047	Prophet	2,740,521.74	463,525.26
2016 Sep	2,378,618	Prophet	2,091,494.52	287,123.48
2016 Oct	1,793,822	Prophet	1,582,335.36	211,486.64
2016 Nov	653,514	Prophet	925,439.24	-271,925.24
2016 Dec	478,510	Prophet	794,516.26	-316,006.26
2017 Jan	495,629	Prophet	805,602.87	-309,973.87
2017 Feb	704,532	Prophet	977,550.08	-273,018.08
2017 Mar	1,015,421	Prophet	1,228,069.78	-212,648.78
2017 Apr	1,765,170	Prophet	1,442,692.21	322,477.79
2017 May	1,970,072	Prophet	1,710,675.93	259,396.07
2017 Jun	2,417,100	Prophet	2,064,544.83	352,555.17
2017 Jul	2,968,641	Prophet	2,562,440.17	406,200.83
2017 Aug	3,295,406	Prophet	2,945,355.96	350,050.04
2017 Sep	2,470,298	Prophet	2,237,408.08	232,889.92
2017 Oct	1,911,961	Prophet	1,724,187.89	187,773.11
2017 Nov	680,373	Prophet	1,029,328.76	-348,955.76
2017 Dec	512,548	Prophet	879,499.96	-366,951.96
2018 Jan	503,908	Prophet	899,912.63	-396,004.63
2018 Feb	731,090	Prophet	1,069,427.18	-338,337.18
2018 Mar	1,151,455	Prophet	1,303,696.13	-152,241.13
2018 Apr	1,575,078	Prophet	1,582,076.40	-6,998.40
2018 May	2,003,996	Prophet	1,802,269.95	201,726.05
2018 Jun	2,381,154	Prophet	2,170,361.62	210,792.38
2018 Jul	2,981,643	Prophet	2,675,334.08	306,308.92
2018 Aug	3,371,918	Prophet	3,065,312.04	306,605.96
2018 Sep	2,499,368	Prophet	2,320,824.32	178,543.68
2018 Oct	1,956,693	Prophet	1,787,796.35	168,896.65
2018 Nov	732,141	Prophet	1,070,843.48	-338,702.48
2018 Dec	554,803	Prophet	949,098.85	-394,295.85
2019 Jan	548,686	Prophet	959,800.63	-411,114.63
2019 Feb	739,981	Prophet	1,140,078.59	-400,097.59
2019 Mar	1,078,918	Prophet	1,352,699.23	-273,781.23
2019 Apr	1,795,494	Prophet	1,657,389.56	138,104.44
2019 May	1,990,529	Prophet	1,871,527.35	119,001.65
2019 Jun	2,425,834	Prophet	2,238,962.84	186,871.16
2019 Jul	2,988,668	Prophet	2,761,206.96	227,461.04
2019 Aug	3,439,271	Prophet	3,168,070.24	271,200.76
2019 Sep	2,573,527	Prophet	2,377,113.51	196,413.49
2019 Oct	1,930,852	Prophet	1,827,094.21	103,757.79
2019 Nov	785,875	Prophet	1,095,650.82	-309,775.82
2019 Dec	602,860	Prophet	995,013.40	-392,153.40
2020 Jan	560,368	Prophet	1,010,011.04	-449,643.04
2020 Feb	844,247	Prophet	1,188,991.41	-344,744.41
2020 Mar	513,360	Prophet	1,452,135.88	-938,775.88
2020 Apr	25,614	Prophet	1,690,850.07	-1,665,236.07
2020 May	40,932	Prophet	1,948,403.52	-1,907,471.52
2020 Jun	330,393	Prophet	2,216,239.56	-1,885,846.56
2020 Jul	1,035,732	Prophet	2,620,390.23	-1,584,658.23
2020 Aug	2,090,569	Prophet	2,932,690.54	-842,121.54
2020 Sep	1,418,185	Prophet	2,170,152.77	-751,967.77
2020 Oct	696,087	Prophet	1,577,278.38	-881,191.38
2020 Nov	181,873	Prophet	761,908.64	-580,035.64
2020 Dec	153,351	Prophet	584,784.98	-431,433.98
2021 Jan	105,336	Prophet	576,245.09	-470,909.09
2021 Feb	66,194	Prophet	741,816.67	-675,622.67
2021 Mar	84,413	Prophet	928,736.46	-844,323.46
2021 Apr	138,661	Prophet	1,075,730.57	-937,069.57
2021 May	502,057	Prophet	1,265,427.72	-763,370.72
2021 Jun	1,182,009	Prophet	1,548,857.82	-366,848.82
2021 Jul	1,551,789	Prophet	2,046,537.90	-494,748.90
2021 Aug	2,762,537	Prophet	2,375,388.88	387,148.12
2021 Sep	1,869,194	Prophet	1,636,862.50	232,331.50
2021 Oct	1,584,764	Prophet	1,078,510.69	506,253.31
2021 Nov	651,051	Prophet	281,630.17	369,420.83
2021 Dec	376,031	Prophet	215,299.00	160,732.00
2022 Jan	344,634	Prophet	231,656.05	112,977.95
2022 Feb	590,122	Prophet	403,439.96	186,682.04
2022 Mar	873,841	Prophet	629,125.43	244,715.57
2022 Apr	1,629,377	Prophet	904,837.96	724,539.04
2022 May	1,867,744	Prophet	1,162,574.03	705,169.97
2022 Jun	2,230,207	Prophet	1,581,536.24	648,670.76
2010 Jan	366,296	Prophet_log	405,936.43	-39,640.43
2010 Feb	533,056	Prophet_log	565,058.23	-32,002.23
2010 Mar	742,227	Prophet_log	740,296.26	1,930.74
2010 Apr	902,745	Prophet_log	895,623.67	7,121.33
2010 May	1,107,303	Prophet_log	1,054,878.16	52,424.84
2010 Jun	1,464,695	Prophet_log	1,301,131.99	163,563.01
2010 Jul	2,050,478	Prophet_log	1,650,128.08	400,349.92
2010 Aug	2,468,924	Prophet_log	1,971,994.90	496,929.10
2010 Sep	1,696,356	Prophet_log	1,422,228.31	274,127.69
2010 Oct	1,104,659	Prophet_log	994,683.39	109,975.61
2010 Nov	445,221	Prophet_log	487,513.76	-42,292.76
2010 Dec	365,490	Prophet_log	375,206.61	-9,716.61
2011 Jan	357,209	Prophet_log	402,394.59	-45,185.59
2011 Feb	503,831	Prophet_log	561,192.71	-57,361.71
2011 Mar	761,343	Prophet_log	728,427.20	32,915.80
2011 Apr	1,177,115	Prophet_log	906,124.87	270,990.13
2011 May	1,169,516	Prophet_log	1,078,387.11	91,128.89
2011 Jun	1,576,730	Prophet_log	1,376,437.10	200,292.90
2011 Jul	2,208,160	Prophet_log	1,795,030.35	413,129.65
2011 Aug	2,572,404	Prophet_log	2,179,119.15	393,284.85
2011 Sep	1,731,056	Prophet_log	1,561,426.34	169,629.66
2011 Oct	1,161,751	Prophet_log	1,072,728.42	89,022.58
2011 Nov	427,550	Prophet_log	523,215.42	-95,665.42
2011 Dec	333,201	Prophet_log	413,723.38	-80,522.38
2012 Jan	359,355	Prophet_log	432,042.52	-72,687.52
2012 Feb	531,709	Prophet_log	598,605.33	-66,896.33
2012 Mar	751,024	Prophet_log	808,618.54	-57,594.54
2012 Apr	1,017,976	Prophet_log	954,898.55	63,077.45
2012 May	1,194,673	Prophet_log	1,209,309.55	-14,636.55
2012 Jun	1,678,327	Prophet_log	1,457,379.36	220,947.64
2012 Jul	2,296,474	Prophet_log	1,855,405.26	441,068.74
2012 Aug	2,622,801	Prophet_log	2,204,830.35	417,970.65
2012 Sep	1,829,252	Prophet_log	1,609,365.84	219,886.16
2012 Oct	1,244,751	Prophet_log	1,135,542.83	109,208.17
2012 Nov	453,958	Prophet_log	542,300.34	-88,342.34
2012 Dec	346,474	Prophet_log	413,069.86	-66,595.86
2013 Jan	369,969	Prophet_log	440,858.05	-70,889.05
2013 Feb	520,055	Prophet_log	622,105.02	-102,050.02
2013 Mar	840,024	Prophet_log	827,714.07	12,309.93
2013 Apr	986,191	Prophet_log	1,019,828.35	-33,637.35
2013 May	1,382,234	Prophet_log	1,221,093.37	161,140.63
2013 Jun	1,814,108	Prophet_log	1,537,622.24	276,485.76
2013 Jul	2,387,304	Prophet_log	1,997,838.21	389,465.79
2013 Aug	2,764,686	Prophet_log	2,375,770.15	388,915.85
2013 Sep	1,943,037	Prophet_log	1,714,332.43	228,704.57
2013 Oct	1,291,360	Prophet_log	1,204,799.18	86,560.82
2013 Nov	455,695	Prophet_log	550,936.20	-95,241.20
2013 Dec	358,062	Prophet_log	422,612.03	-64,550.03
2014 Jan	377,387	Prophet_log	447,387.33	-70,000.33
2014 Feb	543,470	Prophet_log	629,929.39	-86,459.39
2014 Mar	749,773	Prophet_log	854,298.00	-104,525.00
2014 Apr	1,337,145	Prophet_log	1,071,138.68	266,006.32
2014 May	1,538,342	Prophet_log	1,278,249.73	260,092.27
2014 Jun	1,994,167	Prophet_log	1,637,131.53	357,035.47
2014 Jul	2,529,246	Prophet_log	2,162,469.73	366,776.27
2014 Aug	3,069,865	Prophet_log	2,585,404.12	484,460.88
2014 Sep	2,089,656	Prophet_log	1,855,655.83	234,000.17
2014 Oct	1,477,481	Prophet_log	1,287,251.55	190,229.45
2014 Nov	502,473	Prophet_log	587,357.43	-84,884.43
2014 Dec	382,543	Prophet_log	458,120.54	-75,577.54
2015 Jan	381,607	Prophet_log	489,367.05	-107,760.05
2015 Feb	544,777	Prophet_log	677,392.79	-132,615.79
2015 Mar	827,071	Prophet_log	893,665.83	-66,594.83
2015 Apr	1,242,844	Prophet_log	1,198,871.56	43,972.44
2015 May	1,654,526	Prophet_log	1,360,588.06	293,937.94
2015 Jun	2,079,484	Prophet_log	1,759,281.26	320,202.74
2015 Jul	2,688,710	Prophet_log	2,329,350.21	359,359.79
2015 Aug	3,108,357	Prophet_log	2,823,564.70	284,792.30
2015 Sep	2,196,681	Prophet_log	1,983,716.27	212,964.73
2015 Oct	1,553,142	Prophet_log	1,368,873.96	184,268.04
2015 Nov	552,778	Prophet_log	612,181.88	-59,403.88
2015 Dec	426,419	Prophet_log	483,942.93	-57,523.93
2016 Jan	443,150	Prophet_log	516,134.38	-72,984.38
2016 Feb	664,278	Prophet_log	726,906.83	-62,628.83
2016 Mar	1,089,392	Prophet_log	1,027,872.09	61,519.91
2016 Apr	1,335,308	Prophet_log	1,256,032.42	79,275.58
2016 May	1,828,292	Prophet_log	1,578,675.08	249,616.92
2016 Jun	2,288,337	Prophet_log	2,007,158.57	281,178.43
2016 Jul	2,848,570	Prophet_log	2,593,467.14	255,102.86
2016 Aug	3,204,047	Prophet_log	3,056,897.78	147,149.22
2016 Sep	2,378,618	Prophet_log	2,187,804.08	190,813.92
2016 Oct	1,793,822	Prophet_log	1,524,476.11	269,345.89
2016 Nov	653,514	Prophet_log	678,639.96	-25,125.96
2016 Dec	478,510	Prophet_log	522,139.77	-43,629.77
2017 Jan	495,629	Prophet_log	559,460.83	-63,831.83
2017 Feb	704,532	Prophet_log	795,703.49	-91,171.49
2017 Mar	1,015,421	Prophet_log	1,129,439.44	-114,018.44
2017 Apr	1,765,170	Prophet_log	1,409,807.65	355,362.35
2017 May	1,970,072	Prophet_log	1,771,456.85	198,615.15
2017 Jun	2,417,100	Prophet_log	2,256,228.04	160,871.96
2017 Jul	2,968,641	Prophet_log	2,929,832.35	38,808.65
2017 Aug	3,295,406	Prophet_log	3,425,907.68	-130,501.68
2017 Sep	2,470,298	Prophet_log	2,443,633.42	26,664.58
2017 Oct	1,911,961	Prophet_log	1,715,152.89	196,808.11
2017 Nov	680,373	Prophet_log	739,200.07	-58,827.07
2017 Dec	512,548	Prophet_log	569,131.28	-56,583.28
2018 Jan	503,908	Prophet_log	605,666.91	-101,758.91
2018 Feb	731,090	Prophet_log	856,441.51	-125,351.51
2018 Mar	1,151,455	Prophet_log	1,185,482.22	-34,027.22
2018 Apr	1,575,078	Prophet_log	1,583,334.77	-8,256.77
2018 May	2,003,996	Prophet_log	1,888,734.37	115,261.63
2018 Jun	2,381,154	Prophet_log	2,402,542.80	-21,388.80
2018 Jul	2,981,643	Prophet_log	3,101,336.66	-119,693.66
2018 Aug	3,371,918	Prophet_log	3,650,850.68	-278,932.68
2018 Sep	2,499,368	Prophet_log	2,568,299.81	-68,931.81
2018 Oct	1,956,693	Prophet_log	1,791,933.57	164,759.43
2018 Nov	732,141	Prophet_log	763,288.03	-31,147.03
2018 Dec	554,803	Prophet_log	596,494.61	-41,691.61
2019 Jan	548,686	Prophet_log	635,899.43	-87,213.43
2019 Feb	739,981	Prophet_log	902,975.98	-162,994.98
2019 Mar	1,078,918	Prophet_log	1,218,191.98	-139,273.98
2019 Apr	1,795,494	Prophet_log	1,682,429.25	113,064.75
2019 May	1,990,529	Prophet_log	1,967,322.89	23,206.11
2019 Jun	2,425,834	Prophet_log	2,495,810.72	-69,976.72
2019 Jul	2,988,668	Prophet_log	3,243,031.11	-254,363.11
2019 Aug	3,439,271	Prophet_log	3,817,007.20	-377,736.20
2019 Sep	2,573,527	Prophet_log	2,672,170.74	-98,643.74
2019 Oct	1,930,852	Prophet_log	1,858,940.13	71,911.87
2019 Nov	785,875	Prophet_log	785,283.03	591.97
2019 Dec	602,860	Prophet_log	616,617.20	-13,757.20
2020 Jan	560,368	Prophet_log	652,158.23	-91,790.23
2020 Feb	844,247	Prophet_log	924,323.43	-80,076.43
2020 Mar	513,360	Prophet_log	1,342,812.64	-829,452.64
2020 Apr	25,614	Prophet_log	1,582,454.26	-1,556,840.26
2020 May	40,932	Prophet_log	1,816,661.74	-1,775,729.74
2020 Jun	330,393	Prophet_log	1,959,735.42	-1,629,342.42
2020 Jul	1,035,732	Prophet_log	2,280,442.55	-1,244,710.55
2020 Aug	2,090,569	Prophet_log	2,254,203.19	-163,634.19
2020 Sep	1,418,185	Prophet_log	1,569,911.66	-151,726.66
2020 Oct	696,087	Prophet_log	997,996.49	-301,909.49
2020 Nov	181,873	Prophet_log	399,771.27	-217,898.27
2020 Dec	153,351	Prophet_log	299,707.41	-146,356.41
2021 Jan	105,336	Prophet_log	300,716.22	-195,380.22
2021 Feb	66,194	Prophet_log	438,358.37	-372,164.37
2021 Mar	84,413	Prophet_log	501,326.79	-416,913.79
2021 Apr	138,661	Prophet_log	454,789.47	-316,128.47
2021 May	502,057	Prophet_log	518,543.26	-16,486.26
2021 Jun	1,182,009	Prophet_log	699,821.84	482,187.16
2021 Jul	1,551,789	Prophet_log	882,476.03	669,312.97
2021 Aug	2,762,537	Prophet_log	1,105,870.32	1,656,666.68
2021 Sep	1,869,194	Prophet_log	834,829.81	1,034,364.19
2021 Oct	1,584,764	Prophet_log	581,949.45	1,002,814.55
2021 Nov	651,051	Prophet_log	246,272.32	404,778.68
2021 Dec	376,031	Prophet_log	197,956.49	178,074.51
2022 Jan	344,634	Prophet_log	211,378.36	133,255.64
2022 Feb	590,122	Prophet_log	292,839.65	297,282.35
2022 Mar	873,841	Prophet_log	388,153.08	485,687.92
2022 Apr	1,629,377	Prophet_log	519,433.15	1,109,943.85
2022 May	1,867,744	Prophet_log	683,160.89	1,184,583.11
2022 Jun	2,230,207	Prophet_log	963,296.43	1,266,910.57
2010 Jan	366,296	SNaive	411,615.00	-45,319.00
2010 Feb	533,056	SNaive	557,401.00	-24,345.00
2010 Mar	742,227	SNaive	710,502.00	31,725.00
2010 Apr	902,745	SNaive	1,017,779.00	-115,034.00
2010 May	1,107,303	SNaive	1,138,068.00	-30,765.00
2010 Jun	1,464,695	SNaive	1,489,130.00	-24,435.00
2010 Jul	2,050,478	SNaive	1,891,157.00	159,321.00
2010 Aug	2,468,924	SNaive	2,315,586.00	153,338.00
2010 Sep	1,696,356	SNaive	1,539,886.00	156,470.00
2010 Oct	1,104,659	SNaive	1,010,273.00	94,386.00
2010 Nov	445,221	SNaive	475,789.00	-30,568.00
2010 Dec	365,490	SNaive	370,417.00	-4,927.00
2011 Jan	357,209	SNaive	366,296.00	-9,087.00
2011 Feb	503,831	SNaive	533,056.00	-29,225.00
2011 Mar	761,343	SNaive	742,227.00	19,116.00
2011 Apr	1,177,115	SNaive	902,745.00	274,370.00
2011 May	1,169,516	SNaive	1,107,303.00	62,213.00
2011 Jun	1,576,730	SNaive	1,464,695.00	112,035.00
2011 Jul	2,208,160	SNaive	2,050,478.00	157,682.00
2011 Aug	2,572,404	SNaive	2,468,924.00	103,480.00
2011 Sep	1,731,056	SNaive	1,696,356.00	34,700.00
2011 Oct	1,161,751	SNaive	1,104,659.00	57,092.00
2011 Nov	427,550	SNaive	445,221.00	-17,671.00
2011 Dec	333,201	SNaive	365,490.00	-32,289.00
2012 Jan	359,355	SNaive	357,209.00	2,146.00
2012 Feb	531,709	SNaive	503,831.00	27,878.00
2012 Mar	751,024	SNaive	761,343.00	-10,319.00
2012 Apr	1,017,976	SNaive	1,177,115.00	-159,139.00
2012 May	1,194,673	SNaive	1,169,516.00	25,157.00
2012 Jun	1,678,327	SNaive	1,576,730.00	101,597.00
2012 Jul	2,296,474	SNaive	2,208,160.00	88,314.00
2012 Aug	2,622,801	SNaive	2,572,404.00	50,397.00
2012 Sep	1,829,252	SNaive	1,731,056.00	98,196.00
2012 Oct	1,244,751	SNaive	1,161,751.00	83,000.00
2012 Nov	453,958	SNaive	427,550.00	26,408.00
2012 Dec	346,474	SNaive	333,201.00	13,273.00
2013 Jan	369,969	SNaive	359,355.00	10,614.00
2013 Feb	520,055	SNaive	531,709.00	-11,654.00
2013 Mar	840,024	SNaive	751,024.00	89,000.00
2013 Apr	986,191	SNaive	1,017,976.00	-31,785.00
2013 May	1,382,234	SNaive	1,194,673.00	187,561.00
2013 Jun	1,814,108	SNaive	1,678,327.00	135,781.00
2013 Jul	2,387,304	SNaive	2,296,474.00	90,830.00
2013 Aug	2,764,686	SNaive	2,622,801.00	141,885.00
2013 Sep	1,943,037	SNaive	1,829,252.00	113,785.00
2013 Oct	1,291,360	SNaive	1,244,751.00	46,609.00
2013 Nov	455,695	SNaive	453,958.00	1,737.00
2013 Dec	358,062	SNaive	346,474.00	11,588.00
2014 Jan	377,387	SNaive	369,969.00	7,418.00
2014 Feb	543,470	SNaive	520,055.00	23,415.00
2014 Mar	749,773	SNaive	840,024.00	-90,251.00
2014 Apr	1,337,145	SNaive	986,191.00	350,954.00
2014 May	1,538,342	SNaive	1,382,234.00	156,108.00
2014 Jun	1,994,167	SNaive	1,814,108.00	180,059.00
2014 Jul	2,529,246	SNaive	2,387,304.00	141,942.00
2014 Aug	3,069,865	SNaive	2,764,686.00	305,179.00
2014 Sep	2,089,656	SNaive	1,943,037.00	146,619.00
2014 Oct	1,477,481	SNaive	1,291,360.00	186,121.00
2014 Nov	502,473	SNaive	455,695.00	46,778.00
2014 Dec	382,543	SNaive	358,062.00	24,481.00
2015 Jan	381,607	SNaive	377,387.00	4,220.00
2015 Feb	544,777	SNaive	543,470.00	1,307.00
2015 Mar	827,071	SNaive	749,773.00	77,298.00
2015 Apr	1,242,844	SNaive	1,337,145.00	-94,301.00
2015 May	1,654,526	SNaive	1,538,342.00	116,184.00
2015 Jun	2,079,484	SNaive	1,994,167.00	85,317.00
2015 Jul	2,688,710	SNaive	2,529,246.00	159,464.00
2015 Aug	3,108,357	SNaive	3,069,865.00	38,492.00
2015 Sep	2,196,681	SNaive	2,089,656.00	107,025.00
2015 Oct	1,553,142	SNaive	1,477,481.00	75,661.00
2015 Nov	552,778	SNaive	502,473.00	50,305.00
2015 Dec	426,419	SNaive	382,543.00	43,876.00
2016 Jan	443,150	SNaive	381,607.00	61,543.00
2016 Feb	664,278	SNaive	544,777.00	119,501.00
2016 Mar	1,089,392	SNaive	827,071.00	262,321.00
2016 Apr	1,335,308	SNaive	1,242,844.00	92,464.00
2016 May	1,828,292	SNaive	1,654,526.00	173,766.00
2016 Jun	2,288,337	SNaive	2,079,484.00	208,853.00
2016 Jul	2,848,570	SNaive	2,688,710.00	159,860.00
2016 Aug	3,204,047	SNaive	3,108,357.00	95,690.00
2016 Sep	2,378,618	SNaive	2,196,681.00	181,937.00
2016 Oct	1,793,822	SNaive	1,553,142.00	240,680.00
2016 Nov	653,514	SNaive	552,778.00	100,736.00
2016 Dec	478,510	SNaive	426,419.00	52,091.00
2017 Jan	495,629	SNaive	443,150.00	52,479.00
2017 Feb	704,532	SNaive	664,278.00	40,254.00
2017 Mar	1,015,421	SNaive	1,089,392.00	-73,971.00
2017 Apr	1,765,170	SNaive	1,335,308.00	429,862.00
2017 May	1,970,072	SNaive	1,828,292.00	141,780.00
2017 Jun	2,417,100	SNaive	2,288,337.00	128,763.00
2017 Jul	2,968,641	SNaive	2,848,570.00	120,071.00
2017 Aug	3,295,406	SNaive	3,204,047.00	91,359.00
2017 Sep	2,470,298	SNaive	2,378,618.00	91,680.00
2017 Oct	1,911,961	SNaive	1,793,822.00	118,139.00
2017 Nov	680,373	SNaive	653,514.00	26,859.00
2017 Dec	512,548	SNaive	478,510.00	34,038.00
2018 Jan	503,908	SNaive	495,629.00	8,279.00
2018 Feb	731,090	SNaive	704,532.00	26,558.00
2018 Mar	1,151,455	SNaive	1,015,421.00	136,034.00
2018 Apr	1,575,078	SNaive	1,765,170.00	-190,092.00
2018 May	2,003,996	SNaive	1,970,072.00	33,924.00
2018 Jun	2,381,154	SNaive	2,417,100.00	-35,946.00
2018 Jul	2,981,643	SNaive	2,968,641.00	13,002.00
2018 Aug	3,371,918	SNaive	3,295,406.00	76,512.00
2018 Sep	2,499,368	SNaive	2,470,298.00	29,070.00
2018 Oct	1,956,693	SNaive	1,911,961.00	44,732.00
2018 Nov	732,141	SNaive	680,373.00	51,768.00
2018 Dec	554,803	SNaive	512,548.00	42,255.00
2019 Jan	548,686	SNaive	503,908.00	44,778.00
2019 Feb	739,981	SNaive	731,090.00	8,891.00
2019 Mar	1,078,918	SNaive	1,151,455.00	-72,537.00
2019 Apr	1,795,494	SNaive	1,575,078.00	220,416.00
2019 May	1,990,529	SNaive	2,003,996.00	-13,467.00
2019 Jun	2,425,834	SNaive	2,381,154.00	44,680.00
2019 Jul	2,988,668	SNaive	2,981,643.00	7,025.00
2019 Aug	3,439,271	SNaive	3,371,918.00	67,353.00
2019 Sep	2,573,527	SNaive	2,499,368.00	74,159.00
2019 Oct	1,930,852	SNaive	1,956,693.00	-25,841.00
2019 Nov	785,875	SNaive	732,141.00	53,734.00
2019 Dec	602,860	SNaive	554,803.00	48,057.00
2020 Jan	560,368	SNaive	548,686.00	11,682.00
2020 Feb	844,247	SNaive	739,981.00	104,266.00
2020 Mar	513,360	SNaive	1,078,918.00	-565,558.00
2020 Apr	25,614	SNaive	1,795,494.00	-1,769,880.00
2020 May	40,932	SNaive	1,990,529.00	-1,949,597.00
2020 Jun	330,393	SNaive	2,425,834.00	-2,095,441.00
2020 Jul	1,035,732	SNaive	2,988,668.00	-1,952,936.00
2020 Aug	2,090,569	SNaive	3,439,271.00	-1,348,702.00
2020 Sep	1,418,185	SNaive	2,573,527.00	-1,155,342.00
2020 Oct	696,087	SNaive	1,930,852.00	-1,234,765.00
2020 Nov	181,873	SNaive	785,875.00	-604,002.00
2020 Dec	153,351	SNaive	602,860.00	-449,509.00
2021 Jan	105,336	SNaive	560,368.00	-455,032.00
2021 Feb	66,194	SNaive	844,247.00	-778,053.00
2021 Mar	84,413	SNaive	513,360.00	-428,947.00
2021 Apr	138,661	SNaive	25,614.00	113,047.00
2021 May	502,057	SNaive	40,932.00	461,125.00
2021 Jun	1,182,009	SNaive	330,393.00	851,616.00
2021 Jul	1,551,789	SNaive	1,035,732.00	516,057.00
2021 Aug	2,762,537	SNaive	2,090,569.00	671,968.00
2021 Sep	1,869,194	SNaive	1,418,185.00	451,009.00
2021 Oct	1,584,764	SNaive	696,087.00	888,677.00
2021 Nov	651,051	SNaive	181,873.00	469,178.00
2021 Dec	376,031	SNaive	153,351.00	222,680.00
2022 Jan	344,634	SNaive	105,336.00	239,298.00
2022 Feb	590,122	SNaive	66,194.00	523,928.00
2022 Mar	873,841	SNaive	84,413.00	789,428.00
2022 Apr	1,629,377	SNaive	138,661.00	1,490,716.00
2022 May	1,867,744	SNaive	502,057.00	1,365,687.00
2022 Jun	2,230,207	SNaive	1,182,009.00	1,048,198.00
2010 Jan	366,296	SNaive_log	413,177.50	-46,881.50
2010 Feb	533,056	SNaive_log	559,532.29	-26,476.29
2010 Mar	742,227	SNaive_log	713,200.43	29,026.57
2010 Apr	902,745	SNaive_log	1,021,618.38	-118,873.38
2010 May	1,107,303	SNaive_log	1,142,395.90	-35,092.90
2010 Jun	1,464,695	SNaive_log	1,494,747.77	-30,052.77
2010 Jul	2,050,478	SNaive_log	1,898,231.11	152,246.89
2010 Aug	2,468,924	SNaive_log	2,324,238.28	144,685.72
2010 Sep	1,696,356	SNaive_log	1,545,617.53	150,738.47
2010 Oct	1,104,659	SNaive_log	1,014,041.58	90,617.42
2010 Nov	445,221	SNaive_log	477,564.86	-32,343.86
2010 Dec	365,490	SNaive_log	371,794.81	-6,304.81
2011 Jan	357,209	SNaive_log	367,647.40	-10,438.40
2011 Feb	503,831	SNaive_log	535,007.77	-31,176.77
2011 Mar	761,343	SNaive_log	744,932.04	16,410.96
2011 Apr	1,177,115	SNaive_log	906,010.68	271,104.32
2011 May	1,169,516	SNaive_log	1,111,590.81	57,925.19
2011 Jun	1,576,730	SNaive_log	1,470,338.88	106,391.12
2011 Jul	2,208,160	SNaive_log	2,058,360.56	149,799.44
2011 Aug	2,572,404	SNaive_log	2,478,393.79	94,010.21
2011 Sep	1,731,056	SNaive_log	1,702,822.87	28,233.13
2011 Oct	1,161,751	SNaive_log	1,108,839.31	52,911.69
2011 Nov	427,550	SNaive_log	446,897.22	-19,347.22
2011 Dec	333,201	SNaive_log	366,857.82	-33,656.82
2012 Jan	359,355	SNaive_log	358,547.28	807.72
2012 Feb	531,709	SNaive_log	505,704.47	26,004.53
2012 Mar	751,024	SNaive_log	764,161.13	-13,137.13
2012 Apr	1,017,976	SNaive_log	1,181,440.65	-163,464.65
2012 May	1,194,673	SNaive_log	1,173,872.84	20,800.16
2012 Jun	1,678,327	SNaive_log	1,582,563.58	95,763.42
2012 Jul	2,296,474	SNaive_log	2,216,301.74	80,172.26
2012 Aug	2,622,801	SNaive_log	2,581,834.74	40,966.26
2012 Sep	1,829,252	SNaive_log	1,737,359.26	91,892.74
2012 Oct	1,244,751	SNaive_log	1,165,963.80	78,787.20
2012 Nov	453,958	SNaive_log	429,096.65	24,861.35
2012 Dec	346,474	SNaive_log	334,402.10	12,071.90
2013 Jan	369,969	SNaive_log	360,643.29	9,325.71
2013 Feb	520,055	SNaive_log	533,603.59	-13,548.59
2013 Mar	840,024	SNaive_log	753,682.99	86,341.01
2013 Apr	986,191	SNaive_log	1,021,599.04	-35,408.04
2013 May	1,382,234	SNaive_log	1,198,900.24	183,333.76
2013 Jun	1,814,108	SNaive_log	1,684,345.52	129,762.48
2013 Jul	2,387,304	SNaive_log	2,304,700.64	82,603.36
2013 Aug	2,764,686	SNaive_log	2,632,147.48	132,538.52
2013 Sep	1,943,037	SNaive_log	1,835,744.45	107,292.55
2013 Oct	1,291,360	SNaive_log	1,249,154.85	42,205.15
2013 Nov	455,695	SNaive_log	455,555.64	139.36
2013 Dec	358,062	SNaive_log	347,685.51	10,376.49
2014 Jan	377,387	SNaive_log	371,255.66	6,131.34
2014 Feb	543,470	SNaive_log	521,852.75	21,617.25
2014 Mar	749,773	SNaive_log	842,914.62	-93,141.62
2014 Apr	1,337,145	SNaive_log	989,603.31	347,541.69
2014 May	1,538,342	SNaive_log	1,387,387.12	150,954.88
2014 Jun	1,994,167	SNaive_log	1,820,893.69	173,273.31
2014 Jul	2,529,246	SNaive_log	2,396,244.60	133,001.40
2014 Aug	3,069,865	SNaive_log	2,775,004.69	294,860.31
2014 Sep	2,089,656	SNaive_log	1,950,309.76	139,346.24
2014 Oct	1,477,481	SNaive_log	1,296,184.96	181,296.04
2014 Nov	502,473	SNaive_log	457,412.26	45,060.74
2014 Dec	382,543	SNaive_log	359,413.49	23,129.51
2015 Jan	381,607	SNaive_log	378,807.86	2,799.14
2015 Feb	544,777	SNaive_log	545,504.26	-727.26
2015 Mar	827,071	SNaive_log	752,562.98	74,508.02
2015 Apr	1,242,844	SNaive_log	1,342,129.19	-99,285.19
2015 May	1,654,526	SNaive_log	1,544,066.73	110,459.27
2015 Jun	2,079,484	SNaive_log	2,001,575.67	77,908.33
2015 Jul	2,688,710	SNaive_log	2,538,601.33	150,108.67
2015 Aug	3,108,357	SNaive_log	3,081,187.91	27,169.09
2015 Sep	2,196,681	SNaive_log	2,097,320.63	99,360.37
2015 Oct	1,553,142	SNaive_log	1,482,880.04	70,261.96
2015 Nov	552,778	SNaive_log	504,302.35	48,475.65
2015 Dec	426,419	SNaive_log	383,937.67	42,481.33
2016 Jan	443,150	SNaive_log	383,003.03	60,146.97
2016 Feb	664,278	SNaive_log	546,792.58	117,485.42
2016 Mar	1,089,392	SNaive_log	830,203.57	259,188.43
2016 Apr	1,335,308	SNaive_log	1,247,783.32	87,524.68
2016 May	1,828,292	SNaive_log	1,661,088.85	167,203.15
2016 Jun	2,288,337	SNaive_log	2,087,743.95	200,593.05
2016 Jul	2,848,570	SNaive_log	2,699,398.65	149,171.35
2016 Aug	3,204,047	SNaive_log	3,120,675.55	83,371.45
2016 Sep	2,378,618	SNaive_log	2,205,345.61	173,272.39
2016 Oct	1,793,822	SNaive_log	1,559,261.83	234,560.17
2016 Nov	653,514	SNaive_log	554,974.83	98,539.17
2016 Dec	478,510	SNaive_log	428,136.07	50,373.93
2017 Jan	495,629	SNaive_log	444,940.48	50,688.52
2017 Feb	704,532	SNaive_log	666,969.56	37,562.44
2017 Mar	1,015,421	SNaive_log	1,093,793.04	-78,372.04
2017 Apr	1,765,170	SNaive_log	1,340,691.78	424,478.22
2017 May	1,970,072	SNaive_log	1,835,989.08	134,082.92
2017 Jun	2,417,100	SNaive_log	2,297,954.36	119,145.64
2017 Jul	2,968,641	SNaive_log	2,860,502.99	108,138.01
2017 Aug	3,295,406	SNaive_log	3,217,415.39	77,990.61
2017 Sep	2,470,298	SNaive_log	2,388,497.50	81,800.50
2017 Oct	1,911,961	SNaive_log	1,801,241.88	110,719.12
2017 Nov	680,373	SNaive_log	656,210.36	24,162.64
2017 Dec	512,548	SNaive_log	480,476.49	32,071.51
2018 Jan	503,908	SNaive_log	497,661.60	6,246.40
2018 Feb	731,090	SNaive_log	707,407.70	23,682.30
2018 Mar	1,151,455	SNaive_log	1,019,548.91	131,906.09
2018 Apr	1,575,078	SNaive_log	1,772,378.53	-197,300.53
2018 May	2,003,996	SNaive_log	1,978,140.11	25,855.89
2018 Jun	2,381,154	SNaive_log	2,426,953.16	-45,799.16
2018 Jul	2,981,643	SNaive_log	2,980,686.44	956.56
2018 Aug	3,371,918	SNaive_log	3,308,714.09	63,203.91
2018 Sep	2,499,368	SNaive_log	2,480,230.01	19,137.99
2018 Oct	1,956,693	SNaive_log	1,919,612.70	37,080.30
2018 Nov	732,141	SNaive_log	683,083.99	49,057.01
2018 Dec	554,803	SNaive_log	514,587.19	40,215.81
2019 Jan	548,686	SNaive_log	505,910.86	42,775.14
2019 Feb	739,981	SNaive_log	733,994.64	5,986.36
2019 Mar	1,078,918	SNaive_log	1,156,009.16	-77,091.16
2019 Apr	1,795,494	SNaive_log	1,581,294.43	214,199.57
2019 May	1,990,529	SNaive_log	2,011,947.44	-21,418.44
2019 Jun	2,425,834	SNaive_log	2,390,559.42	35,274.58
2019 Jul	2,988,668	SNaive_log	2,993,369.58	-4,701.58
2019 Aug	3,439,271	SNaive_log	3,385,120.08	54,150.92
2019 Sep	2,573,527	SNaive_log	2,509,112.28	64,414.72
2019 Oct	1,930,852	SNaive_log	1,964,291.37	-33,439.37
2019 Nov	785,875	SNaive_log	734,971.81	50,903.19
2019 Dec	602,860	SNaive_log	556,944.81	45,915.19
2020 Jan	560,368	SNaive_log	550,803.21	9,564.79
2020 Feb	844,247	SNaive_log	742,824.61	101,422.39
2020 Mar	513,360	SNaive_log	1,083,086.81	-569,726.81
2020 Apr	25,614	SNaive_log	1,804,545.48	-1,778,931.48
2020 May	40,932	SNaive_log	2,078,003.58	-2,037,071.58
2020 Jun	330,393	SNaive_log	2,610,520.19	-2,280,127.19
2020 Jul	1,035,732	SNaive_log	3,240,614.26	-2,204,882.26
2020 Aug	2,090,569	SNaive_log	3,736,187.27	-1,645,618.27
2020 Sep	1,418,185	SNaive_log	2,796,112.42	-1,377,927.42
2020 Oct	696,087	SNaive_log	2,098,594.04	-1,402,507.04
2020 Nov	181,873	SNaive_log	855,579.25	-673,706.25
2020 Dec	153,351	SNaive_log	658,809.02	-505,458.02
2021 Jan	105,336	SNaive_log	614,344.64	-509,008.64
2021 Feb	66,194	SNaive_log	930,123.75	-863,929.75
2021 Mar	84,413	SNaive_log	572,237.72	-487,824.72
2021 Apr	138,661	SNaive_log	28,711.36	109,949.64
2021 May	502,057	SNaive_log	46,100.65	455,956.35
2021 Jun	1,182,009	SNaive_log	376,179.91	805,829.09
2021 Jul	1,551,789	SNaive_log	1,182,104.05	369,684.95
2021 Aug	2,762,537	SNaive_log	2,385,508.68	377,028.32
2021 Sep	1,869,194	SNaive_log	1,617,679.37	251,514.63
2021 Oct	1,584,764	SNaive_log	793,718.05	791,045.95
2021 Nov	651,051	SNaive_log	207,526.13	443,524.87
2021 Dec	376,031	SNaive_log	175,391.74	200,639.26
2022 Jan	344,634	SNaive_log	120,583.74	224,050.26
2022 Feb	590,122	SNaive_log	75,921.73	514,200.27
2022 Mar	873,841	SNaive_log	97,564.63	776,276.37
2022 Apr	1,629,377	SNaive_log	161,664.93	1,467,712.07
2022 May	1,867,744	SNaive_log	590,976.18	1,276,767.82
2022 Jun	2,230,207	SNaive_log	1,394,508.88	835,698.12
2010 Jan	366,296	TSLM	443,287.46	-76,991.46
2010 Feb	533,056	TSLM	635,536.81	-102,480.81
2010 Mar	742,227	TSLM	863,710.75	-121,483.75
2010 Apr	902,745	TSLM	1,041,493.38	-138,748.38
2010 May	1,107,303	TSLM	1,251,371.77	-144,068.77
2010 Jun	1,464,695	TSLM	1,528,014.90	-63,319.90
2010 Jul	2,050,478	TSLM	1,925,603.28	124,874.72
2010 Aug	2,468,924	TSLM	2,268,598.34	200,325.66
2010 Sep	1,696,356	TSLM	1,609,127.60	87,228.40
2010 Oct	1,104,659	TSLM	1,111,559.61	-6,900.61
2010 Nov	445,221	TSLM	514,128.00	-68,907.00
2010 Dec	365,490	TSLM	389,846.69	-24,356.69
2011 Jan	357,209	TSLM	421,676.97	-64,467.97
2011 Feb	503,831	TSLM	611,928.40	-108,097.40
2011 Mar	761,343	TSLM	838,252.74	-76,909.74
2011 Apr	1,177,115	TSLM	1,015,509.05	161,605.95
2011 May	1,169,516	TSLM	1,231,730.01	-62,214.01
2011 Jun	1,576,730	TSLM	1,517,525.84	59,204.16
2011 Jul	2,208,160	TSLM	1,934,880.43	273,279.57
2011 Aug	2,572,404	TSLM	2,287,909.07	284,494.93
2011 Sep	1,731,056	TSLM	1,619,944.78	111,111.22
2011 Oct	1,161,751	TSLM	1,114,324.99	47,426.01
2011 Nov	427,550	TSLM	512,341.33	-84,791.33
2011 Dec	333,201	TSLM	391,780.30	-58,579.30
2012 Jan	359,355	TSLM	420,604.86	-61,249.86
2012 Feb	531,709	TSLM	607,300.75	-75,591.75
2012 Mar	751,024	TSLM	836,940.04	-85,916.04
2012 Apr	1,017,976	TSLM	1,033,884.20	-15,908.20
2012 May	1,194,673	TSLM	1,227,755.28	-33,082.28
2012 Jun	1,678,327	TSLM	1,524,261.47	154,065.53
2012 Jul	2,296,474	TSLM	1,961,357.19	335,116.81
2012 Aug	2,622,801	TSLM	2,316,561.44	306,239.56
2012 Sep	1,829,252	TSLM	1,634,604.67	194,647.33
2012 Oct	1,244,751	TSLM	1,125,271.76	119,479.24
2012 Nov	453,958	TSLM	513,613.09	-59,655.09
2012 Dec	346,474	TSLM	395,675.78	-49,201.78
2013 Jan	369,969	TSLM	425,872.50	-55,903.50
2013 Feb	520,055	TSLM	611,580.69	-91,525.69
2013 Mar	840,024	TSLM	840,112.18	-88.18
2013 Apr	986,191	TSLM	1,044,127.22	-57,936.22
2013 May	1,382,234	TSLM	1,235,868.98	146,365.02
2013 Jun	1,814,108	TSLM	1,550,155.97	263,952.03
2013 Jul	2,387,304	TSLM	2,003,222.43	384,081.57
2013 Aug	2,764,686	TSLM	2,357,123.19	407,562.81
2013 Sep	1,943,037	TSLM	1,668,424.10	274,612.90
2013 Oct	1,291,360	TSLM	1,154,736.72	136,623.28
2013 Nov	455,695	TSLM	529,611.68	-73,916.68
2013 Dec	358,062	TSLM	412,226.85	-54,164.85
2014 Jan	377,387	TSLM	443,755.01	-66,368.01
2014 Feb	543,470	TSLM	626,725.92	-83,255.92
2014 Mar	749,773	TSLM	861,946.65	-112,173.65
2014 Apr	1,337,145	TSLM	1,059,791.77	277,353.23
2014 May	1,538,342	TSLM	1,272,113.79	266,228.21
2014 Jun	1,994,167	TSLM	1,596,906.18	397,260.82
2014 Jul	2,529,246	TSLM	2,060,863.79	468,382.21
2014 Aug	3,069,865	TSLM	2,417,895.97	651,969.03
2014 Sep	2,089,656	TSLM	1,723,808.55	365,847.45
2014 Oct	1,477,481	TSLM	1,201,788.62	275,692.38
2014 Nov	502,473	TSLM	563,884.34	-61,411.34
2014 Dec	382,543	TSLM	448,098.91	-65,555.91
2015 Jan	381,607	TSLM	481,478.01	-99,871.01
2015 Feb	544,777	TSLM	662,739.69	-117,962.69
2015 Mar	827,071	TSLM	895,437.72	-68,366.72
2015 Apr	1,242,844	TSLM	1,119,996.09	122,847.91
2015 May	1,654,526	TSLM	1,329,001.36	325,524.64
2015 Jun	2,079,484	TSLM	1,663,506.43	415,977.57
2015 Jul	2,688,710	TSLM	2,132,522.08	556,187.92
2015 Aug	3,108,357	TSLM	2,503,212.32	605,144.68
2015 Sep	2,196,681	TSLM	1,789,363.78	407,317.22
2015 Oct	1,553,142	TSLM	1,262,002.26	291,139.74
2015 Nov	552,778	TSLM	601,885.40	-49,107.40
2015 Dec	426,419	TSLM	486,000.52	-59,581.52
2016 Jan	443,150	TSLM	519,869.20	-76,719.20
2016 Feb	664,278	TSLM	700,385.07	-36,107.07
2016 Mar	1,089,392	TSLM	937,507.20	151,884.80
2016 Apr	1,335,308	TSLM	1,177,513.70	157,794.30
2016 May	1,828,292	TSLM	1,399,732.29	428,559.71
2016 Jun	2,288,337	TSLM	1,741,480.96	546,856.04
2016 Jul	2,848,570	TSLM	2,221,255.47	627,314.53
2016 Aug	3,204,047	TSLM	2,596,091.81	607,955.19
2016 Sep	2,378,618	TSLM	1,869,955.14	508,662.86
2016 Oct	1,793,822	TSLM	1,336,829.69	456,992.31
2016 Nov	653,514	TSLM	657,840.34	-4,326.34
2016 Dec	478,510	TSLM	541,927.03	-63,417.03
2017 Jan	495,629	TSLM	577,840.09	-82,211.09
2017 Feb	704,532	TSLM	760,663.83	-56,131.83
2017 Mar	1,015,421	TSLM	1,008,541.94	6,879.06
2017 Apr	1,765,170	TSLM	1,246,729.67	518,440.33
2017 May	1,970,072	TSLM	1,490,179.26	479,892.74
2017 Jun	2,417,100	TSLM	1,839,636.11	577,463.89
2017 Jul	2,968,641	TSLM	2,324,594.66	644,046.34
2017 Aug	3,295,406	TSLM	2,698,551.14	596,854.86
2017 Sep	2,470,298	TSLM	1,966,448.79	503,849.21
2017 Oct	1,911,961	TSLM	1,430,247.66	481,713.34
2017 Nov	680,373	TSLM	724,487.12	-44,114.12
2017 Dec	512,548	TSLM	604,567.05	-92,019.05
2018 Jan	503,908	TSLM	642,027.53	-138,119.53
2018 Feb	731,090	TSLM	825,492.91	-94,402.91
2018 Mar	1,151,455	TSLM	1,076,326.24	75,128.76
2018 Apr	1,575,078	TSLM	1,343,895.22	231,182.78
2018 May	2,003,996	TSLM	1,581,213.59	422,782.41
2018 Jun	2,381,154	TSLM	1,935,314.02	445,839.98
2018 Jul	2,981,643	TSLM	2,422,205.28	559,437.72
2018 Aug	3,371,918	TSLM	2,792,432.06	579,485.94
2018 Sep	2,499,368	TSLM	2,054,958.43	444,409.57
2018 Oct	1,956,693	TSLM	1,516,780.48	439,912.52
2018 Nov	732,141	TSLM	781,299.22	-49,158.22
2018 Dec	554,803	TSLM	658,651.02	-103,848.02
2019 Jan	548,686	TSLM	695,763.32	-147,077.32
2019 Feb	739,981	TSLM	881,411.19	-141,430.19
2019 Mar	1,078,918	TSLM	1,140,533.66	-61,615.66
2019 Apr	1,795,494	TSLM	1,414,492.01	381,001.99
2019 May	1,990,529	TSLM	1,663,865.88	326,663.12
2019 Jun	2,425,834	TSLM	2,017,935.52	407,898.48
2019 Jul	2,988,668	TSLM	2,510,327.30	478,340.70
2019 Aug	3,439,271	TSLM	2,880,597.62	558,673.38
2019 Sep	2,573,527	TSLM	2,135,774.61	437,752.39
2019 Oct	1,930,852	TSLM	1,597,296.54	333,555.46
2019 Nov	785,875	TSLM	834,799.40	-48,924.40
2019 Dec	602,860	TSLM	709,272.84	-106,412.84
2020 Jan	560,368	TSLM	745,979.50	-185,611.50
2020 Feb	844,247	TSLM	931,413.21	-87,166.21
2020 Mar	513,360	TSLM	1,195,224.55	-681,864.55
2020 Apr	25,614	TSLM	1,483,463.05	-1,457,849.05
2020 May	40,932	TSLM	1,707,134.34	-1,666,202.34
2020 Jun	330,393	TSLM	2,040,665.09	-1,710,272.09
2020 Jul	1,035,732	TSLM	2,510,754.01	-1,475,022.01
2020 Aug	2,090,569	TSLM	2,861,517.41	-770,948.41
2020 Sep	1,418,185	TSLM	2,094,836.16	-676,651.16
2020 Oct	696,087	TSLM	1,538,053.50	-841,966.50
2020 Nov	181,873	TSLM	742,777.70	-560,904.70
2020 Dec	153,351	TSLM	608,489.52	-455,138.52
2021 Jan	105,336	TSLM	631,608.24	-526,272.24
2021 Feb	66,194	TSLM	817,528.38	-751,334.38
2021 Mar	84,413	TSLM	1,044,922.44	-960,509.44
2021 Apr	138,661	TSLM	1,292,857.08	-1,154,196.08
2021 May	502,057	TSLM	1,510,221.70	-1,008,164.70
2021 Jun	1,182,009	TSLM	1,849,383.99	-667,374.99
2021 Jul	1,551,789	TSLM	2,342,778.91	-790,989.91
2021 Aug	2,762,537	TSLM	2,734,902.88	27,634.12
2021 Sep	1,869,194	TSLM	1,981,766.90	-112,572.90
2021 Oct	1,584,764	TSLM	1,423,428.75	161,335.25
2021 Nov	651,051	TSLM	652,653.56	-1,602.56
2021 Dec	376,031	TSLM	529,524.42	-153,493.42
2022 Jan	344,634	TSLM	550,446.38	-205,812.38
2022 Feb	590,122	TSLM	729,916.97	-139,794.97
2022 Mar	873,841	TSLM	954,923.68	-81,082.68
2022 Apr	1,629,377	TSLM	1,204,168.78	425,208.22
2022 May	1,867,744	TSLM	1,446,118.97	421,625.03
2022 Jun	2,230,207	TSLM	1,816,830.69	413,376.31
2010 Jan	366,296	TSLM_log	451,085.59	-84,789.59
2010 Feb	533,056	TSLM_log	633,824.66	-100,768.66
2010 Mar	742,227	TSLM_log	848,186.88	-105,959.88
2010 Apr	902,745	TSLM_log	1,017,550.90	-114,805.90
2010 May	1,107,303	TSLM_log	1,218,625.59	-111,322.59
2010 Jun	1,464,695	TSLM_log	1,481,607.36	-16,912.36
2010 Jul	2,050,478	TSLM_log	1,858,316.92	192,161.08
2010 Aug	2,468,924	TSLM_log	2,184,098.05	284,825.95
2010 Sep	1,696,356	TSLM_log	1,560,682.57	135,673.43
2010 Oct	1,104,659	TSLM_log	1,087,439.90	17,219.10
2010 Nov	445,221	TSLM_log	519,604.82	-74,383.82
2010 Dec	365,490	TSLM_log	401,475.67	-35,985.67
2011 Jan	357,209	TSLM_log	431,914.22	-74,705.22
2011 Feb	503,831	TSLM_log	609,103.86	-105,272.86
2011 Mar	761,343	TSLM_log	817,768.75	-56,425.75
2011 Apr	1,177,115	TSLM_log	983,663.33	193,451.67
2011 May	1,169,516	TSLM_log	1,188,763.56	-19,247.56
2011 Jun	1,576,730	TSLM_log	1,458,948.55	117,781.45
2011 Jul	2,208,160	TSLM_log	1,851,908.28	356,251.72
2011 Aug	2,572,404	TSLM_log	2,185,187.26	387,216.74
2011 Sep	1,731,056	TSLM_log	1,557,334.97	173,721.03
2011 Oct	1,161,751	TSLM_log	1,078,992.64	82,758.36
2011 Nov	427,550	TSLM_log	508,260.08	-80,710.08
2011 Dec	333,201	TSLM_log	394,731.85	-61,530.85
2012 Jan	359,355	TSLM_log	420,961.06	-61,606.06
2012 Feb	531,709	TSLM_log	594,078.30	-62,369.30
2012 Mar	751,024	TSLM_log	806,824.42	-55,800.42
2012 Apr	1,017,976	TSLM_log	991,020.46	26,955.54
2012 May	1,194,673	TSLM_log	1,174,388.93	20,284.07
2012 Jun	1,678,327	TSLM_log	1,453,635.93	224,691.07
2012 Jul	2,296,474	TSLM_log	1,862,925.13	433,548.87
2012 Aug	2,622,801	TSLM_log	2,197,431.70	425,369.30
2012 Sep	1,829,252	TSLM_log	1,559,074.30	270,177.70
2012 Oct	1,244,751	TSLM_log	1,078,514.86	166,236.14
2012 Nov	453,958	TSLM_log	498,370.26	-44,412.26
2012 Dec	346,474	TSLM_log	387,683.77	-41,209.77
2013 Jan	369,969	TSLM_log	414,842.04	-44,873.04
2013 Feb	520,055	TSLM_log	588,090.98	-68,035.98
2013 Mar	840,024	TSLM_log	800,931.61	39,092.39
2013 Apr	986,191	TSLM_log	993,587.10	-7,396.10
2013 May	1,382,234	TSLM_log	1,175,776.62	206,457.38
2013 Jun	1,814,108	TSLM_log	1,473,753.81	340,354.19
2013 Jul	2,387,304	TSLM_log	1,900,672.38	486,631.62
2013 Aug	2,764,686	TSLM_log	2,237,274.01	527,411.99
2013 Sep	1,943,037	TSLM_log	1,586,346.07	356,690.93
2013 Oct	1,291,360	TSLM_log	1,096,906.02	194,453.98
2013 Nov	455,695	TSLM_log	497,918.33	-42,223.33
2013 Dec	358,062	TSLM_log	386,791.74	-28,729.74
2014 Jan	377,387	TSLM_log	414,754.81	-37,367.81
2014 Feb	543,470	TSLM_log	587,835.97	-44,365.97
2014 Mar	749,773	TSLM_log	811,055.62	-61,282.62
2014 Apr	1,337,145	TSLM_log	999,908.68	337,236.32
2014 May	1,538,342	TSLM_log	1,204,376.55	333,965.45
2014 Jun	1,994,167	TSLM_log	1,516,960.45	477,206.55
2014 Jul	2,529,246	TSLM_log	1,961,673.59	567,572.41
2014 Aug	3,069,865	TSLM_log	2,307,569.23	762,295.77
2014 Sep	2,089,656	TSLM_log	1,637,402.59	452,253.41
2014 Oct	1,477,481	TSLM_log	1,129,873.32	347,607.68
2014 Nov	502,473	TSLM_log	504,681.68	-2,208.68
2014 Dec	382,543	TSLM_log	392,882.96	-10,339.96
2015 Jan	381,607	TSLM_log	422,046.92	-40,439.92
2015 Feb	544,777	TSLM_log	598,754.61	-53,977.61
2015 Mar	827,071	TSLM_log	825,907.16	1,163.84
2015 Apr	1,242,844	TSLM_log	1,045,005.29	197,838.71
2015 May	1,654,526	TSLM_log	1,252,214.90	402,311.10
2015 Jun	2,079,484	TSLM_log	1,581,229.01	498,254.99
2015 Jul	2,688,710	TSLM_log	2,042,200.47	646,509.53
2015 Aug	3,108,357	TSLM_log	2,408,253.56	700,103.44
2015 Sep	2,196,681	TSLM_log	1,703,286.74	493,394.26
2015 Oct	1,553,142	TSLM_log	1,177,490.14	375,651.86
2015 Nov	552,778	TSLM_log	516,572.11	36,205.89
2015 Dec	426,419	TSLM_log	401,984.87	24,434.13
2016 Jan	443,150	TSLM_log	431,171.72	11,978.28
2016 Feb	664,278	TSLM_log	613,222.08	51,055.92
2016 Mar	1,089,392	TSLM_log	853,355.79	236,036.21
2016 Apr	1,335,308	TSLM_log	1,095,816.69	239,491.31
2016 May	1,828,292	TSLM_log	1,322,316.56	505,975.44
2016 Jun	2,288,337	TSLM_log	1,670,581.38	617,755.62
2016 Jul	2,848,570	TSLM_log	2,159,272.64	689,297.36
2016 Aug	3,204,047	TSLM_log	2,543,303.97	660,743.03
2016 Sep	2,378,618	TSLM_log	1,798,064.36	580,553.64
2016 Oct	1,793,822	TSLM_log	1,245,302.44	548,519.56
2016 Nov	653,514	TSLM_log	540,006.70	113,507.30
2016 Dec	478,510	TSLM_log	420,765.55	57,744.45
2017 Jan	495,629	TSLM_log	451,919.30	43,709.70
2017 Feb	704,532	TSLM_log	645,388.28	59,143.72
2017 Mar	1,015,421	TSLM_log	906,957.07	108,463.93
2017 Apr	1,765,170	TSLM_log	1,159,059.70	606,110.30
2017 May	1,970,072	TSLM_log	1,414,220.49	555,851.51
2017 Jun	2,417,100	TSLM_log	1,785,964.50	631,135.50
2017 Jul	2,968,641	TSLM_log	2,302,925.24	665,715.76
2017 Aug	3,295,406	TSLM_log	2,704,266.79	591,139.21
2017 Sep	2,470,298	TSLM_log	1,916,459.93	553,838.07
2017 Oct	1,911,961	TSLM_log	1,333,487.51	578,473.49
2017 Nov	680,373	TSLM_log	572,334.34	108,038.66
2017 Dec	512,548	TSLM_log	444,226.10	68,321.90
2018 Jan	503,908	TSLM_log	477,112.17	26,795.83
2018 Feb	731,090	TSLM_log	680,815.62	50,274.38
2018 Mar	1,151,455	TSLM_log	957,866.85	193,588.15
2018 Apr	1,575,078	TSLM_log	1,246,554.84	328,523.16
2018 May	2,003,996	TSLM_log	1,509,110.84	494,885.16
2018 Jun	2,381,154	TSLM_log	1,901,385.51	479,768.49
2018 Jul	2,981,643	TSLM_log	2,442,364.99	539,278.01
2018 Aug	3,371,918	TSLM_log	2,856,863.73	515,054.27
2018 Sep	2,499,368	TSLM_log	2,030,050.12	469,317.88
2018 Oct	1,956,693	TSLM_log	1,420,013.77	536,679.23
2018 Nov	732,141	TSLM_log	602,829.45	129,311.55
2018 Dec	554,803	TSLM_log	467,263.86	87,539.14
2019 Jan	548,686	TSLM_log	500,354.41	48,331.59
2019 Feb	739,981	TSLM_log	714,986.84	24,994.16
2019 Mar	1,078,918	TSLM_log	1,011,425.18	67,492.82
2019 Apr	1,795,494	TSLM_log	1,317,522.05	477,971.95
2019 May	1,990,529	TSLM_log	1,600,958.60	389,570.40
2019 Jun	2,425,834	TSLM_log	2,009,039.19	416,794.81
2019 Jul	2,988,668	TSLM_log	2,575,916.64	412,751.36
2019 Aug	3,439,271	TSLM_log	3,005,702.97	433,568.03
2019 Sep	2,573,527	TSLM_log	2,139,710.74	433,816.26
2019 Oct	1,930,852	TSLM_log	1,505,172.37	425,679.63
2019 Nov	785,875	TSLM_log	634,150.09	151,724.91
2019 Dec	602,860	TSLM_log	491,092.10	111,767.90
2020 Jan	560,368	TSLM_log	524,482.38	35,885.62
2020 Feb	844,247	TSLM_log	747,040.81	97,206.19
2020 Mar	513,360	TSLM_log	1,059,601.14	-546,241.14
2020 Apr	25,614	TSLM_log	1,384,898.22	-1,359,284.22
2020 May	40,932	TSLM_log	1,640,866.33	-1,599,934.33
2020 Jun	330,393	TSLM_log	2,013,230.97	-1,682,837.97
2020 Jul	1,035,732	TSLM_log	2,530,351.17	-1,494,619.17
2020 Aug	2,090,569	TSLM_log	2,918,897.90	-828,328.90
2020 Sep	1,418,185	TSLM_log	2,072,782.18	-654,597.18
2020 Oct	696,087	TSLM_log	1,454,020.49	-757,933.49
2020 Nov	181,873	TSLM_log	605,310.84	-423,437.84
2020 Dec	153,351	TSLM_log	462,285.44	-308,934.44
2021 Jan	105,336	TSLM_log	480,194.94	-374,858.94
2021 Feb	66,194	TSLM_log	675,560.88	-609,366.88
2021 Mar	84,413	TSLM_log	902,320.58	-817,907.58
2021 Apr	138,661	TSLM_log	998,937.42	-860,276.42
2021 May	502,057	TSLM_log	1,199,933.66	-697,876.66
2021 Jun	1,182,009	TSLM_log	1,624,960.82	-442,951.82
2021 Jul	1,551,789	TSLM_log	2,158,873.83	-607,084.83
2021 Aug	2,762,537	TSLM_log	2,571,844.72	190,692.28
2021 Sep	1,869,194	TSLM_log	1,831,086.10	38,107.90
2021 Oct	1,584,764	TSLM_log	1,268,619.87	316,144.13
2021 Nov	651,051	TSLM_log	521,867.90	129,183.10
2021 Dec	376,031	TSLM_log	405,958.50	-29,927.50
2022 Jan	344,634	TSLM_log	416,807.61	-72,173.61
2022 Feb	590,122	TSLM_log	572,174.48	17,947.52
2022 Mar	873,841	TSLM_log	776,911.31	96,929.69
2022 Apr	1,629,377	TSLM_log	892,961.21	736,415.79
2022 May	1,867,744	TSLM_log	1,155,211.55	712,532.45
2022 Jun	2,230,207	TSLM_log	1,628,075.33	602,131.67

# Show Point Forecasts in Plot: 2000-2022
error_fc_algarve_stretch %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_until2022, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2000-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2010-2022
tourism_algarve_from2010 <- tourism_algarve_until2022 %>%
  filter(year(Month) >= 2010)

error_fc_algarve_stretch %>%
  filter(year(Month) >= 2010) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_from2010, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2010-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2019-2022
tourism_algarve_from2019 <- tourism_algarve_until2022 %>%
  filter(year(Month) >= 2019)

error_fc_algarve_stretch %>%
  filter(year(Month) >= 2019) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_from2019, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2019-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2020-2022
tourism_algarve_from2020 <- tourism_algarve_until2022 %>%
  filter(year(Month) >= 2020)

error_fc_algarve_stretch %>%
  filter(year(Month) >= 2020) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_from2020, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2020-2022") +
  ylab("Overnight_Stays")

2.2.1.4 Change of RMSE: 2010-2019 vs. 2010-2022

All Models

Note: In the following, “All Models” means that all 20 models are shown. Each model appears twice: With the original & with the log-transformed variable.

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_stretch, tourism_algarve_until2019) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_stretch, tourism_algarve_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
Drift_STL	14	116,436.33	1	192,094.8
ARIMA_auto	1	91,874.23	2	201,552.5
ARIMA_d0D1	2	92,494.37	3	202,684.9
ARIMA_d1D1	4	96,707.66	4	208,197.1
ARIMA_d0D1_log	3	95,436.73	5	216,534.9
ARIMA_auto_log	6	102,104.80	6	219,552.0
HWA_log	12	113,161.96	7	231,042.4
ETS_auto_log	9	110,633.52	8	234,012.4
Drift_STL_log	8	107,486.85	9	245,453.4
ARIMA_d1D1_log	5	101,846.83	10	249,164.4
HWA	7	105,505.57	11	259,472.2
ETS_auto	10	110,673.75	12	270,982.4
Prophet_log	15	191,988.54	13	415,098.3
Prophet	16	241,566.98	14	437,125.8
TSLM	17	294,055.70	15	439,795.6
TSLM_log	18	333,098.41	16	444,344.4
SNaive	13	114,889.37	17	464,522.7
SNaive_log	11	111,193.17	18	484,382.9
Naive	19	517,678.97	19	519,314.1
Naive_log	20	543,912.12	20	544,703.7

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

Note: In the following, “Each Model once” means that each model appears only once: Either with the original or with the log-transformed variable (depending on the lowest RMSE for the 2010-2022 Forecasts).

# Save best models according to the RMSE of Forecasts from 2010-2022
best_models_fc_algarve_stretch <- c("ARIMA_d0D1", "Drift_STL", "ARIMA_d1D1", "ARIMA_auto", "HWA_log", "ETS_auto_log", "Naive", "Prophet_log", "TSLM", "SNaive")

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_stretch, tourism_algarve_until2019) %>%
  filter(.model %in% best_models_fc_algarve_stretch) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_stretch, tourism_algarve_until2022) %>%
  filter(.model %in% best_models_fc_algarve_stretch) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
Drift_STL	7	116,436.33	1	192,094.8
ARIMA_auto	1	91,874.23	2	201,552.5
ARIMA_d0D1	2	92,494.37	3	202,684.9
ARIMA_d1D1	3	96,707.66	4	208,197.1
HWA_log	5	113,161.96	5	231,042.4
ETS_auto_log	4	110,633.52	6	234,012.4
Prophet_log	8	191,988.54	7	415,098.3
TSLM	9	294,055.70	8	439,795.6
SNaive	6	114,889.37	9	464,522.7
Naive	10	517,678.97	10	519,314.1

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.2.1.5 RMSE Development by including more Years in Time Series

# Compute RMSE and RMSSE for 2010 and create tibble
tourism_until_i <- tourism_algarve_until2022 %>%
    filter(year(Month) <= 2010)

accuracy_algarve_stretch <- accuracy(fc_algarve_stretch, tourism_until_i) %>%
  select(c(.model, RMSE, RMSSE)) %>%
  mutate(Until_Year = 2010)

# Create tsibble of summarized RMSE and RMSSE, beginning in 2010 and including more years
for (i in 2011:2022){
  tourism_until_i <- tourism_algarve_until2022 %>%
    filter(year(Month) <= i)

  accuracy_next_year <- accuracy(fc_algarve_stretch, tourism_until_i) %>%
    select(c(.model, RMSE, RMSSE)) %>%
    mutate(Until_Year = i)

  accuracy_algarve_stretch <- rbind(accuracy_algarve_stretch, accuracy_next_year)
}

rm(accuracy_next_year, tourism_until_i) # remove variables from R environment

accuracy_algarve_stretch <- accuracy_algarve_stretch %>%
  rename(Model = .model) %>%
  select(c(Until_Year, Model, RMSE, RMSSE)) %>%
  as_tsibble(key = Model, index = Until_Year)

# Show table
accuracy_algarve_stretch %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	70,105.28	0.74
2011	ARIMA_auto	88,219.55	0.92
2012	ARIMA_auto	82,998.84	0.88
2013	ARIMA_auto	84,728.32	0.90
2014	ARIMA_auto	98,749.30	0.97
2015	ARIMA_auto	94,889.10	0.94
2016	ARIMA_auto	94,832.65	0.90
2017	ARIMA_auto	99,089.94	0.91
2018	ARIMA_auto	94,657.73	0.88
2019	ARIMA_auto	91,874.23	0.87
2020	ARIMA_auto	190,802.64	0.61
2021	ARIMA_auto	197,601.91	0.60
2022	ARIMA_auto	201,552.55	0.57
2010	ARIMA_auto_log	96,429.23	1.02
2011	ARIMA_auto_log	109,714.22	1.15
2012	ARIMA_auto_log	97,604.16	1.04
2013	ARIMA_auto_log	93,502.01	0.99
2014	ARIMA_auto_log	99,456.90	0.98
2015	ARIMA_auto_log	92,483.80	0.92
2016	ARIMA_auto_log	99,261.48	0.94
2017	ARIMA_auto_log	108,596.05	1.00
2018	ARIMA_auto_log	105,136.43	0.98
2019	ARIMA_auto_log	102,104.80	0.96
2020	ARIMA_auto_log	189,604.31	0.61
2021	ARIMA_auto_log	201,041.05	0.61
2022	ARIMA_auto_log	219,551.98	0.62
2010	ARIMA_d0D1	70,105.28	0.74
2011	ARIMA_d0D1	88,219.55	0.92
2012	ARIMA_d0D1	82,998.84	0.88
2013	ARIMA_d0D1	84,728.32	0.90
2014	ARIMA_d0D1	97,136.65	0.95
2015	ARIMA_d0D1	93,037.90	0.92
2016	ARIMA_d0D1	94,849.01	0.90
2017	ARIMA_d0D1	100,052.76	0.92
2018	ARIMA_d0D1	95,311.20	0.89
2019	ARIMA_d0D1	92,494.37	0.87
2020	ARIMA_d0D1	192,160.88	0.62
2021	ARIMA_d0D1	198,804.73	0.61
2022	ARIMA_d0D1	202,684.90	0.57
2010	ARIMA_d0D1_log	96,429.23	1.02
2011	ARIMA_d0D1_log	109,714.22	1.15
2012	ARIMA_d0D1_log	97,604.16	1.04
2013	ARIMA_d0D1_log	93,502.01	0.99
2014	ARIMA_d0D1_log	99,447.31	0.98
2015	ARIMA_d0D1_log	93,197.96	0.93
2016	ARIMA_d0D1_log	96,373.57	0.91
2017	ARIMA_d0D1_log	102,437.90	0.94
2018	ARIMA_d0D1_log	98,234.12	0.92
2019	ARIMA_d0D1_log	95,436.73	0.90
2020	ARIMA_d0D1_log	186,277.02	0.60
2021	ARIMA_d0D1_log	197,603.09	0.60
2022	ARIMA_d0D1_log	216,534.92	0.61
2010	ARIMA_d1D1	80,215.39	0.85
2011	ARIMA_d1D1	108,115.13	1.13
2012	ARIMA_d1D1	99,533.88	1.06
2013	ARIMA_d1D1	98,316.74	1.05
2014	ARIMA_d1D1	107,584.46	1.06
2015	ARIMA_d1D1	102,582.17	1.02
2016	ARIMA_d1D1	101,466.10	0.96
2017	ARIMA_d1D1	104,681.35	0.96
2018	ARIMA_d1D1	99,864.20	0.93
2019	ARIMA_d1D1	96,707.66	0.91
2020	ARIMA_d1D1	198,239.14	0.64
2021	ARIMA_d1D1	203,907.93	0.62
2022	ARIMA_d1D1	208,197.08	0.59
2010	ARIMA_d1D1_log	123,270.24	1.30
2011	ARIMA_d1D1_log	113,392.85	1.19
2012	ARIMA_d1D1_log	100,970.89	1.07
2013	ARIMA_d1D1_log	96,041.76	1.02
2014	ARIMA_d1D1_log	98,926.47	0.97
2015	ARIMA_d1D1_log	92,008.50	0.91
2016	ARIMA_d1D1_log	98,882.14	0.94
2017	ARIMA_d1D1_log	108,292.82	1.00
2018	ARIMA_d1D1_log	104,858.04	0.98
2019	ARIMA_d1D1_log	101,846.83	0.96
2020	ARIMA_d1D1_log	199,885.77	0.64
2021	ARIMA_d1D1_log	227,673.02	0.69
2022	ARIMA_d1D1_log	249,164.43	0.70
2010	Drift_STL	62,287.94	0.66
2011	Drift_STL	94,627.90	0.99
2012	Drift_STL	91,281.09	0.97
2013	Drift_STL	93,708.78	1.00
2014	Drift_STL	108,584.57	1.07
2015	Drift_STL	109,478.68	1.09
2016	Drift_STL	113,967.55	1.08
2017	Drift_STL	120,561.42	1.11
2018	Drift_STL	118,289.65	1.10
2019	Drift_STL	116,436.33	1.10
2020	Drift_STL	183,322.91	0.59
2021	Drift_STL	191,819.80	0.58
2022	Drift_STL	192,094.84	0.54
2010	Drift_STL_log	74,684.55	0.79
2011	Drift_STL_log	101,290.84	1.06
2012	Drift_STL_log	94,037.91	1.00
2013	Drift_STL_log	91,867.05	0.98
2014	Drift_STL_log	98,393.40	0.97
2015	Drift_STL_log	95,049.07	0.94
2016	Drift_STL_log	100,437.43	0.95
2017	Drift_STL_log	108,879.62	1.00
2018	Drift_STL_log	107,348.60	1.00
2019	Drift_STL_log	107,486.85	1.02
2020	Drift_STL_log	178,555.20	0.57
2021	Drift_STL_log	192,742.56	0.59
2022	Drift_STL_log	245,453.38	0.69
2010	ETS_auto	146,020.67	1.54
2011	ETS_auto	139,752.96	1.46
2012	ETS_auto	133,469.61	1.42
2013	ETS_auto	123,352.49	1.31
2014	ETS_auto	123,380.66	1.21
2015	ETS_auto	116,988.18	1.16
2016	ETS_auto	115,563.87	1.10
2017	ETS_auto	118,885.83	1.09
2018	ETS_auto	114,030.20	1.06
2019	ETS_auto	110,673.75	1.05
2020	ETS_auto	272,351.63	0.87
2021	ETS_auto	273,142.91	0.83
2022	ETS_auto	270,982.43	0.77
2010	ETS_auto_log	154,702.00	1.64
2011	ETS_auto_log	138,551.81	1.45
2012	ETS_auto_log	126,522.49	1.35
2013	ETS_auto_log	117,174.49	1.25
2014	ETS_auto_log	118,135.40	1.16
2015	ETS_auto_log	111,620.94	1.11
2016	ETS_auto_log	111,126.55	1.05
2017	ETS_auto_log	116,802.40	1.07
2018	ETS_auto_log	113,332.97	1.06
2019	ETS_auto_log	110,633.52	1.05
2020	ETS_auto_log	212,743.61	0.68
2021	ETS_auto_log	226,387.68	0.69
2022	ETS_auto_log	234,012.40	0.66
2010	HWA	105,694.55	1.12
2011	HWA	119,634.03	1.25
2012	HWA	111,480.71	1.19
2013	HWA	109,190.62	1.16
2014	HWA	117,851.46	1.16
2015	HWA	115,094.44	1.14
2016	HWA	111,504.74	1.06
2017	HWA	112,628.17	1.04
2018	HWA	109,063.50	1.02
2019	HWA	105,505.57	1.00
2020	HWA	257,231.23	0.83
2021	HWA	261,241.23	0.80
2022	HWA	259,472.18	0.73
2010	HWA_log	144,308.93	1.53
2011	HWA_log	129,070.56	1.35
2012	HWA_log	119,177.03	1.27
2013	HWA_log	111,819.30	1.19
2014	HWA_log	114,244.18	1.12
2015	HWA_log	107,811.44	1.07
2016	HWA_log	110,037.94	1.04
2017	HWA_log	118,055.02	1.09
2018	HWA_log	114,925.72	1.07
2019	HWA_log	113,161.96	1.07
2020	HWA_log	212,664.31	0.68
2021	HWA_log	223,950.71	0.68
2022	HWA_log	231,042.43	0.65
2010	Naive	425,572.00	4.50
2011	Naive	443,060.84	4.63
2012	Naive	447,928.19	4.77
2013	Naive	456,249.31	4.85
2014	Naive	474,952.55	4.67
2015	Naive	485,530.92	4.82
2016	Naive	494,166.22	4.69
2017	Naive	504,209.78	4.64
2018	Naive	511,349.21	4.77
2019	Naive	517,678.97	4.89
2020	Naive	518,752.28	1.67
2021	Naive	524,088.42	1.60
2022	Naive	519,314.08	1.47
2010	Naive_log	442,384.55	4.68
2011	Naive_log	460,997.16	4.82
2012	Naive_log	466,584.80	4.96
2013	Naive_log	475,800.24	5.06
2014	Naive_log	495,843.31	4.87
2015	Naive_log	507,544.18	5.04
2016	Naive_log	517,348.00	4.91
2017	Naive_log	528,599.96	4.86
2018	Naive_log	536,716.06	5.01
2019	Naive_log	543,912.12	5.14
2020	Naive_log	545,592.70	1.75
2021	Naive_log	552,369.34	1.68
2022	Naive_log	544,703.71	1.54
2010	Prophet	111,342.02	1.18
2011	Prophet	132,093.41	1.38
2012	Prophet	148,460.68	1.58
2013	Prophet	160,310.99	1.71
2014	Prophet	187,486.66	1.84
2015	Prophet	203,981.99	2.03
2016	Prophet	219,930.48	2.09
2017	Prophet	232,914.08	2.14
2018	Prophet	237,774.61	2.22
2019	Prophet	241,566.98	2.28
2020	Prophet	419,754.59	1.35
2021	Prophet	433,904.67	1.32
2022	Prophet	437,125.80	1.23
2010	Prophet_log	209,859.77	2.22
2011	Prophet_log	207,610.46	2.17
2012	Prophet_log	206,981.87	2.20
2013	Prophet_log	206,023.98	2.19
2014	Prophet_log	216,012.06	2.12
2015	Prophet_log	214,753.16	2.13
2016	Prophet_log	209,292.25	1.99
2017	Prophet_log	203,129.51	1.87
2018	Prophet_log	195,526.02	1.82
2019	Prophet_log	191,988.54	1.81
2020	Prophet_log	338,410.46	1.09
2021	Prophet_log	384,271.44	1.17
2022	Prophet_log	415,098.34	1.17
2010	SNaive	92,048.59	0.97
2011	SNaive	99,177.61	1.04
2012	SNaive	91,436.27	0.97
2013	SNaive	92,129.31	0.98
2014	SNaive	113,161.42	1.11
2015	SNaive	108,815.62	1.08
2016	SNaive	117,533.45	1.12
2017	SNaive	122,419.19	1.13
2018	SNaive	118,239.07	1.10
2019	SNaive	114,889.37	1.09
2020	SNaive	411,007.46	1.32
2021	SNaive	426,762.60	1.30
2022	SNaive	464,522.72	1.31
2010	SNaive_log	89,507.69	0.95
2011	SNaive_log	96,186.32	1.01
2012	SNaive_log	88,621.88	0.94
2013	SNaive_log	88,970.64	0.95
2014	SNaive_log	109,713.02	1.08
2015	SNaive_log	105,286.62	1.05
2016	SNaive_log	113,656.02	1.08
2017	SNaive_log	118,405.33	1.09
2018	SNaive_log	114,477.73	1.07
2019	SNaive_log	111,193.17	1.05
2020	SNaive_log	447,861.23	1.44
2021	SNaive_log	454,866.45	1.38
2022	SNaive_log	484,382.86	1.37
2010	TSLM	109,516.56	1.16
2011	TSLM	125,832.25	1.32
2012	TSLM	138,058.91	1.47
2013	TSLM	158,654.72	1.69
2014	TSLM	200,005.25	1.97
2015	TSLM	225,307.23	2.24
2016	TSLM	254,193.09	2.41
2017	TSLM	280,205.32	2.58
2018	TSLM	289,556.46	2.70
2019	TSLM	294,055.70	2.78
2020	TSLM	418,948.94	1.35
2021	TSLM	444,215.10	1.35
2022	TSLM	439,795.57	1.24
2010	TSLM_log	128,456.75	1.36
2011	TSLM_log	157,282.58	1.64
2012	TSLM_log	177,116.98	1.88
2013	TSLM_log	203,031.66	2.16
2014	TSLM_log	247,233.56	2.43
2015	TSLM_log	274,262.86	2.72
2016	TSLM_log	303,455.25	2.88
2017	TSLM_log	327,193.31	3.01
2018	TSLM_log	333,192.10	3.11
2019	TSLM_log	333,098.41	3.15
2020	TSLM_log	435,722.72	1.40
2021	TSLM_log	442,442.70	1.35
2022	TSLM_log	444,344.45	1.25

All Models

# Plot development of RMSE for period 2010-2022
accuracy_algarve_stretch %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_algarve_stretch %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_algarve_stretch %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_algarve_stretch %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_algarve_stretch %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	517,678.97	518,752.3	1,073.31	0.0021
Naive_log	543,912.12	545,592.7	1,680.58	0.0031
TSLM_log	333,098.41	435,722.7	102,624.30	0.3081
TSLM	294,055.70	418,948.9	124,893.25	0.4247
Drift_STL	116,436.33	183,322.9	66,886.58	0.5744
Drift_STL_log	107,486.85	178,555.2	71,068.35	0.6612
Prophet	241,566.98	419,754.6	178,187.61	0.7376
Prophet_log	191,988.54	338,410.5	146,421.92	0.7627
ARIMA_auto_log	102,104.80	189,604.3	87,499.52	0.8570
HWA_log	113,161.96	212,664.3	99,502.35	0.8793
ETS_auto_log	110,633.52	212,743.6	102,110.09	0.9230
ARIMA_d0D1_log	95,436.73	186,277.0	90,840.29	0.9518
ARIMA_d1D1_log	101,846.83	199,885.8	98,038.95	0.9626
ARIMA_d1D1	96,707.66	198,239.1	101,531.48	1.0499
ARIMA_auto	91,874.23	190,802.6	98,928.41	1.0768
ARIMA_d0D1	92,494.37	192,160.9	99,666.51	1.0775
HWA	105,505.57	257,231.2	151,725.66	1.4381
ETS_auto	110,673.75	272,351.6	161,677.88	1.4609
SNaive	114,889.37	411,007.5	296,118.09	2.5774
SNaive_log	111,193.17	447,861.2	336,668.06	3.0278

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

Each Model once

# Plot development of RMSE for period 2010-2022
accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	517,678.97	518,752.3	1,073.31	0.0021
TSLM	294,055.70	418,948.9	124,893.25	0.4247
Drift_STL	116,436.33	183,322.9	66,886.58	0.5744
Prophet_log	191,988.54	338,410.5	146,421.92	0.7627
HWA_log	113,161.96	212,664.3	99,502.35	0.8793
ETS_auto_log	110,633.52	212,743.6	102,110.09	0.9230
ARIMA_d1D1	96,707.66	198,239.1	101,531.48	1.0499
ARIMA_auto	91,874.23	190,802.6	98,928.41	1.0768
ARIMA_d0D1	92,494.37	192,160.9	99,666.51	1.0775
SNaive	114,889.37	411,007.5	296,118.09	2.5774

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

2.2.1.6 RMSE per Year

All Models

# Calculate RMSE per year and save as tsibble
rmse_pyear_algarve_stretch <- error_fc_algarve_stretch %>%
  mutate(Year = year(Month)) %>%
  index_by(Year) %>%
  group_by(Model) %>%
  summarise(RMSE = (mean(Forecast_Error**2))**0.5)

# Create Plot for 2010-2022
rmse_pyear_algarve_stretch %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Create Plot for 2020-2022
rmse_pyear_algarve_stretch %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_algarve_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	529,365.7	-42,134.88	-0.0737
Naive_log	562,122.2	-42,713.95	-0.0706
TSLM_log	989,369.3	657,115.22	1.9777
TSLM	1,032,479.0	700,664.20	2.1116
Prophet	1,163,867.3	890,526.49	3.2579
Drift_STL_log	484,940.5	376,217.36	3.4603
Drift_STL	483,845.0	385,650.22	3.9274
Prophet_log	944,003.2	787,407.53	5.0283
HWA_log	607,808.3	511,969.89	5.3420
ETS_auto_log	612,748.3	530,295.41	6.4315
ARIMA_auto_log	539,623.8	470,552.22	6.8125
ARIMA_d0D1_log	539,081.4	474,025.89	7.2865
ARIMA_d1D1_log	579,456.5	510,384.86	7.3892
ARIMA_auto	562,186.2	500,802.37	8.1585
ARIMA_d0D1	566,243.5	504,647.65	8.1929
ARIMA_d1D1	582,033.2	520,649.29	8.4819
ETS_auto	832,732.1	758,834.65	10.2688
HWA	785,196.0	719,922.55	11.0293
SNaive	1,313,850.4	1,235,292.24	15.7246
SNaive_log	1,443,169.2	1,367,718.15	18.1272

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_algarve_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ETS_auto	281,700.4	-551,031.71	-0.6617
SNaive_log	525,799.7	-917,369.47	-0.6357
HWA	301,855.6	-483,340.39	-0.6156
SNaive	572,116.5	-741,733.82	-0.5645
ARIMA_d1D1	258,176.4	-323,856.81	-0.5564
ARIMA_d0D1	260,952.2	-305,291.36	-0.5392
ARIMA_auto	260,952.2	-301,234.05	-0.5358
Prophet	566,697.5	-597,169.77	-0.5131
TSLM_log	510,557.9	-478,811.39	-0.4840
HWA_log	323,047.8	-284,760.54	-0.4685
ARIMA_d0D1_log	294,742.8	-244,338.56	-0.4532
Drift_STL	268,063.1	-215,781.91	-0.4460
ARIMA_auto_log	299,269.6	-240,354.22	-0.4454
ETS_auto_log	342,283.9	-270,464.42	-0.4414
Drift_STL_log	308,374.4	-176,566.13	-0.3641
TSLM	661,229.4	-371,249.62	-0.3596
ARIMA_d1D1_log	427,226.5	-152,229.91	-0.2627
Prophet_log	715,706.9	-228,296.25	-0.2418
Naive	579,552.2	50,186.51	0.0948
Naive_log	622,058.9	59,936.65	0.1066

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_algarve_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
TSLM	315,680.6	-345,548.78	-0.5226
Naive_log	308,006.6	-314,052.33	-0.5049
Naive	387,466.0	-192,086.23	-0.3314
HWA	212,644.7	-89,210.90	-0.2955
Drift_STL	198,581.7	-69,481.37	-0.2592
ETS_auto	212,644.7	-69,055.69	-0.2451
Prophet	508,346.2	-58,351.30	-0.1030
TSLM_log	487,767.0	-22,790.92	-0.0446
ARIMA_auto	280,124.0	19,171.78	0.0735
ARIMA_d0D1	280,124.0	19,171.78	0.0735
ETS_auto_log	372,843.0	30,559.06	0.0893
HWA_log	361,691.8	38,644.05	0.1196
ARIMA_d1D1	292,861.7	34,685.29	0.1343
Prophet_log	873,909.0	158,202.04	0.2210
ARIMA_d1D1_log	555,006.9	127,780.40	0.2991
ARIMA_auto_log	484,826.5	185,556.92	0.6200
ARIMA_d0D1_log	484,826.5	190,083.70	0.6449
SNaive	1,011,683.0	439,566.46	0.7683
SNaive_log	948,675.5	422,875.82	0.8043
Drift_STL_log	783,958.8	475,584.35	1.5422

Each Model once

# Create Plot for 2010-2022
rmse_pyear_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022")

# Create Plot for 2020-2022
rmse_pyear_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022")

# Show RMSE of specific years with Difference to year before
# Show RMSE of 2020
rmse_pyear_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	529,365.7	-42,134.88	-0.0737
TSLM	1,032,479.0	700,664.20	2.1116
Drift_STL	483,845.0	385,650.22	3.9274
Prophet_log	944,003.2	787,407.53	5.0283
HWA_log	607,808.3	511,969.89	5.3420
ETS_auto_log	612,748.3	530,295.41	6.4315
ARIMA_auto	562,186.2	500,802.37	8.1585
ARIMA_d0D1	566,243.5	504,647.65	8.1929
ARIMA_d1D1	582,033.2	520,649.29	8.4819
SNaive	1,313,850.4	1,235,292.24	15.7246

# Show RMSE of 2021
rmse_pyear_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
SNaive	572,116.5	-741,733.82	-0.5645
ARIMA_d1D1	258,176.4	-323,856.81	-0.5564
ARIMA_d0D1	260,952.2	-305,291.36	-0.5392
ARIMA_auto	260,952.2	-301,234.05	-0.5358
HWA_log	323,047.8	-284,760.54	-0.4685
Drift_STL	268,063.1	-215,781.91	-0.4460
ETS_auto_log	342,283.9	-270,464.42	-0.4414
TSLM	661,229.4	-371,249.62	-0.3596
Prophet_log	715,706.9	-228,296.25	-0.2418
Naive	579,552.2	50,186.51	0.0948

# Show RMSE of 2022
rmse_pyear_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
TSLM	315,680.6	-345,548.78	-0.5226
Naive	387,466.0	-192,086.23	-0.3314
Drift_STL	198,581.7	-69,481.37	-0.2592
ARIMA_auto	280,124.0	19,171.78	0.0735
ARIMA_d0D1	280,124.0	19,171.78	0.0735
ETS_auto_log	372,843.0	30,559.06	0.0893
HWA_log	361,691.8	38,644.05	0.1196
ARIMA_d1D1	292,861.7	34,685.29	0.1343
Prophet_log	873,909.0	158,202.04	0.2210
SNaive	1,011,683.0	439,566.46	0.7683

2.2.1.7 Change of RMSSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_stretch, tourism_algarve_until2019) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_stretch, tourism_algarve_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
Drift_STL	14	1.0999	1	0.5424
ARIMA_auto	1	0.8679	2	0.5691
ARIMA_d0D1	2	0.8737	3	0.5723
ARIMA_d1D1	4	0.9135	4	0.5878
ARIMA_d0D1_log	3	0.9015	5	0.6114
ARIMA_auto_log	6	0.9645	6	0.6199
HWA_log	12	1.0690	7	0.6523
ETS_auto_log	9	1.0451	8	0.6607
Drift_STL_log	8	1.0153	9	0.6930
ARIMA_d1D1_log	5	0.9621	10	0.7035
HWA	7	0.9966	11	0.7326
ETS_auto	10	1.0455	12	0.7651
Prophet_log	15	1.8136	13	1.1720
Prophet	16	2.2819	14	1.2342
TSLM	17	2.7777	15	1.2417
TSLM_log	18	3.1465	16	1.2546
SNaive	13	1.0853	17	1.3115
SNaive_log	11	1.0504	18	1.3676
Naive	19	4.8901	19	1.4662
Naive_log	20	5.1379	20	1.5379

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_stretch, tourism_algarve_until2019) %>%
  filter(.model %in% best_models_fc_algarve_stretch) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_stretch, tourism_algarve_until2022) %>%
  filter(.model %in% best_models_fc_algarve_stretch) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
Drift_STL	7	1.0999	1	0.5424
ARIMA_auto	1	0.8679	2	0.5691
ARIMA_d0D1	2	0.8737	3	0.5723
ARIMA_d1D1	3	0.9135	4	0.5878
HWA_log	5	1.0690	5	0.6523
ETS_auto_log	4	1.0451	6	0.6607
Prophet_log	8	1.8136	7	1.1720
TSLM	9	2.7777	8	1.2417
SNaive	6	1.0853	9	1.3115
Naive	10	4.8901	10	1.4662

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.2.1.8 RMSSE Development by including more Years in Time Series

All Models

# Plot development of RMSSE for period 2010-2022
accuracy_algarve_stretch %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_algarve_stretch %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_algarve_stretch %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

Each Model once

# Plot development of RMSSE for period 2010-2022
accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_algarve_stretch %>%
  filter(Model %in% best_models_fc_algarve_stretch) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSSE")

2.2.2 Rolling Window Cross-Validation

2.2.2.1 Time series Cross-Validation & Seasonal Strength Test

# Cross-Validation with sliding Window to create Training sets
data_slide_algarve <- tourism_algarve_until2022 %>%
  slide_tsibble (.size = 120, .step = 1) %>%
  filter (.id != max(.id))

# Testing for Seasonal Strength
data_slide_algarve %>%
  features(Overnight_Stays, unitroot_nsdiffs) %>%
  group_by(Region) %>%
  summarise(Mean_nsdiffs = (mean(nsdiffs))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Strength Test</span>", align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Strength Test

Region	Mean_nsdiffs
Algarve	1

2.2.2.2 Fitting Models and one-step ahead Forecasts

# Fit models
fit_algarve_slide <- data_slide_algarve %>%
  model(
    SNaive = SNAIVE(Overnight_Stays),
    Drift_STL = decomposition_model(STL(Overnight_Stays),RW(season_adjust ~ drift())),
    Naive = NAIVE(Overnight_Stays),
    TSLM = TSLM(Overnight_Stays ~ trend() + season()),
    ETS_auto = ETS(Overnight_Stays),
    HWA = ETS(Overnight_Stays ~ error("A") + trend("A") + season("A")),
    ARIMA_auto = ARIMA(Overnight_Stays),
    ARIMA_d1D1 = ARIMA(Overnight_Stays ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)),
    Prophet = fable.prophet::prophet(Overnight_Stays ~ season(period = 12)),
    SNaive_log = SNAIVE(log(Overnight_Stays)),
    Drift_STL_log = decomposition_model(STL(log(Overnight_Stays)),RW(season_adjust ~ drift())),
    Naive_log = NAIVE(log(Overnight_Stays)),
    TSLM_log = TSLM(log(Overnight_Stays) ~ trend() + season()),
    ETS_auto_log = ETS(log(Overnight_Stays)),
    HWA_log = ETS(log(Overnight_Stays) ~ error("A") + trend("A") + season("A")),
    ARIMA_auto_log = ARIMA(log(Overnight_Stays)),
    ARIMA_d1D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)),
    Prophet_log = fable.prophet::prophet(log(Overnight_Stays) ~ season(period = 12))
    )

# Perform a one-step ahead Forecast
fc_algarve_slide <- fit_algarve_slide %>% forecast(h=1)

2.2.2.3 Forecast Errors

# Calculate forecast error per observation and model
error_fc_algarve_slide <- merge(tourism_algarve_until2022, fc_algarve_slide, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# Show table
error_fc_algarve_slide %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Forecast Error per Observation and Model</span>", digits = 2, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Forecast Error per Observation and Model

Month	Overnight_Stays	Model	Point_Forecast	Forecast_Error
2010 Jan	366,296	ARIMA_auto	383,209.18	-16,913.18
2010 Feb	533,056	ARIMA_auto	553,747.81	-20,691.81
2010 Mar	742,227	ARIMA_auto	776,070.91	-33,843.91
2010 Apr	902,745	ARIMA_auto	963,800.05	-61,055.05
2010 May	1,107,303	ARIMA_auto	1,169,244.00	-61,941.00
2010 Jun	1,464,695	ARIMA_auto	1,443,666.83	21,028.17
2010 Jul	2,050,478	ARIMA_auto	1,889,200.31	161,277.69
2010 Aug	2,468,924	ARIMA_auto	2,342,001.53	126,922.47
2010 Sep	1,696,356	ARIMA_auto	1,665,270.23	31,085.77
2010 Oct	1,104,659	ARIMA_auto	1,134,281.75	-29,622.75
2010 Nov	445,221	ARIMA_auto	525,011.54	-79,790.54
2010 Dec	365,490	ARIMA_auto	398,582.21	-33,092.21
2011 Jan	357,209	ARIMA_auto	390,697.37	-33,488.37
2011 Feb	503,831	ARIMA_auto	547,744.56	-43,913.56
2011 Mar	761,343	ARIMA_auto	760,865.78	477.22
2011 Apr	1,177,115	ARIMA_auto	947,934.38	229,180.62
2011 May	1,169,516	ARIMA_auto	1,236,421.95	-66,905.95
2011 Jun	1,576,730	ARIMA_auto	1,522,343.38	54,386.62
2011 Jul	2,208,160	ARIMA_auto	2,011,182.78	196,977.22
2011 Aug	2,572,404	ARIMA_auto	2,494,140.49	78,263.51
2011 Sep	1,731,056	ARIMA_auto	1,774,907.59	-43,851.59
2011 Oct	1,161,751	ARIMA_auto	1,179,161.62	-17,410.62
2011 Nov	427,550	ARIMA_auto	533,211.22	-105,661.22
2011 Dec	333,201	ARIMA_auto	387,919.21	-54,718.21
2012 Jan	359,355	ARIMA_auto	316,172.02	43,182.98
2012 Feb	531,709	ARIMA_auto	506,064.67	25,644.33
2012 Mar	751,024	ARIMA_auto	764,774.07	-13,750.07
2012 Apr	1,017,976	ARIMA_auto	1,049,740.84	-31,764.84
2012 May	1,194,673	ARIMA_auto	1,163,003.23	31,669.77
2012 Jun	1,678,327	ARIMA_auto	1,523,142.37	155,184.63
2012 Jul	2,296,474	ARIMA_auto	2,130,757.92	165,716.08
2012 Aug	2,622,801	ARIMA_auto	2,610,979.05	11,821.95
2012 Sep	1,829,252	ARIMA_auto	1,815,672.84	13,579.16
2012 Oct	1,244,751	ARIMA_auto	1,220,034.83	24,716.17
2012 Nov	453,958	ARIMA_auto	537,828.98	-83,870.98
2012 Dec	346,474	ARIMA_auto	393,653.13	-47,179.13
2013 Jan	369,969	ARIMA_auto	357,984.96	11,984.04
2013 Feb	520,055	ARIMA_auto	520,320.09	-265.09
2013 Mar	840,024	ARIMA_auto	755,280.63	84,743.37
2013 Apr	986,191	ARIMA_auto	1,068,003.28	-81,812.28
2013 May	1,382,234	ARIMA_auto	1,193,694.67	188,539.33
2013 Jun	1,814,108	ARIMA_auto	1,644,474.44	169,633.56
2013 Jul	2,387,304	ARIMA_auto	2,336,871.43	50,432.57
2013 Aug	2,764,686	ARIMA_auto	2,720,708.39	43,977.61
2013 Sep	1,943,037	ARIMA_auto	1,906,278.51	36,758.49
2013 Oct	1,291,360	ARIMA_auto	1,317,260.82	-25,900.82
2013 Nov	455,695	ARIMA_auto	543,153.58	-87,458.58
2013 Dec	358,062	ARIMA_auto	381,742.27	-23,680.27
2014 Jan	377,387	ARIMA_auto	359,355.81	18,031.19
2014 Feb	543,470	ARIMA_auto	506,468.49	37,001.51
2014 Mar	749,773	ARIMA_auto	810,556.86	-60,783.86
2014 Apr	1,337,145	ARIMA_auto	1,011,807.46	325,337.54
2014 May	1,538,342	ARIMA_auto	1,380,047.41	158,294.59
2014 Jun	1,994,167	ARIMA_auto	1,922,404.08	71,762.92
2014 Jul	2,529,246	ARIMA_auto	2,568,525.94	-39,279.94
2014 Aug	3,069,865	ARIMA_auto	2,868,855.58	201,009.42
2014 Sep	2,089,656	ARIMA_auto	2,145,805.84	-56,149.84
2014 Oct	1,477,481	ARIMA_auto	1,493,296.89	-15,815.89
2014 Nov	502,473	ARIMA_auto	674,376.09	-171,903.09
2014 Dec	382,543	ARIMA_auto	514,599.15	-132,056.15
2015 Jan	381,607	ARIMA_auto	483,566.52	-101,959.52
2015 Feb	544,777	ARIMA_auto	605,863.33	-61,086.33
2015 Mar	827,071	ARIMA_auto	830,922.73	-3,851.73
2015 Apr	1,242,844	ARIMA_auto	1,295,334.10	-52,490.10
2015 May	1,654,526	ARIMA_auto	1,521,644.03	132,881.97
2015 Jun	2,079,484	ARIMA_auto	2,025,568.90	53,915.10
2015 Jul	2,688,710	ARIMA_auto	2,592,973.54	95,736.46
2015 Aug	3,108,357	ARIMA_auto	3,130,860.88	-22,503.88
2015 Sep	2,196,681	ARIMA_auto	2,183,488.34	13,192.66
2015 Oct	1,553,142	ARIMA_auto	1,566,536.14	-13,394.14
2015 Nov	552,778	ARIMA_auto	623,827.56	-71,049.56
2015 Dec	426,419	ARIMA_auto	479,056.69	-52,637.69
2016 Jan	443,150	ARIMA_auto	461,129.06	-17,979.06
2016 Feb	664,278	ARIMA_auto	612,808.58	51,469.42
2016 Mar	1,089,392	ARIMA_auto	900,073.10	189,318.90
2016 Apr	1,335,308	ARIMA_auto	1,446,392.58	-111,084.58
2016 May	1,828,292	ARIMA_auto	1,749,763.85	78,528.15
2016 Jun	2,288,337	ARIMA_auto	2,173,145.38	115,191.62
2016 Jul	2,848,570	ARIMA_auto	2,836,949.72	11,620.28
2016 Aug	3,204,047	ARIMA_auto	3,277,298.07	-73,251.07
2016 Sep	2,378,618	ARIMA_auto	2,310,420.93	68,197.07
2016 Oct	1,793,822	ARIMA_auto	1,706,785.08	87,036.92
2016 Nov	653,514	ARIMA_auto	727,224.71	-73,710.71
2016 Dec	478,510	ARIMA_auto	535,974.79	-57,464.79
2017 Jan	495,629	ARIMA_auto	522,821.69	-27,192.69
2017 Feb	704,532	ARIMA_auto	716,133.63	-11,601.63
2017 Mar	1,015,421	ARIMA_auto	1,115,007.20	-99,586.20
2017 Apr	1,765,170	ARIMA_auto	1,447,373.17	317,796.83
2017 May	1,970,072	ARIMA_auto	1,992,718.95	-22,646.95
2017 Jun	2,417,100	ARIMA_auto	2,513,064.15	-95,964.15
2017 Jul	2,968,641	ARIMA_auto	3,064,175.65	-95,534.65
2017 Aug	3,295,406	ARIMA_auto	3,416,895.79	-121,489.79
2017 Sep	2,470,298	ARIMA_auto	2,430,967.07	39,330.93
2017 Oct	1,911,961	ARIMA_auto	1,877,242.62	34,718.38
2017 Nov	680,373	ARIMA_auto	771,108.75	-90,735.75
2017 Dec	512,548	ARIMA_auto	575,419.46	-62,871.46
2018 Jan	503,908	ARIMA_auto	577,019.23	-73,111.23
2018 Feb	731,090	ARIMA_auto	765,591.35	-34,501.35
2018 Mar	1,151,455	ARIMA_auto	1,066,492.41	84,962.59
2018 Apr	1,575,078	ARIMA_auto	1,656,810.39	-81,732.39
2018 May	2,003,996	ARIMA_auto	1,957,722.25	46,273.75
2018 Jun	2,381,154	ARIMA_auto	2,394,792.73	-13,638.73
2018 Jul	2,981,643	ARIMA_auto	2,992,114.15	-10,471.15
2018 Aug	3,371,918	ARIMA_auto	3,275,465.48	96,452.52
2018 Sep	2,499,368	ARIMA_auto	2,547,936.11	-48,568.11
2018 Oct	1,956,693	ARIMA_auto	1,866,233.33	90,459.67
2018 Nov	732,141	ARIMA_auto	749,200.79	-17,059.79
2018 Dec	554,803	ARIMA_auto	589,050.19	-34,247.19
2019 Jan	548,686	ARIMA_auto	578,958.80	-30,272.80
2019 Feb	739,981	ARIMA_auto	829,537.60	-89,556.60
2019 Mar	1,078,918	ARIMA_auto	1,230,625.16	-151,707.16
2019 Apr	1,795,494	ARIMA_auto	1,674,215.31	121,278.69
2019 May	1,990,529	ARIMA_auto	2,088,829.83	-98,300.83
2019 Jun	2,425,834	ARIMA_auto	2,494,152.66	-68,318.66
2019 Jul	2,988,668	ARIMA_auto	3,075,242.77	-86,574.77
2019 Aug	3,439,271	ARIMA_auto	3,433,572.40	5,698.60
2019 Sep	2,573,527	ARIMA_auto	2,572,059.64	1,467.36
2019 Oct	1,930,852	ARIMA_auto	2,014,225.55	-83,373.55
2019 Nov	785,875	ARIMA_auto	813,564.03	-27,689.03
2019 Dec	602,860	ARIMA_auto	644,571.01	-41,711.01
2020 Jan	560,368	ARIMA_auto	613,909.41	-53,541.41
2020 Feb	844,247	ARIMA_auto	805,378.31	38,868.69
2020 Mar	513,360	ARIMA_auto	1,181,042.08	-667,682.08
2020 Apr	25,614	ARIMA_auto	1,830,957.65	-1,805,343.65
2020 May	40,932	ARIMA_auto	169,128.30	-128,196.30
2020 Jun	330,393	ARIMA_auto	494,251.40	-163,858.40
2020 Jul	1,035,732	ARIMA_auto	940,908.79	94,823.21
2020 Aug	2,090,569	ARIMA_auto	1,460,524.75	630,044.25
2020 Sep	1,418,185	ARIMA_auto	1,401,786.37	16,398.63
2020 Oct	696,087	ARIMA_auto	740,960.02	-44,873.02
2020 Nov	181,873	ARIMA_auto	-463,983.61	645,856.61
2020 Dec	153,351	ARIMA_auto	137,651.71	15,699.29
2021 Jan	105,336	ARIMA_auto	124,934.05	-19,598.05
2021 Feb	66,194	ARIMA_auto	339,544.26	-273,350.26
2021 Mar	84,413	ARIMA_auto	10,773.17	73,639.83
2021 Apr	138,661	ARIMA_auto	339,843.25	-201,182.25
2021 May	502,057	ARIMA_auto	320,110.87	181,946.13
2021 Jun	1,182,009	ARIMA_auto	974,295.33	207,713.67
2021 Jul	1,551,789	ARIMA_auto	1,882,573.58	-330,784.58
2021 Aug	2,762,537	ARIMA_auto	2,008,506.97	754,030.03
2021 Sep	1,869,194	ARIMA_auto	2,090,163.80	-220,969.80
2021 Oct	1,584,764	ARIMA_auto	1,164,396.89	420,367.11
2021 Nov	651,051	ARIMA_auto	781,633.35	-130,582.35
2021 Dec	376,031	ARIMA_auto	570,638.49	-194,607.49
2022 Jan	344,634	ARIMA_auto	363,573.17	-18,939.17
2022 Feb	590,122	ARIMA_auto	394,543.48	195,578.52
2022 Mar	873,841	ARIMA_auto	735,377.39	138,463.61
2022 Apr	1,629,377	ARIMA_auto	1,118,324.65	511,052.35
2022 May	1,867,744	ARIMA_auto	1,939,005.04	-71,261.04
2022 Jun	2,230,207	ARIMA_auto	2,359,081.60	-128,874.60
2010 Jan	366,296	ARIMA_auto_log	410,896.99	-44,600.99
2010 Feb	533,056	ARIMA_auto_log	548,146.21	-15,090.21
2010 Mar	742,227	ARIMA_auto_log	735,160.14	7,066.86
2010 Apr	902,745	ARIMA_auto_log	940,375.08	-37,630.08
2010 May	1,107,303	ARIMA_auto_log	1,109,063.95	-1,760.95
2010 Jun	1,464,695	ARIMA_auto_log	1,370,515.87	94,179.13
2010 Jul	2,050,478	ARIMA_auto_log	1,800,902.48	249,575.52
2010 Aug	2,468,924	ARIMA_auto_log	2,271,431.31	197,492.69
2010 Sep	1,696,356	ARIMA_auto_log	1,656,195.88	40,160.12
2010 Oct	1,104,659	ARIMA_auto_log	1,141,999.88	-37,340.88
2010 Nov	445,221	ARIMA_auto_log	533,029.55	-87,808.55
2010 Dec	365,490	ARIMA_auto_log	396,275.68	-30,785.68
2011 Jan	357,209	ARIMA_auto_log	392,493.52	-35,284.52
2011 Feb	503,831	ARIMA_auto_log	526,269.99	-22,438.99
2011 Mar	761,343	ARIMA_auto_log	710,660.40	50,682.60
2011 Apr	1,177,115	ARIMA_auto_log	914,005.93	263,109.07
2011 May	1,169,516	ARIMA_auto_log	1,200,032.50	-30,516.50
2011 Jun	1,576,730	ARIMA_auto_log	1,519,244.07	57,485.93
2011 Jul	2,208,160	ARIMA_auto_log	2,054,282.59	153,877.41
2011 Aug	2,572,404	ARIMA_auto_log	2,527,376.76	45,027.24
2011 Sep	1,731,056	ARIMA_auto_log	1,732,512.05	-1,456.05
2011 Oct	1,161,751	ARIMA_auto_log	1,138,727.54	23,023.46
2011 Nov	427,550	ARIMA_auto_log	498,068.21	-70,518.21
2011 Dec	333,201	ARIMA_auto_log	381,462.81	-48,261.81
2012 Jan	359,355	ARIMA_auto_log	361,485.92	-2,130.92
2012 Feb	531,709	ARIMA_auto_log	493,276.40	38,432.60
2012 Mar	751,024	ARIMA_auto_log	752,109.58	-1,085.58
2012 Apr	1,017,976	ARIMA_auto_log	1,053,137.75	-35,161.75
2012 May	1,194,673	ARIMA_auto_log	1,140,813.59	53,859.41
2012 Jun	1,678,327	ARIMA_auto_log	1,531,096.02	147,230.98
2012 Jul	2,296,474	ARIMA_auto_log	2,181,692.41	114,781.59
2012 Aug	2,622,801	ARIMA_auto_log	2,642,859.07	-20,058.07
2012 Sep	1,829,252	ARIMA_auto_log	1,771,282.22	57,969.78
2012 Oct	1,244,751	ARIMA_auto_log	1,177,369.48	67,381.52
2012 Nov	453,958	ARIMA_auto_log	477,424.28	-23,466.28
2012 Dec	346,474	ARIMA_auto_log	369,726.42	-23,252.42
2013 Jan	369,969	ARIMA_auto_log	366,115.71	3,853.29
2013 Feb	520,055	ARIMA_auto_log	532,737.23	-12,682.23
2013 Mar	840,024	ARIMA_auto_log	761,881.08	78,142.92
2013 Apr	986,191	ARIMA_auto_log	1,129,303.52	-143,112.52
2013 May	1,382,234	ARIMA_auto_log	1,183,530.44	198,703.56
2013 Jun	1,814,108	ARIMA_auto_log	1,668,585.88	145,522.12
2013 Jul	2,387,304	ARIMA_auto_log	2,368,957.96	18,346.04
2013 Aug	2,764,686	ARIMA_auto_log	2,734,614.23	30,071.77
2013 Sep	1,943,037	ARIMA_auto_log	1,883,224.44	59,812.56
2013 Oct	1,291,360	ARIMA_auto_log	1,276,296.04	15,063.96
2013 Nov	455,695	ARIMA_auto_log	476,541.97	-20,846.97
2013 Dec	358,062	ARIMA_auto_log	362,205.81	-4,143.81
2014 Jan	377,387	ARIMA_auto_log	380,662.49	-3,275.49
2014 Feb	543,470	ARIMA_auto_log	539,338.18	4,131.82
2014 Mar	749,773	ARIMA_auto_log	831,671.99	-81,898.99
2014 Apr	1,337,145	ARIMA_auto_log	1,006,265.63	330,879.37
2014 May	1,538,342	ARIMA_auto_log	1,403,135.06	135,206.94
2014 Jun	1,994,167	ARIMA_auto_log	1,914,847.46	79,319.54
2014 Jul	2,529,246	ARIMA_auto_log	2,677,934.26	-148,688.26
2014 Aug	3,069,865	ARIMA_auto_log	2,945,111.30	124,753.70
2014 Sep	2,089,656	ARIMA_auto_log	2,068,833.34	20,822.66
2014 Oct	1,477,481	ARIMA_auto_log	1,379,059.46	98,421.54
2014 Nov	502,473	ARIMA_auto_log	491,049.94	11,423.06
2014 Dec	382,543	ARIMA_auto_log	381,666.50	876.50
2015 Jan	381,607	ARIMA_auto_log	403,484.24	-21,877.24
2015 Feb	544,777	ARIMA_auto_log	585,462.43	-40,685.43
2015 Mar	827,071	ARIMA_auto_log	825,832.35	1,238.65
2015 Apr	1,242,844	ARIMA_auto_log	1,305,025.19	-62,181.19
2015 May	1,654,526	ARIMA_auto_log	1,566,623.26	87,902.74
2015 Jun	2,079,484	ARIMA_auto_log	2,073,227.91	6,256.09
2015 Jul	2,688,710	ARIMA_auto_log	2,666,491.96	22,218.04
2015 Aug	3,108,357	ARIMA_auto_log	3,195,700.66	-87,343.66
2015 Sep	2,196,681	ARIMA_auto_log	2,183,784.58	12,896.42
2015 Oct	1,553,142	ARIMA_auto_log	1,515,783.83	37,358.17
2015 Nov	552,778	ARIMA_auto_log	525,923.15	26,854.85
2015 Dec	426,419	ARIMA_auto_log	410,747.40	15,671.60
2016 Jan	443,150	ARIMA_auto_log	422,136.45	21,013.55
2016 Feb	664,278	ARIMA_auto_log	614,218.78	50,059.22
2016 Mar	1,089,392	ARIMA_auto_log	925,753.17	163,638.83
2016 Apr	1,335,308	ARIMA_auto_log	1,574,039.17	-238,731.17
2016 May	1,828,292	ARIMA_auto_log	1,892,288.89	-63,996.89
2016 Jun	2,288,337	ARIMA_auto_log	2,378,383.26	-90,046.26
2016 Jul	2,848,570	ARIMA_auto_log	2,997,142.31	-148,572.31
2016 Aug	3,204,047	ARIMA_auto_log	3,496,251.91	-292,204.91
2016 Sep	2,378,618	ARIMA_auto_log	2,371,014.46	7,603.54
2016 Oct	1,793,822	ARIMA_auto_log	1,680,176.52	113,645.48
2016 Nov	653,514	ARIMA_auto_log	596,589.04	56,924.96
2016 Dec	478,510	ARIMA_auto_log	468,865.25	9,644.75
2017 Jan	495,629	ARIMA_auto_log	478,749.36	16,879.64
2017 Feb	704,532	ARIMA_auto_log	710,523.63	-5,991.63
2017 Mar	1,015,421	ARIMA_auto_log	1,079,915.55	-64,494.55
2017 Apr	1,765,170	ARIMA_auto_log	1,530,011.82	235,158.18
2017 May	1,970,072	ARIMA_auto_log	2,130,989.97	-160,917.97
2017 Jun	2,417,100	ARIMA_auto_log	2,583,588.66	-166,488.66
2017 Jul	2,968,641	ARIMA_auto_log	3,200,558.49	-231,917.49
2017 Aug	3,295,406	ARIMA_auto_log	3,610,188.23	-314,782.23
2017 Sep	2,470,298	ARIMA_auto_log	2,556,993.64	-86,695.64
2017 Oct	1,911,961	ARIMA_auto_log	1,872,151.02	39,809.98
2017 Nov	680,373	ARIMA_auto_log	678,873.20	1,499.80
2017 Dec	512,548	ARIMA_auto_log	508,696.21	3,851.79
2018 Jan	503,908	ARIMA_auto_log	524,897.26	-20,989.26
2018 Feb	731,090	ARIMA_auto_log	760,204.55	-29,114.55
2018 Mar	1,151,455	ARIMA_auto_log	1,166,635.99	-15,180.99
2018 Apr	1,575,078	ARIMA_auto_log	1,697,787.74	-122,709.74
2018 May	2,003,996	ARIMA_auto_log	2,074,631.68	-70,635.68
2018 Jun	2,381,154	ARIMA_auto_log	2,546,388.29	-165,234.29
2018 Jul	2,981,643	ARIMA_auto_log	3,101,215.24	-119,572.24
2018 Aug	3,371,918	ARIMA_auto_log	3,455,170.91	-83,252.91
2018 Sep	2,499,368	ARIMA_auto_log	2,589,236.63	-89,868.63
2018 Oct	1,956,693	ARIMA_auto_log	1,976,813.73	-20,120.73
2018 Nov	732,141	ARIMA_auto_log	727,043.20	5,097.80
2018 Dec	554,803	ARIMA_auto_log	543,272.92	11,530.08
2019 Jan	548,686	ARIMA_auto_log	557,018.24	-8,332.24
2019 Feb	739,981	ARIMA_auto_log	796,151.00	-56,170.00
2019 Mar	1,078,918	ARIMA_auto_log	1,159,911.36	-80,993.36
2019 Apr	1,795,494	ARIMA_auto_log	1,645,699.45	149,794.55
2019 May	1,990,529	ARIMA_auto_log	2,169,975.71	-179,446.71
2019 Jun	2,425,834	ARIMA_auto_log	2,518,404.71	-92,570.71
2019 Jul	2,988,668	ARIMA_auto_log	3,097,610.58	-108,942.58
2019 Aug	3,439,271	ARIMA_auto_log	3,321,281.13	117,989.87
2019 Sep	2,573,527	ARIMA_auto_log	2,592,717.21	-19,190.21
2019 Oct	1,930,852	ARIMA_auto_log	2,046,108.58	-115,256.58
2019 Nov	785,875	ARIMA_auto_log	735,072.90	50,802.10
2019 Dec	602,860	ARIMA_auto_log	567,564.05	35,295.95
2020 Jan	560,368	ARIMA_auto_log	582,822.35	-22,454.35
2020 Feb	844,247	ARIMA_auto_log	806,165.80	38,081.20
2020 Mar	513,360	ARIMA_auto_log	1,241,535.01	-728,175.01
2020 Apr	25,614	ARIMA_auto_log	1,892,926.55	-1,867,312.55
2020 May	40,932	ARIMA_auto_log	2,169,608.43	-2,128,676.43
2020 Jun	330,393	ARIMA_auto_log	924,926.64	-594,533.64
2020 Jul	1,035,732	ARIMA_auto_log	972,655.97	63,076.03
2020 Aug	2,090,569	ARIMA_auto_log	2,069,226.87	21,342.13
2020 Sep	1,418,185	ARIMA_auto_log	2,098,240.28	-680,055.28
2020 Oct	696,087	ARIMA_auto_log	1,194,719.85	-498,632.85
2020 Nov	181,873	ARIMA_auto_log	263,262.27	-81,389.27
2020 Dec	153,351	ARIMA_auto_log	146,875.98	6,475.02
2021 Jan	105,336	ARIMA_auto_log	193,682.11	-88,346.11
2021 Feb	66,194	ARIMA_auto_log	151,652.37	-85,458.37
2021 Mar	84,413	ARIMA_auto_log	70,804.43	13,608.57
2021 Apr	138,661	ARIMA_auto_log	50,618.45	88,042.55
2021 May	502,057	ARIMA_auto_log	244,896.62	257,160.38
2021 Jun	1,182,009	ARIMA_auto_log	1,221,324.38	-39,315.38
2021 Jul	1,551,789	ARIMA_auto_log	1,825,754.75	-273,965.75
2021 Aug	2,762,537	ARIMA_auto_log	2,381,213.34	381,323.66
2021 Sep	1,869,194	ARIMA_auto_log	2,504,750.60	-635,556.60
2021 Oct	1,584,764	ARIMA_auto_log	1,166,331.53	418,432.47
2021 Nov	651,051	ARIMA_auto_log	725,878.24	-74,827.24
2021 Dec	376,031	ARIMA_auto_log	485,920.03	-109,889.03
2022 Jan	344,634	ARIMA_auto_log	301,182.04	43,451.96
2022 Feb	590,122	ARIMA_auto_log	463,364.69	126,757.31
2022 Mar	873,841	ARIMA_auto_log	816,388.57	57,452.43
2022 Apr	1,629,377	ARIMA_auto_log	694,718.89	934,658.11
2022 May	1,867,744	ARIMA_auto_log	3,343,082.76	-1,475,338.76
2022 Jun	2,230,207	ARIMA_auto_log	2,166,684.35	63,522.65
2010 Jan	366,296	ARIMA_d0D1	383,209.18	-16,913.18
2010 Feb	533,056	ARIMA_d0D1	553,747.81	-20,691.81
2010 Mar	742,227	ARIMA_d0D1	776,070.91	-33,843.91
2010 Apr	902,745	ARIMA_d0D1	963,800.05	-61,055.05
2010 May	1,107,303	ARIMA_d0D1	1,169,244.00	-61,941.00
2010 Jun	1,464,695	ARIMA_d0D1	1,443,666.83	21,028.17
2010 Jul	2,050,478	ARIMA_d0D1	1,889,200.31	161,277.69
2010 Aug	2,468,924	ARIMA_d0D1	2,342,001.53	126,922.47
2010 Sep	1,696,356	ARIMA_d0D1	1,665,270.23	31,085.77
2010 Oct	1,104,659	ARIMA_d0D1	1,134,281.75	-29,622.75
2010 Nov	445,221	ARIMA_d0D1	525,011.54	-79,790.54
2010 Dec	365,490	ARIMA_d0D1	398,582.21	-33,092.21
2011 Jan	357,209	ARIMA_d0D1	390,697.37	-33,488.37
2011 Feb	503,831	ARIMA_d0D1	547,744.56	-43,913.56
2011 Mar	761,343	ARIMA_d0D1	760,865.78	477.22
2011 Apr	1,177,115	ARIMA_d0D1	947,934.38	229,180.62
2011 May	1,169,516	ARIMA_d0D1	1,236,421.95	-66,905.95
2011 Jun	1,576,730	ARIMA_d0D1	1,522,343.38	54,386.62
2011 Jul	2,208,160	ARIMA_d0D1	2,011,182.78	196,977.22
2011 Aug	2,572,404	ARIMA_d0D1	2,494,140.49	78,263.51
2011 Sep	1,731,056	ARIMA_d0D1	1,774,907.59	-43,851.59
2011 Oct	1,161,751	ARIMA_d0D1	1,179,161.62	-17,410.62
2011 Nov	427,550	ARIMA_d0D1	533,211.22	-105,661.22
2011 Dec	333,201	ARIMA_d0D1	387,919.21	-54,718.21
2012 Jan	359,355	ARIMA_d0D1	316,172.02	43,182.98
2012 Feb	531,709	ARIMA_d0D1	506,064.67	25,644.33
2012 Mar	751,024	ARIMA_d0D1	764,774.07	-13,750.07
2012 Apr	1,017,976	ARIMA_d0D1	1,049,740.84	-31,764.84
2012 May	1,194,673	ARIMA_d0D1	1,163,003.23	31,669.77
2012 Jun	1,678,327	ARIMA_d0D1	1,523,142.37	155,184.63
2012 Jul	2,296,474	ARIMA_d0D1	2,130,757.92	165,716.08
2012 Aug	2,622,801	ARIMA_d0D1	2,610,979.05	11,821.95
2012 Sep	1,829,252	ARIMA_d0D1	1,815,672.84	13,579.16
2012 Oct	1,244,751	ARIMA_d0D1	1,220,034.83	24,716.17
2012 Nov	453,958	ARIMA_d0D1	537,828.98	-83,870.98
2012 Dec	346,474	ARIMA_d0D1	393,653.13	-47,179.13
2013 Jan	369,969	ARIMA_d0D1	357,984.96	11,984.04
2013 Feb	520,055	ARIMA_d0D1	520,320.09	-265.09
2013 Mar	840,024	ARIMA_d0D1	755,280.63	84,743.37
2013 Apr	986,191	ARIMA_d0D1	1,068,003.28	-81,812.28
2013 May	1,382,234	ARIMA_d0D1	1,193,694.67	188,539.33
2013 Jun	1,814,108	ARIMA_d0D1	1,644,474.44	169,633.56
2013 Jul	2,387,304	ARIMA_d0D1	2,336,871.43	50,432.57
2013 Aug	2,764,686	ARIMA_d0D1	2,720,708.39	43,977.61
2013 Sep	1,943,037	ARIMA_d0D1	1,906,278.51	36,758.49
2013 Oct	1,291,360	ARIMA_d0D1	1,317,260.82	-25,900.82
2013 Nov	455,695	ARIMA_d0D1	543,153.58	-87,458.58
2013 Dec	358,062	ARIMA_d0D1	381,742.27	-23,680.27
2014 Jan	377,387	ARIMA_d0D1	359,355.81	18,031.19
2014 Feb	543,470	ARIMA_d0D1	506,468.49	37,001.51
2014 Mar	749,773	ARIMA_d0D1	810,556.86	-60,783.86
2014 Apr	1,337,145	ARIMA_d0D1	1,011,807.46	325,337.54
2014 May	1,538,342	ARIMA_d0D1	1,380,047.41	158,294.59
2014 Jun	1,994,167	ARIMA_d0D1	1,922,404.08	71,762.92
2014 Jul	2,529,246	ARIMA_d0D1	2,568,525.94	-39,279.94
2014 Aug	3,069,865	ARIMA_d0D1	2,868,855.58	201,009.42
2014 Sep	2,089,656	ARIMA_d0D1	2,062,895.43	26,760.57
2014 Oct	1,477,481	ARIMA_d0D1	1,428,183.92	49,297.08
2014 Nov	502,473	ARIMA_d0D1	630,732.25	-128,259.25
2014 Dec	382,543	ARIMA_d0D1	434,075.44	-51,532.44
2015 Jan	381,607	ARIMA_d0D1	371,719.89	9,887.11
2015 Feb	544,777	ARIMA_d0D1	495,098.66	49,678.34
2015 Mar	827,071	ARIMA_d0D1	740,484.14	86,586.86
2015 Apr	1,242,844	ARIMA_d0D1	1,245,929.47	-3,085.47
2015 May	1,654,526	ARIMA_d0D1	1,498,510.97	156,015.03
2015 Jun	2,079,484	ARIMA_d0D1	1,998,116.67	81,367.33
2015 Jul	2,688,710	ARIMA_d0D1	2,615,692.54	73,017.46
2015 Aug	3,108,357	ARIMA_d0D1	3,125,781.76	-17,424.76
2015 Sep	2,196,681	ARIMA_d0D1	2,179,432.39	17,248.61
2015 Oct	1,553,142	ARIMA_d0D1	1,528,348.63	24,793.37
2015 Nov	552,778	ARIMA_d0D1	581,926.26	-29,148.26
2015 Dec	426,419	ARIMA_d0D1	435,631.25	-9,212.25
2016 Jan	443,150	ARIMA_d0D1	413,688.63	29,461.37
2016 Feb	664,278	ARIMA_d0D1	574,207.69	90,070.31
2016 Mar	1,089,392	ARIMA_d0D1	876,263.40	213,128.60
2016 Apr	1,335,308	ARIMA_d0D1	1,407,443.77	-72,135.77
2016 May	1,828,292	ARIMA_d0D1	1,771,941.26	56,350.74
2016 Jun	2,288,337	ARIMA_d0D1	2,173,226.74	115,110.26
2016 Jul	2,848,570	ARIMA_d0D1	2,787,525.15	61,044.85
2016 Aug	3,204,047	ARIMA_d0D1	3,271,289.24	-67,242.24
2016 Sep	2,378,618	ARIMA_d0D1	2,286,559.62	92,058.38
2016 Oct	1,793,822	ARIMA_d0D1	1,646,858.70	146,963.30
2016 Nov	653,514	ARIMA_d0D1	710,937.80	-57,423.80
2016 Dec	478,510	ARIMA_d0D1	574,002.34	-95,492.34
2017 Jan	495,629	ARIMA_d0D1	533,327.93	-37,698.93
2017 Feb	704,532	ARIMA_d0D1	677,347.51	27,184.49
2017 Mar	1,015,421	ARIMA_d0D1	1,065,965.64	-50,544.64
2017 Apr	1,765,170	ARIMA_d0D1	1,335,265.90	429,904.10
2017 May	1,970,072	ARIMA_d0D1	2,047,156.11	-77,084.11
2017 Jun	2,417,100	ARIMA_d0D1	2,438,050.84	-20,950.84
2017 Jul	2,968,641	ARIMA_d0D1	2,973,717.35	-5,076.35
2017 Aug	3,295,406	ARIMA_d0D1	3,413,699.99	-118,293.99
2017 Sep	2,470,298	ARIMA_d0D1	2,469,304.51	993.49
2017 Oct	1,911,961	ARIMA_d0D1	1,856,028.98	55,932.02
2017 Nov	680,373	ARIMA_d0D1	724,874.24	-44,501.24
2017 Dec	512,548	ARIMA_d0D1	542,699.25	-30,151.25
2018 Jan	503,908	ARIMA_d0D1	539,980.15	-36,072.15
2018 Feb	731,090	ARIMA_d0D1	758,759.11	-27,669.11
2018 Mar	1,151,455	ARIMA_d0D1	1,137,274.77	14,180.23
2018 Apr	1,575,078	ARIMA_d0D1	1,631,840.99	-56,762.99
2018 May	2,003,996	ARIMA_d0D1	1,942,309.43	61,686.57
2018 Jun	2,381,154	ARIMA_d0D1	2,457,910.26	-76,756.26
2018 Jul	2,981,643	ARIMA_d0D1	2,989,103.39	-7,460.39
2018 Aug	3,371,918	ARIMA_d0D1	3,269,823.34	102,094.66
2018 Sep	2,499,368	ARIMA_d0D1	2,517,870.13	-18,502.13
2018 Oct	1,956,693	ARIMA_d0D1	1,866,233.33	90,459.67
2018 Nov	732,141	ARIMA_d0D1	749,200.79	-17,059.79
2018 Dec	554,803	ARIMA_d0D1	589,050.19	-34,247.19
2019 Jan	548,686	ARIMA_d0D1	578,958.80	-30,272.80
2019 Feb	739,981	ARIMA_d0D1	829,537.60	-89,556.60
2019 Mar	1,078,918	ARIMA_d0D1	1,230,625.16	-151,707.16
2019 Apr	1,795,494	ARIMA_d0D1	1,674,215.31	121,278.69
2019 May	1,990,529	ARIMA_d0D1	2,088,829.83	-98,300.83
2019 Jun	2,425,834	ARIMA_d0D1	2,494,152.66	-68,318.66
2019 Jul	2,988,668	ARIMA_d0D1	3,075,242.77	-86,574.77
2019 Aug	3,439,271	ARIMA_d0D1	3,433,572.40	5,698.60
2019 Sep	2,573,527	ARIMA_d0D1	2,572,059.64	1,467.36
2019 Oct	1,930,852	ARIMA_d0D1	2,014,225.55	-83,373.55
2019 Nov	785,875	ARIMA_d0D1	813,564.03	-27,689.03
2019 Dec	602,860	ARIMA_d0D1	644,571.01	-41,711.01
2020 Jan	560,368	ARIMA_d0D1	613,909.41	-53,541.41
2020 Feb	844,247	ARIMA_d0D1	805,378.31	38,868.69
2020 Mar	513,360	ARIMA_d0D1	1,181,042.08	-667,682.08
2020 Apr	25,614	ARIMA_d0D1	1,830,957.65	-1,805,343.65
2020 May	40,932	ARIMA_d0D1	169,128.30	-128,196.30
2020 Jun	330,393	ARIMA_d0D1	494,251.40	-163,858.40
2020 Jul	1,035,732	ARIMA_d0D1	940,908.79	94,823.21
2020 Aug	2,090,569	ARIMA_d0D1	1,562,731.21	527,837.79
2020 Sep	1,418,185	ARIMA_d0D1	1,732,467.87	-314,282.87
2020 Oct	696,087	ARIMA_d0D1	1,133,204.73	-437,117.73
2020 Nov	181,873	ARIMA_d0D1	-358,018.18	539,891.18
2020 Dec	153,351	ARIMA_d0D1	294,113.70	-140,762.70
2021 Jan	105,336	ARIMA_d0D1	313,948.75	-208,612.75
2021 Feb	66,194	ARIMA_d0D1	385,513.84	-319,319.84
2021 Mar	84,413	ARIMA_d0D1	77,013.73	7,399.27
2021 Apr	138,661	ARIMA_d0D1	429,807.53	-291,146.53
2021 May	502,057	ARIMA_d0D1	395,010.18	107,046.82
2021 Jun	1,182,009	ARIMA_d0D1	1,019,669.37	162,339.63
2021 Jul	1,551,789	ARIMA_d0D1	1,934,669.19	-382,880.19
2021 Aug	2,762,537	ARIMA_d0D1	2,066,985.14	695,551.86
2021 Sep	1,869,194	ARIMA_d0D1	2,090,163.80	-220,969.80
2021 Oct	1,584,764	ARIMA_d0D1	1,164,396.89	420,367.11
2021 Nov	651,051	ARIMA_d0D1	781,633.35	-130,582.35
2021 Dec	376,031	ARIMA_d0D1	570,638.49	-194,607.49
2022 Jan	344,634	ARIMA_d0D1	363,573.17	-18,939.17
2022 Feb	590,122	ARIMA_d0D1	394,543.48	195,578.52
2022 Mar	873,841	ARIMA_d0D1	735,377.39	138,463.61
2022 Apr	1,629,377	ARIMA_d0D1	1,118,324.65	511,052.35
2022 May	1,867,744	ARIMA_d0D1	1,939,005.04	-71,261.04
2022 Jun	2,230,207	ARIMA_d0D1	2,359,081.60	-128,874.60
2010 Jan	366,296	ARIMA_d0D1_log	410,896.99	-44,600.99
2010 Feb	533,056	ARIMA_d0D1_log	548,146.21	-15,090.21
2010 Mar	742,227	ARIMA_d0D1_log	735,160.14	7,066.86
2010 Apr	902,745	ARIMA_d0D1_log	940,375.08	-37,630.08
2010 May	1,107,303	ARIMA_d0D1_log	1,109,063.95	-1,760.95
2010 Jun	1,464,695	ARIMA_d0D1_log	1,370,515.87	94,179.13
2010 Jul	2,050,478	ARIMA_d0D1_log	1,800,902.48	249,575.52
2010 Aug	2,468,924	ARIMA_d0D1_log	2,271,431.31	197,492.69
2010 Sep	1,696,356	ARIMA_d0D1_log	1,656,195.88	40,160.12
2010 Oct	1,104,659	ARIMA_d0D1_log	1,141,999.88	-37,340.88
2010 Nov	445,221	ARIMA_d0D1_log	533,029.55	-87,808.55
2010 Dec	365,490	ARIMA_d0D1_log	396,275.68	-30,785.68
2011 Jan	357,209	ARIMA_d0D1_log	392,493.52	-35,284.52
2011 Feb	503,831	ARIMA_d0D1_log	526,269.99	-22,438.99
2011 Mar	761,343	ARIMA_d0D1_log	710,660.40	50,682.60
2011 Apr	1,177,115	ARIMA_d0D1_log	914,005.93	263,109.07
2011 May	1,169,516	ARIMA_d0D1_log	1,200,032.50	-30,516.50
2011 Jun	1,576,730	ARIMA_d0D1_log	1,519,244.07	57,485.93
2011 Jul	2,208,160	ARIMA_d0D1_log	2,054,282.59	153,877.41
2011 Aug	2,572,404	ARIMA_d0D1_log	2,527,376.76	45,027.24
2011 Sep	1,731,056	ARIMA_d0D1_log	1,732,512.05	-1,456.05
2011 Oct	1,161,751	ARIMA_d0D1_log	1,138,727.54	23,023.46
2011 Nov	427,550	ARIMA_d0D1_log	498,068.21	-70,518.21
2011 Dec	333,201	ARIMA_d0D1_log	381,462.81	-48,261.81
2012 Jan	359,355	ARIMA_d0D1_log	361,485.92	-2,130.92
2012 Feb	531,709	ARIMA_d0D1_log	493,276.40	38,432.60
2012 Mar	751,024	ARIMA_d0D1_log	752,109.58	-1,085.58
2012 Apr	1,017,976	ARIMA_d0D1_log	1,053,137.75	-35,161.75
2012 May	1,194,673	ARIMA_d0D1_log	1,140,813.59	53,859.41
2012 Jun	1,678,327	ARIMA_d0D1_log	1,531,096.02	147,230.98
2012 Jul	2,296,474	ARIMA_d0D1_log	2,181,692.41	114,781.59
2012 Aug	2,622,801	ARIMA_d0D1_log	2,642,859.07	-20,058.07
2012 Sep	1,829,252	ARIMA_d0D1_log	1,771,282.22	57,969.78
2012 Oct	1,244,751	ARIMA_d0D1_log	1,177,369.48	67,381.52
2012 Nov	453,958	ARIMA_d0D1_log	477,424.28	-23,466.28
2012 Dec	346,474	ARIMA_d0D1_log	369,726.42	-23,252.42
2013 Jan	369,969	ARIMA_d0D1_log	366,115.71	3,853.29
2013 Feb	520,055	ARIMA_d0D1_log	532,737.23	-12,682.23
2013 Mar	840,024	ARIMA_d0D1_log	761,881.08	78,142.92
2013 Apr	986,191	ARIMA_d0D1_log	1,129,303.52	-143,112.52
2013 May	1,382,234	ARIMA_d0D1_log	1,183,530.44	198,703.56
2013 Jun	1,814,108	ARIMA_d0D1_log	1,668,585.88	145,522.12
2013 Jul	2,387,304	ARIMA_d0D1_log	2,368,957.96	18,346.04
2013 Aug	2,764,686	ARIMA_d0D1_log	2,734,614.23	30,071.77
2013 Sep	1,943,037	ARIMA_d0D1_log	1,883,224.44	59,812.56
2013 Oct	1,291,360	ARIMA_d0D1_log	1,276,296.04	15,063.96
2013 Nov	455,695	ARIMA_d0D1_log	476,541.97	-20,846.97
2013 Dec	358,062	ARIMA_d0D1_log	362,205.81	-4,143.81
2014 Jan	377,387	ARIMA_d0D1_log	380,662.49	-3,275.49
2014 Feb	543,470	ARIMA_d0D1_log	539,338.18	4,131.82
2014 Mar	749,773	ARIMA_d0D1_log	831,671.99	-81,898.99
2014 Apr	1,337,145	ARIMA_d0D1_log	1,006,265.63	330,879.37
2014 May	1,538,342	ARIMA_d0D1_log	1,403,135.06	135,206.94
2014 Jun	1,994,167	ARIMA_d0D1_log	1,914,847.46	79,319.54
2014 Jul	2,529,246	ARIMA_d0D1_log	2,677,934.26	-148,688.26
2014 Aug	3,069,865	ARIMA_d0D1_log	2,945,111.30	124,753.70
2014 Sep	2,089,656	ARIMA_d0D1_log	2,068,833.34	20,822.66
2014 Oct	1,477,481	ARIMA_d0D1_log	1,379,059.46	98,421.54
2014 Nov	502,473	ARIMA_d0D1_log	503,288.64	-815.64
2014 Dec	382,543	ARIMA_d0D1_log	390,826.18	-8,283.18
2015 Jan	381,607	ARIMA_d0D1_log	408,106.43	-26,499.43
2015 Feb	544,777	ARIMA_d0D1_log	571,657.64	-26,880.64
2015 Mar	827,071	ARIMA_d0D1_log	808,105.04	18,965.96
2015 Apr	1,242,844	ARIMA_d0D1_log	1,271,644.61	-28,800.61
2015 May	1,654,526	ARIMA_d0D1_log	1,542,580.38	111,945.62
2015 Jun	2,079,484	ARIMA_d0D1_log	2,045,339.72	34,144.28
2015 Jul	2,688,710	ARIMA_d0D1_log	2,631,267.96	57,442.04
2015 Aug	3,108,357	ARIMA_d0D1_log	3,152,709.47	-44,352.47
2015 Sep	2,196,681	ARIMA_d0D1_log	2,154,143.89	42,537.11
2015 Oct	1,553,142	ARIMA_d0D1_log	1,495,471.25	57,670.75
2015 Nov	552,778	ARIMA_d0D1_log	519,180.60	33,597.40
2015 Dec	426,419	ARIMA_d0D1_log	405,481.05	20,937.95
2016 Jan	443,150	ARIMA_d0D1_log	416,378.21	26,771.79
2016 Feb	664,278	ARIMA_d0D1_log	605,500.89	58,777.11
2016 Mar	1,089,392	ARIMA_d0D1_log	911,751.57	177,640.43
2016 Apr	1,335,308	ARIMA_d0D1_log	1,547,323.61	-212,015.61
2016 May	1,828,292	ARIMA_d0D1_log	1,850,907.16	-22,615.16
2016 Jun	2,288,337	ARIMA_d0D1_log	2,329,417.58	-41,080.58
2016 Jul	2,848,570	ARIMA_d0D1_log	2,933,540.27	-84,970.27
2016 Aug	3,204,047	ARIMA_d0D1_log	3,420,390.28	-216,343.28
2016 Sep	2,378,618	ARIMA_d0D1_log	2,315,207.75	63,410.25
2016 Oct	1,793,822	ARIMA_d0D1_log	1,648,378.42	145,443.58
2016 Nov	653,514	ARIMA_d0D1_log	588,562.51	64,951.49
2016 Dec	478,510	ARIMA_d0D1_log	464,767.82	13,742.18
2017 Jan	495,629	ARIMA_d0D1_log	474,848.71	20,780.29
2017 Feb	704,532	ARIMA_d0D1_log	704,821.07	-289.07
2017 Mar	1,015,421	ARIMA_d0D1_log	1,103,532.80	-88,111.80
2017 Apr	1,765,170	ARIMA_d0D1_log	1,516,974.20	248,195.80
2017 May	1,970,072	ARIMA_d0D1_log	2,051,284.72	-81,212.72
2017 Jun	2,417,100	ARIMA_d0D1_log	2,554,737.94	-137,637.94
2017 Jul	2,968,641	ARIMA_d0D1_log	3,155,931.39	-187,290.39
2017 Aug	3,295,406	ARIMA_d0D1_log	3,543,308.07	-247,902.07
2017 Sep	2,470,298	ARIMA_d0D1_log	2,506,236.53	-35,938.53
2017 Oct	1,911,961	ARIMA_d0D1_log	1,840,961.20	70,999.80
2017 Nov	680,373	ARIMA_d0D1_log	671,073.45	9,299.55
2017 Dec	512,548	ARIMA_d0D1_log	504,241.08	8,306.92
2018 Jan	503,908	ARIMA_d0D1_log	520,625.21	-16,717.21
2018 Feb	731,090	ARIMA_d0D1_log	753,546.40	-22,456.40
2018 Mar	1,151,455	ARIMA_d0D1_log	1,156,032.80	-4,577.80
2018 Apr	1,575,078	ARIMA_d0D1_log	1,626,592.47	-51,514.47
2018 May	2,003,996	ARIMA_d0D1_log	2,058,575.13	-54,579.13
2018 Jun	2,381,154	ARIMA_d0D1_log	2,527,320.43	-146,166.43
2018 Jul	2,981,643	ARIMA_d0D1_log	3,077,995.45	-96,352.45
2018 Aug	3,371,918	ARIMA_d0D1_log	3,425,258.10	-53,340.10
2018 Sep	2,499,368	ARIMA_d0D1_log	2,570,398.33	-71,030.33
2018 Oct	1,956,693	ARIMA_d0D1_log	1,964,335.06	-7,642.06
2018 Nov	732,141	ARIMA_d0D1_log	722,786.19	9,354.81
2018 Dec	554,803	ARIMA_d0D1_log	539,861.21	14,941.79
2019 Jan	548,686	ARIMA_d0D1_log	553,924.55	-5,238.55
2019 Feb	739,981	ARIMA_d0D1_log	796,151.00	-56,170.00
2019 Mar	1,078,918	ARIMA_d0D1_log	1,159,911.36	-80,993.36
2019 Apr	1,795,494	ARIMA_d0D1_log	1,645,699.45	149,794.55
2019 May	1,990,529	ARIMA_d0D1_log	2,169,975.71	-179,446.71
2019 Jun	2,425,834	ARIMA_d0D1_log	2,518,404.71	-92,570.71
2019 Jul	2,988,668	ARIMA_d0D1_log	3,097,610.58	-108,942.58
2019 Aug	3,439,271	ARIMA_d0D1_log	3,321,281.13	117,989.87
2019 Sep	2,573,527	ARIMA_d0D1_log	2,592,717.21	-19,190.21
2019 Oct	1,930,852	ARIMA_d0D1_log	2,046,108.58	-115,256.58
2019 Nov	785,875	ARIMA_d0D1_log	735,072.90	50,802.10
2019 Dec	602,860	ARIMA_d0D1_log	567,564.05	35,295.95
2020 Jan	560,368	ARIMA_d0D1_log	582,822.35	-22,454.35
2020 Feb	844,247	ARIMA_d0D1_log	806,165.80	38,081.20
2020 Mar	513,360	ARIMA_d0D1_log	1,241,535.01	-728,175.01
2020 Apr	25,614	ARIMA_d0D1_log	1,892,926.55	-1,867,312.55
2020 May	40,932	ARIMA_d0D1_log	2,169,608.43	-2,128,676.43
2020 Jun	330,393	ARIMA_d0D1_log	924,926.64	-594,533.64
2020 Jul	1,035,732	ARIMA_d0D1_log	972,655.97	63,076.03
2020 Aug	2,090,569	ARIMA_d0D1_log	2,069,226.87	21,342.13
2020 Sep	1,418,185	ARIMA_d0D1_log	2,098,240.28	-680,055.28
2020 Oct	696,087	ARIMA_d0D1_log	1,194,719.85	-498,632.85
2020 Nov	181,873	ARIMA_d0D1_log	326,037.01	-144,164.01
2020 Dec	153,351	ARIMA_d0D1_log	185,549.87	-32,198.87
2021 Jan	105,336	ARIMA_d0D1_log	237,547.04	-132,211.04
2021 Feb	66,194	ARIMA_d0D1_log	183,787.84	-117,593.84
2021 Mar	84,413	ARIMA_d0D1_log	87,542.65	-3,129.65
2021 Apr	138,661	ARIMA_d0D1_log	63,162.81	75,498.19
2021 May	502,057	ARIMA_d0D1_log	348,407.91	153,649.09
2021 Jun	1,182,009	ARIMA_d0D1_log	1,626,991.04	-444,982.04
2021 Jul	1,551,789	ARIMA_d0D1_log	1,825,754.75	-273,965.75
2021 Aug	2,762,537	ARIMA_d0D1_log	2,381,213.34	381,323.66
2021 Sep	1,869,194	ARIMA_d0D1_log	2,504,750.60	-635,556.60
2021 Oct	1,584,764	ARIMA_d0D1_log	1,166,331.53	418,432.47
2021 Nov	651,051	ARIMA_d0D1_log	725,878.24	-74,827.24
2021 Dec	376,031	ARIMA_d0D1_log	485,920.03	-109,889.03
2022 Jan	344,634	ARIMA_d0D1_log	301,182.04	43,451.96
2022 Feb	590,122	ARIMA_d0D1_log	463,364.69	126,757.31
2022 Mar	873,841	ARIMA_d0D1_log	816,388.57	57,452.43
2022 Apr	1,629,377	ARIMA_d0D1_log	694,718.89	934,658.11
2022 May	1,867,744	ARIMA_d0D1_log	3,343,082.76	-1,475,338.76
2022 Jun	2,230,207	ARIMA_d0D1_log	2,166,684.35	63,522.65
2010 Jan	366,296	ARIMA_d1D1	353,423.74	12,872.26
2010 Feb	533,056	ARIMA_d1D1	526,316.49	6,739.51
2010 Mar	742,227	ARIMA_d1D1	751,903.59	-9,676.59
2010 Apr	902,745	ARIMA_d1D1	974,094.83	-71,349.83
2010 May	1,107,303	ARIMA_d1D1	1,148,536.39	-41,233.39
2010 Jun	1,464,695	ARIMA_d1D1	1,423,198.81	41,496.19
2010 Jul	2,050,478	ARIMA_d1D1	1,867,338.68	183,139.32
2010 Aug	2,468,924	ARIMA_d1D1	2,316,500.28	152,423.72
2010 Sep	1,696,356	ARIMA_d1D1	1,646,855.14	49,500.86
2010 Oct	1,104,659	ARIMA_d1D1	1,120,958.39	-16,299.39
2010 Nov	445,221	ARIMA_d1D1	513,127.63	-67,906.63
2010 Dec	365,490	ARIMA_d1D1	387,763.86	-22,273.86
2011 Jan	357,209	ARIMA_d1D1	377,966.90	-20,757.90
2011 Feb	503,831	ARIMA_d1D1	534,565.20	-30,734.20
2011 Mar	761,343	ARIMA_d1D1	749,868.84	11,474.16
2011 Apr	1,177,115	ARIMA_d1D1	933,690.03	243,424.97
2011 May	1,169,516	ARIMA_d1D1	1,238,276.95	-68,760.95
2011 Jun	1,576,730	ARIMA_d1D1	1,520,540.20	56,189.80
2011 Jul	2,208,160	ARIMA_d1D1	2,031,240.03	176,919.97
2011 Aug	2,572,404	ARIMA_d1D1	2,509,678.29	62,725.71
2011 Sep	1,731,056	ARIMA_d1D1	1,774,365.24	-43,309.24
2011 Oct	1,161,751	ARIMA_d1D1	1,200,877.33	-39,126.33
2011 Nov	427,550	ARIMA_d1D1	576,136.06	-148,586.06
2011 Dec	333,201	ARIMA_d1D1	431,121.84	-97,920.84
2012 Jan	359,355	ARIMA_d1D1	394,178.08	-34,823.08
2012 Feb	531,709	ARIMA_d1D1	538,683.55	-6,974.55
2012 Mar	751,024	ARIMA_d1D1	768,321.34	-17,297.34
2012 Apr	1,017,976	ARIMA_d1D1	1,036,398.96	-18,422.96
2012 May	1,194,673	ARIMA_d1D1	1,150,895.13	43,777.87
2012 Jun	1,678,327	ARIMA_d1D1	1,521,838.03	156,488.97
2012 Jul	2,296,474	ARIMA_d1D1	2,141,724.20	154,749.80
2012 Aug	2,622,801	ARIMA_d1D1	2,608,595.64	14,205.36
2012 Sep	1,829,252	ARIMA_d1D1	1,819,553.36	9,698.64
2012 Oct	1,244,751	ARIMA_d1D1	1,258,645.59	-13,894.59
2012 Nov	453,958	ARIMA_d1D1	581,761.31	-127,803.31
2012 Dec	346,474	ARIMA_d1D1	437,340.92	-90,866.92
2013 Jan	369,969	ARIMA_d1D1	383,023.22	-13,054.22
2013 Feb	520,055	ARIMA_d1D1	530,180.14	-10,125.14
2013 Mar	840,024	ARIMA_d1D1	765,886.42	74,137.58
2013 Apr	986,191	ARIMA_d1D1	1,082,960.19	-96,769.19
2013 May	1,382,234	ARIMA_d1D1	1,177,322.32	204,911.68
2013 Jun	1,814,108	ARIMA_d1D1	1,691,995.01	122,112.99
2013 Jul	2,387,304	ARIMA_d1D1	2,342,519.79	44,784.21
2013 Aug	2,764,686	ARIMA_d1D1	2,710,554.33	54,131.67
2013 Sep	1,943,037	ARIMA_d1D1	1,930,815.69	12,221.31
2013 Oct	1,291,360	ARIMA_d1D1	1,356,970.36	-65,610.36
2013 Nov	455,695	ARIMA_d1D1	578,995.59	-123,300.59
2013 Dec	358,062	ARIMA_d1D1	431,332.17	-73,270.17
2014 Jan	377,387	ARIMA_d1D1	425,494.66	-48,107.66
2014 Feb	543,470	ARIMA_d1D1	563,121.63	-19,651.63
2014 Mar	749,773	ARIMA_d1D1	844,821.13	-95,048.13
2014 Apr	1,337,145	ARIMA_d1D1	1,004,603.42	332,541.58
2014 May	1,538,342	ARIMA_d1D1	1,423,009.49	115,332.51
2014 Jun	1,994,167	ARIMA_d1D1	1,904,848.15	89,318.85
2014 Jul	2,529,246	ARIMA_d1D1	2,525,006.67	4,239.33
2014 Aug	3,069,865	ARIMA_d1D1	2,890,730.62	179,134.38
2014 Sep	2,089,656	ARIMA_d1D1	2,145,805.84	-56,149.84
2014 Oct	1,477,481	ARIMA_d1D1	1,493,296.89	-15,815.89
2014 Nov	502,473	ARIMA_d1D1	674,376.09	-171,903.09
2014 Dec	382,543	ARIMA_d1D1	514,599.15	-132,056.15
2015 Jan	381,607	ARIMA_d1D1	483,566.52	-101,959.52
2015 Feb	544,777	ARIMA_d1D1	605,863.33	-61,086.33
2015 Mar	827,071	ARIMA_d1D1	830,922.73	-3,851.73
2015 Apr	1,242,844	ARIMA_d1D1	1,295,334.10	-52,490.10
2015 May	1,654,526	ARIMA_d1D1	1,521,644.03	132,881.97
2015 Jun	2,079,484	ARIMA_d1D1	2,025,568.90	53,915.10
2015 Jul	2,688,710	ARIMA_d1D1	2,592,973.54	95,736.46
2015 Aug	3,108,357	ARIMA_d1D1	3,130,860.88	-22,503.88
2015 Sep	2,196,681	ARIMA_d1D1	2,183,488.34	13,192.66
2015 Oct	1,553,142	ARIMA_d1D1	1,566,536.14	-13,394.14
2015 Nov	552,778	ARIMA_d1D1	623,827.56	-71,049.56
2015 Dec	426,419	ARIMA_d1D1	479,056.69	-52,637.69
2016 Jan	443,150	ARIMA_d1D1	461,129.06	-17,979.06
2016 Feb	664,278	ARIMA_d1D1	612,808.58	51,469.42
2016 Mar	1,089,392	ARIMA_d1D1	900,073.10	189,318.90
2016 Apr	1,335,308	ARIMA_d1D1	1,446,392.58	-111,084.58
2016 May	1,828,292	ARIMA_d1D1	1,749,763.85	78,528.15
2016 Jun	2,288,337	ARIMA_d1D1	2,173,145.38	115,191.62
2016 Jul	2,848,570	ARIMA_d1D1	2,836,949.72	11,620.28
2016 Aug	3,204,047	ARIMA_d1D1	3,277,298.07	-73,251.07
2016 Sep	2,378,618	ARIMA_d1D1	2,310,420.93	68,197.07
2016 Oct	1,793,822	ARIMA_d1D1	1,706,785.08	87,036.92
2016 Nov	653,514	ARIMA_d1D1	727,224.71	-73,710.71
2016 Dec	478,510	ARIMA_d1D1	535,974.79	-57,464.79
2017 Jan	495,629	ARIMA_d1D1	522,821.69	-27,192.69
2017 Feb	704,532	ARIMA_d1D1	716,133.63	-11,601.63
2017 Mar	1,015,421	ARIMA_d1D1	1,115,007.20	-99,586.20
2017 Apr	1,765,170	ARIMA_d1D1	1,447,373.17	317,796.83
2017 May	1,970,072	ARIMA_d1D1	1,992,718.95	-22,646.95
2017 Jun	2,417,100	ARIMA_d1D1	2,513,064.15	-95,964.15
2017 Jul	2,968,641	ARIMA_d1D1	3,064,175.65	-95,534.65
2017 Aug	3,295,406	ARIMA_d1D1	3,416,895.79	-121,489.79
2017 Sep	2,470,298	ARIMA_d1D1	2,430,967.07	39,330.93
2017 Oct	1,911,961	ARIMA_d1D1	1,877,242.62	34,718.38
2017 Nov	680,373	ARIMA_d1D1	771,108.75	-90,735.75
2017 Dec	512,548	ARIMA_d1D1	575,419.46	-62,871.46
2018 Jan	503,908	ARIMA_d1D1	577,019.23	-73,111.23
2018 Feb	731,090	ARIMA_d1D1	765,591.35	-34,501.35
2018 Mar	1,151,455	ARIMA_d1D1	1,066,492.41	84,962.59
2018 Apr	1,575,078	ARIMA_d1D1	1,656,810.39	-81,732.39
2018 May	2,003,996	ARIMA_d1D1	1,957,722.25	46,273.75
2018 Jun	2,381,154	ARIMA_d1D1	2,394,792.73	-13,638.73
2018 Jul	2,981,643	ARIMA_d1D1	2,992,114.15	-10,471.15
2018 Aug	3,371,918	ARIMA_d1D1	3,275,465.48	96,452.52
2018 Sep	2,499,368	ARIMA_d1D1	2,547,936.11	-48,568.11
2018 Oct	1,956,693	ARIMA_d1D1	1,955,814.58	878.42
2018 Nov	732,141	ARIMA_d1D1	692,617.12	39,523.88
2018 Dec	554,803	ARIMA_d1D1	513,497.39	41,305.61
2019 Jan	548,686	ARIMA_d1D1	545,477.21	3,208.79
2019 Feb	739,981	ARIMA_d1D1	790,173.31	-50,192.31
2019 Mar	1,078,918	ARIMA_d1D1	1,192,602.98	-113,684.98
2019 Apr	1,795,494	ARIMA_d1D1	1,726,928.64	68,565.36
2019 May	1,990,529	ARIMA_d1D1	2,094,947.82	-104,418.82
2019 Jun	2,425,834	ARIMA_d1D1	2,457,864.33	-32,030.33
2019 Jul	2,988,668	ARIMA_d1D1	3,046,939.19	-58,271.19
2019 Aug	3,439,271	ARIMA_d1D1	3,276,286.00	162,985.00
2019 Sep	2,573,527	ARIMA_d1D1	2,559,202.64	14,324.36
2019 Oct	1,930,852	ARIMA_d1D1	2,051,095.65	-120,243.65
2019 Nov	785,875	ARIMA_d1D1	708,744.79	77,130.21
2019 Dec	602,860	ARIMA_d1D1	531,226.28	71,633.72
2020 Jan	560,368	ARIMA_d1D1	540,819.47	19,548.53
2020 Feb	844,247	ARIMA_d1D1	765,810.32	78,436.68
2020 Mar	513,360	ARIMA_d1D1	1,175,866.45	-662,506.45
2020 Apr	25,614	ARIMA_d1D1	1,740,715.13	-1,715,101.13
2020 May	40,932	ARIMA_d1D1	88,670.46	-47,738.46
2020 Jun	330,393	ARIMA_d1D1	366,958.65	-36,565.65
2020 Jul	1,035,732	ARIMA_d1D1	873,438.55	162,293.45
2020 Aug	2,090,569	ARIMA_d1D1	1,460,524.75	630,044.25
2020 Sep	1,418,185	ARIMA_d1D1	1,401,786.37	16,398.63
2020 Oct	696,087	ARIMA_d1D1	740,960.02	-44,873.02
2020 Nov	181,873	ARIMA_d1D1	-463,983.61	645,856.61
2020 Dec	153,351	ARIMA_d1D1	137,651.71	15,699.29
2021 Jan	105,336	ARIMA_d1D1	124,934.05	-19,598.05
2021 Feb	66,194	ARIMA_d1D1	339,544.26	-273,350.26
2021 Mar	84,413	ARIMA_d1D1	10,773.17	73,639.83
2021 Apr	138,661	ARIMA_d1D1	339,843.25	-201,182.25
2021 May	502,057	ARIMA_d1D1	320,110.87	181,946.13
2021 Jun	1,182,009	ARIMA_d1D1	974,295.33	207,713.67
2021 Jul	1,551,789	ARIMA_d1D1	1,882,573.58	-330,784.58
2021 Aug	2,762,537	ARIMA_d1D1	2,008,506.97	754,030.03
2021 Sep	1,869,194	ARIMA_d1D1	2,075,193.24	-205,999.24
2021 Oct	1,584,764	ARIMA_d1D1	1,164,175.06	420,588.94
2021 Nov	651,051	ARIMA_d1D1	789,627.75	-138,576.75
2021 Dec	376,031	ARIMA_d1D1	509,092.19	-133,061.19
2022 Jan	344,634	ARIMA_d1D1	283,685.66	60,948.34
2022 Feb	590,122	ARIMA_d1D1	451,987.23	138,134.77
2022 Mar	873,841	ARIMA_d1D1	501,821.76	372,019.24
2022 Apr	1,629,377	ARIMA_d1D1	1,039,145.82	590,231.18
2022 May	1,867,744	ARIMA_d1D1	1,995,702.66	-127,958.66
2022 Jun	2,230,207	ARIMA_d1D1	2,424,682.84	-194,475.84
2010 Jan	366,296	ARIMA_d1D1_log	403,467.67	-37,171.67
2010 Feb	533,056	ARIMA_d1D1_log	539,725.60	-6,669.60
2010 Mar	742,227	ARIMA_d1D1_log	722,851.81	19,375.19
2010 Apr	902,745	ARIMA_d1D1_log	902,749.31	-4.31
2010 May	1,107,303	ARIMA_d1D1_log	1,092,860.76	14,442.24
2010 Jun	1,464,695	ARIMA_d1D1_log	1,349,418.19	115,276.81
2010 Jul	2,050,478	ARIMA_d1D1_log	1,766,635.13	283,842.87
2010 Aug	2,468,924	ARIMA_d1D1_log	2,215,926.79	252,997.21
2010 Sep	1,696,356	ARIMA_d1D1_log	1,605,422.12	90,933.88
2010 Oct	1,104,659	ARIMA_d1D1_log	1,106,196.74	-1,537.74
2010 Nov	445,221	ARIMA_d1D1_log	520,120.58	-74,899.58
2010 Dec	365,490	ARIMA_d1D1_log	394,874.94	-29,384.94
2011 Jan	357,209	ARIMA_d1D1_log	380,000.83	-22,791.83
2011 Feb	503,831	ARIMA_d1D1_log	518,970.51	-15,139.51
2011 Mar	761,343	ARIMA_d1D1_log	701,042.35	60,300.65
2011 Apr	1,177,115	ARIMA_d1D1_log	895,471.40	281,643.60
2011 May	1,169,516	ARIMA_d1D1_log	1,180,486.73	-10,970.73
2011 Jun	1,576,730	ARIMA_d1D1_log	1,507,629.41	69,100.59
2011 Jul	2,208,160	ARIMA_d1D1_log	2,050,649.89	157,510.11
2011 Aug	2,572,404	ARIMA_d1D1_log	2,538,377.23	34,026.77
2011 Sep	1,731,056	ARIMA_d1D1_log	1,744,081.18	-13,025.18
2011 Oct	1,161,751	ARIMA_d1D1_log	1,147,712.63	14,038.37
2011 Nov	427,550	ARIMA_d1D1_log	501,270.33	-73,720.33
2011 Dec	333,201	ARIMA_d1D1_log	384,835.00	-51,634.00
2012 Jan	359,355	ARIMA_d1D1_log	364,054.63	-4,699.63
2012 Feb	531,709	ARIMA_d1D1_log	512,786.35	18,922.65
2012 Mar	751,024	ARIMA_d1D1_log	750,913.86	110.14
2012 Apr	1,017,976	ARIMA_d1D1_log	1,049,125.24	-31,149.24
2012 May	1,194,673	ARIMA_d1D1_log	1,131,684.13	62,988.87
2012 Jun	1,678,327	ARIMA_d1D1_log	1,520,906.76	157,420.24
2012 Jul	2,296,474	ARIMA_d1D1_log	2,162,405.77	134,068.23
2012 Aug	2,622,801	ARIMA_d1D1_log	2,671,601.89	-48,800.89
2012 Sep	1,829,252	ARIMA_d1D1_log	1,795,725.05	33,526.95
2012 Oct	1,244,751	ARIMA_d1D1_log	1,194,020.62	50,730.38
2012 Nov	453,958	ARIMA_d1D1_log	472,597.64	-18,639.64
2012 Dec	346,474	ARIMA_d1D1_log	370,120.59	-23,646.59
2013 Jan	369,969	ARIMA_d1D1_log	370,530.33	-561.33
2013 Feb	520,055	ARIMA_d1D1_log	538,334.85	-18,279.85
2013 Mar	840,024	ARIMA_d1D1_log	775,069.57	64,954.43
2013 Apr	986,191	ARIMA_d1D1_log	1,157,277.57	-171,086.57
2013 May	1,382,234	ARIMA_d1D1_log	1,187,498.76	194,735.24
2013 Jun	1,814,108	ARIMA_d1D1_log	1,719,282.26	94,825.74
2013 Jul	2,387,304	ARIMA_d1D1_log	2,399,495.11	-12,191.11
2013 Aug	2,764,686	ARIMA_d1D1_log	2,774,845.65	-10,159.65
2013 Sep	1,943,037	ARIMA_d1D1_log	1,909,616.01	33,420.99
2013 Oct	1,291,360	ARIMA_d1D1_log	1,299,814.30	-8,454.30
2013 Nov	455,695	ARIMA_d1D1_log	475,161.53	-19,466.53
2013 Dec	358,062	ARIMA_d1D1_log	361,722.59	-3,660.59
2014 Jan	377,387	ARIMA_d1D1_log	386,866.66	-9,479.66
2014 Feb	543,470	ARIMA_d1D1_log	550,716.15	-7,246.15
2014 Mar	749,773	ARIMA_d1D1_log	844,843.30	-95,070.30
2014 Apr	1,337,145	ARIMA_d1D1_log	1,014,498.59	322,646.41
2014 May	1,538,342	ARIMA_d1D1_log	1,400,736.75	137,605.25
2014 Jun	1,994,167	ARIMA_d1D1_log	2,004,928.50	-10,761.50
2014 Jul	2,529,246	ARIMA_d1D1_log	2,741,665.77	-212,419.77
2014 Aug	3,069,865	ARIMA_d1D1_log	3,071,946.89	-2,081.89
2014 Sep	2,089,656	ARIMA_d1D1_log	2,136,073.76	-46,417.76
2014 Oct	1,477,481	ARIMA_d1D1_log	1,425,065.18	52,415.82
2014 Nov	502,473	ARIMA_d1D1_log	491,049.94	11,423.06
2014 Dec	382,543	ARIMA_d1D1_log	381,666.50	876.50
2015 Jan	381,607	ARIMA_d1D1_log	403,484.24	-21,877.24
2015 Feb	544,777	ARIMA_d1D1_log	585,462.43	-40,685.43
2015 Mar	827,071	ARIMA_d1D1_log	825,832.35	1,238.65
2015 Apr	1,242,844	ARIMA_d1D1_log	1,305,025.19	-62,181.19
2015 May	1,654,526	ARIMA_d1D1_log	1,566,623.26	87,902.74
2015 Jun	2,079,484	ARIMA_d1D1_log	2,073,227.91	6,256.09
2015 Jul	2,688,710	ARIMA_d1D1_log	2,666,491.96	22,218.04
2015 Aug	3,108,357	ARIMA_d1D1_log	3,195,700.66	-87,343.66
2015 Sep	2,196,681	ARIMA_d1D1_log	2,183,784.58	12,896.42
2015 Oct	1,553,142	ARIMA_d1D1_log	1,515,783.83	37,358.17
2015 Nov	552,778	ARIMA_d1D1_log	525,923.15	26,854.85
2015 Dec	426,419	ARIMA_d1D1_log	410,747.40	15,671.60
2016 Jan	443,150	ARIMA_d1D1_log	422,136.45	21,013.55
2016 Feb	664,278	ARIMA_d1D1_log	614,218.78	50,059.22
2016 Mar	1,089,392	ARIMA_d1D1_log	925,753.17	163,638.83
2016 Apr	1,335,308	ARIMA_d1D1_log	1,574,039.17	-238,731.17
2016 May	1,828,292	ARIMA_d1D1_log	1,892,288.89	-63,996.89
2016 Jun	2,288,337	ARIMA_d1D1_log	2,378,383.26	-90,046.26
2016 Jul	2,848,570	ARIMA_d1D1_log	2,997,142.31	-148,572.31
2016 Aug	3,204,047	ARIMA_d1D1_log	3,496,251.91	-292,204.91
2016 Sep	2,378,618	ARIMA_d1D1_log	2,371,014.46	7,603.54
2016 Oct	1,793,822	ARIMA_d1D1_log	1,680,176.52	113,645.48
2016 Nov	653,514	ARIMA_d1D1_log	596,589.04	56,924.96
2016 Dec	478,510	ARIMA_d1D1_log	468,865.25	9,644.75
2017 Jan	495,629	ARIMA_d1D1_log	478,749.36	16,879.64
2017 Feb	704,532	ARIMA_d1D1_log	710,523.63	-5,991.63
2017 Mar	1,015,421	ARIMA_d1D1_log	1,079,915.55	-64,494.55
2017 Apr	1,765,170	ARIMA_d1D1_log	1,530,011.82	235,158.18
2017 May	1,970,072	ARIMA_d1D1_log	2,130,989.97	-160,917.97
2017 Jun	2,417,100	ARIMA_d1D1_log	2,583,588.66	-166,488.66
2017 Jul	2,968,641	ARIMA_d1D1_log	3,200,558.49	-231,917.49
2017 Aug	3,295,406	ARIMA_d1D1_log	3,610,188.23	-314,782.23
2017 Sep	2,470,298	ARIMA_d1D1_log	2,556,993.64	-86,695.64
2017 Oct	1,911,961	ARIMA_d1D1_log	1,872,151.02	39,809.98
2017 Nov	680,373	ARIMA_d1D1_log	678,873.20	1,499.80
2017 Dec	512,548	ARIMA_d1D1_log	508,696.21	3,851.79
2018 Jan	503,908	ARIMA_d1D1_log	524,897.26	-20,989.26
2018 Feb	731,090	ARIMA_d1D1_log	760,204.55	-29,114.55
2018 Mar	1,151,455	ARIMA_d1D1_log	1,166,635.99	-15,180.99
2018 Apr	1,575,078	ARIMA_d1D1_log	1,697,787.74	-122,709.74
2018 May	2,003,996	ARIMA_d1D1_log	2,074,631.68	-70,635.68
2018 Jun	2,381,154	ARIMA_d1D1_log	2,546,388.29	-165,234.29
2018 Jul	2,981,643	ARIMA_d1D1_log	3,101,215.24	-119,572.24
2018 Aug	3,371,918	ARIMA_d1D1_log	3,455,170.91	-83,252.91
2018 Sep	2,499,368	ARIMA_d1D1_log	2,589,236.63	-89,868.63
2018 Oct	1,956,693	ARIMA_d1D1_log	1,976,813.73	-20,120.73
2018 Nov	732,141	ARIMA_d1D1_log	727,043.20	5,097.80
2018 Dec	554,803	ARIMA_d1D1_log	543,272.92	11,530.08
2019 Jan	548,686	ARIMA_d1D1_log	557,018.24	-8,332.24
2019 Feb	739,981	ARIMA_d1D1_log	799,661.40	-59,680.40
2019 Mar	1,078,918	ARIMA_d1D1_log	1,184,596.17	-105,678.17
2019 Apr	1,795,494	ARIMA_d1D1_log	1,720,034.55	75,459.45
2019 May	1,990,529	ARIMA_d1D1_log	2,141,204.22	-150,675.22
2019 Jun	2,425,834	ARIMA_d1D1_log	2,490,086.67	-64,252.67
2019 Jul	2,988,668	ARIMA_d1D1_log	3,062,410.76	-73,742.76
2019 Aug	3,439,271	ARIMA_d1D1_log	3,329,407.34	109,863.66
2019 Sep	2,573,527	ARIMA_d1D1_log	2,597,821.84	-24,294.84
2019 Oct	1,930,852	ARIMA_d1D1_log	2,048,474.41	-117,622.41
2019 Nov	785,875	ARIMA_d1D1_log	735,373.03	50,501.97
2019 Dec	602,860	ARIMA_d1D1_log	568,624.21	34,235.79
2020 Jan	560,368	ARIMA_d1D1_log	575,760.62	-15,392.62
2020 Feb	844,247	ARIMA_d1D1_log	792,930.78	51,316.22
2020 Mar	513,360	ARIMA_d1D1_log	1,234,873.76	-721,513.76
2020 Apr	25,614	ARIMA_d1D1_log	1,668,558.09	-1,642,944.09
2020 May	40,932	ARIMA_d1D1_log	642.42	40,289.58
2020 Jun	330,393	ARIMA_d1D1_log	52,870.32	277,522.68
2020 Jul	1,035,732	ARIMA_d1D1_log	873,168.50	162,563.50
2020 Aug	2,090,569	ARIMA_d1D1_log	1,057,567.75	1,033,001.25
2020 Sep	1,418,185	ARIMA_d1D1_log	1,811,148.60	-392,963.60
2020 Oct	696,087	ARIMA_d1D1_log	1,016,788.15	-320,701.15
2020 Nov	181,873	ARIMA_d1D1_log	263,262.27	-81,389.27
2020 Dec	153,351	ARIMA_d1D1_log	146,875.98	6,475.02
2021 Jan	105,336	ARIMA_d1D1_log	193,682.11	-88,346.11
2021 Feb	66,194	ARIMA_d1D1_log	151,652.37	-85,458.37
2021 Mar	84,413	ARIMA_d1D1_log	70,804.43	13,608.57
2021 Apr	138,661	ARIMA_d1D1_log	50,618.45	88,042.55
2021 May	502,057	ARIMA_d1D1_log	244,896.62	257,160.38
2021 Jun	1,182,009	ARIMA_d1D1_log	1,221,324.38	-39,315.38
2021 Jul	1,551,789	ARIMA_d1D1_log	1,219,513.01	332,275.99
2021 Aug	2,762,537	ARIMA_d1D1_log	1,608,311.74	1,154,225.26
2021 Sep	1,869,194	ARIMA_d1D1_log	2,019,494.34	-150,300.34
2021 Oct	1,584,764	ARIMA_d1D1_log	961,324.54	623,439.46
2021 Nov	651,051	ARIMA_d1D1_log	621,380.24	29,670.76
2021 Dec	376,031	ARIMA_d1D1_log	466,646.34	-90,615.34
2022 Jan	344,634	ARIMA_d1D1_log	296,209.77	48,424.23
2022 Feb	590,122	ARIMA_d1D1_log	501,197.99	88,924.01
2022 Mar	873,841	ARIMA_d1D1_log	529,717.50	344,123.50
2022 Apr	1,629,377	ARIMA_d1D1_log	779,551.91	849,825.09
2022 May	1,867,744	ARIMA_d1D1_log	3,883,940.82	-2,016,196.82
2022 Jun	2,230,207	ARIMA_d1D1_log	2,128,331.97	101,875.03
2010 Jan	366,296	Drift_STL	388,925.98	-22,629.98
2010 Feb	533,056	Drift_STL	547,970.87	-14,914.87
2010 Mar	742,227	Drift_STL	765,982.44	-23,755.44
2010 Apr	902,745	Drift_STL	936,313.25	-33,568.25
2010 May	1,107,303	Drift_STL	1,133,356.15	-26,053.15
2010 Jun	1,464,695	Drift_STL	1,390,819.29	73,875.71
2010 Jul	2,050,478	Drift_STL	1,889,116.26	161,361.74
2010 Aug	2,468,924	Drift_STL	2,415,440.67	53,483.33
2010 Sep	1,696,356	Drift_STL	1,708,976.64	-12,620.64
2010 Oct	1,104,659	Drift_STL	1,162,962.48	-58,303.48
2010 Nov	445,221	Drift_STL	519,050.06	-73,829.06
2010 Dec	365,490	Drift_STL	359,998.18	5,491.82
2011 Jan	357,209	Drift_STL	390,705.68	-33,496.68
2011 Feb	503,831	Drift_STL	544,591.05	-40,760.05
2011 Mar	761,343	Drift_STL	744,431.49	16,911.51
2011 Apr	1,177,115	Drift_STL	954,459.39	222,655.61
2011 May	1,169,516	Drift_STL	1,374,673.33	-205,157.33
2011 Jun	1,576,730	Drift_STL	1,472,207.25	104,522.75
2011 Jul	2,208,160	Drift_STL	2,032,783.74	175,376.26
2011 Aug	2,572,404	Drift_STL	2,574,245.96	-1,841.96
2011 Sep	1,731,056	Drift_STL	1,806,741.94	-75,685.94
2011 Oct	1,161,751	Drift_STL	1,191,189.04	-29,438.04
2011 Nov	427,550	Drift_STL	568,146.21	-140,596.21
2011 Dec	333,201	Drift_STL	359,181.28	-25,980.28
2012 Jan	359,355	Drift_STL	361,836.61	-2,481.61
2012 Feb	531,709	Drift_STL	541,882.82	-10,173.82
2012 Mar	751,024	Drift_STL	774,423.21	-23,399.21
2012 Apr	1,017,976	Drift_STL	987,937.16	30,038.84
2012 May	1,194,673	Drift_STL	1,194,154.93	518.07
2012 Jun	1,678,327	Drift_STL	1,509,976.79	168,350.21
2012 Jul	2,296,474	Drift_STL	2,151,915.83	144,558.17
2012 Aug	2,622,801	Drift_STL	2,642,588.94	-19,787.94
2012 Sep	1,829,252	Drift_STL	1,830,741.02	-1,489.02
2012 Oct	1,244,751	Drift_STL	1,266,850.92	-22,099.92
2012 Nov	453,958	Drift_STL	619,302.43	-165,344.43
2012 Dec	346,474	Drift_STL	388,762.86	-42,288.86
2013 Jan	369,969	Drift_STL	380,675.84	-10,706.84
2013 Feb	520,055	Drift_STL	556,074.12	-36,019.12
2013 Mar	840,024	Drift_STL	769,136.75	70,887.25
2013 Apr	986,191	Drift_STL	1,083,016.33	-96,825.33
2013 May	1,382,234	Drift_STL	1,166,823.30	215,410.70
2013 Jun	1,814,108	Drift_STL	1,715,888.79	98,219.21
2013 Jul	2,387,304	Drift_STL	2,313,223.51	74,080.49
2013 Aug	2,764,686	Drift_STL	2,725,795.66	38,890.34
2013 Sep	1,943,037	Drift_STL	1,958,420.49	-15,383.49
2013 Oct	1,291,360	Drift_STL	1,368,775.85	-77,415.85
2013 Nov	455,695	Drift_STL	638,357.76	-182,662.76
2013 Dec	358,062	Drift_STL	398,154.28	-40,092.28
2014 Jan	377,387	Drift_STL	400,267.16	-22,880.16
2014 Feb	543,470	Drift_STL	564,584.74	-21,114.74
2014 Mar	749,773	Drift_STL	809,596.77	-59,823.77
2014 Apr	1,337,145	Drift_STL	999,564.80	337,580.20
2014 May	1,538,342	Drift_STL	1,506,890.93	31,451.07
2014 Jun	1,994,167	Drift_STL	1,889,497.18	104,669.82
2014 Jul	2,529,246	Drift_STL	2,504,887.32	24,358.68
2014 Aug	3,069,865	Drift_STL	2,868,000.92	201,864.08
2014 Sep	2,089,656	Drift_STL	2,229,733.22	-140,077.22
2014 Oct	1,477,481	Drift_STL	1,499,977.71	-22,496.71
2014 Nov	502,473	Drift_STL	782,048.07	-279,575.07
2014 Dec	382,543	Drift_STL	461,168.87	-78,625.87
2015 Jan	381,607	Drift_STL	443,891.90	-62,284.90
2015 Feb	544,777	Drift_STL	584,458.18	-39,681.18
2015 Mar	827,071	Drift_STL	817,465.39	9,605.61
2015 Apr	1,242,844	Drift_STL	1,143,907.23	98,936.77
2015 May	1,654,526	Drift_STL	1,429,646.49	224,879.51
2015 Jun	2,079,484	Drift_STL	2,014,083.40	65,400.60
2015 Jul	2,688,710	Drift_STL	2,587,469.71	101,240.29
2015 Aug	3,108,357	Drift_STL	3,037,647.55	70,709.45
2015 Sep	2,196,681	Drift_STL	2,228,226.03	-31,545.03
2015 Oct	1,553,142	Drift_STL	1,583,663.48	-30,521.48
2015 Nov	552,778	Drift_STL	786,277.06	-233,499.06
2015 Dec	426,419	Drift_STL	501,978.37	-75,559.37
2016 Jan	443,150	Drift_STL	484,628.71	-41,478.71
2016 Feb	664,278	Drift_STL	643,494.59	20,783.41
2016 Mar	1,089,392	Drift_STL	938,199.62	151,192.38
2016 Apr	1,335,308	Drift_STL	1,416,947.15	-81,639.15
2016 May	1,828,292	Drift_STL	1,570,451.63	257,840.37
2016 Jun	2,288,337	Drift_STL	2,199,795.79	88,541.21
2016 Jul	2,848,570	Drift_STL	2,809,439.37	39,130.63
2016 Aug	3,204,047	Drift_STL	3,210,696.15	-6,649.15
2016 Sep	2,378,618	Drift_STL	2,313,744.34	64,873.66
2016 Oct	1,793,822	Drift_STL	1,747,718.34	46,103.66
2016 Nov	653,514	Drift_STL	950,913.60	-297,399.60
2016 Dec	478,510	Drift_STL	600,489.47	-121,979.47
2017 Jan	495,629	Drift_STL	547,786.60	-52,157.60
2017 Feb	704,532	Drift_STL	713,439.39	-8,907.39
2017 Mar	1,015,421	Drift_STL	1,017,295.60	-1,874.60
2017 Apr	1,765,170	Drift_STL	1,360,192.52	404,977.48
2017 May	1,970,072	Drift_STL	2,006,270.72	-36,198.72
2017 Jun	2,417,100	Drift_STL	2,355,629.95	61,470.05
2017 Jul	2,968,641	Drift_STL	2,945,522.30	23,118.70
2017 Aug	3,295,406	Drift_STL	3,332,916.63	-37,510.63
2017 Sep	2,470,298	Drift_STL	2,409,437.29	60,860.71
2017 Oct	1,911,961	Drift_STL	1,840,466.18	71,494.82
2017 Nov	680,373	Drift_STL	983,528.14	-303,155.14
2017 Dec	512,548	Drift_STL	612,695.03	-100,147.03
2018 Jan	503,908	Drift_STL	581,036.04	-77,128.04
2018 Feb	731,090	Drift_STL	731,417.69	-327.69
2018 Mar	1,151,455	Drift_STL	1,054,569.45	96,885.55
2018 Apr	1,575,078	Drift_STL	1,565,709.80	9,368.20
2018 May	2,003,996	Drift_STL	1,852,921.71	151,074.29
2018 Jun	2,381,154	Drift_STL	2,395,476.49	-14,322.49
2018 Jul	2,981,643	Drift_STL	2,915,779.30	65,863.70
2018 Aug	3,371,918	Drift_STL	3,336,103.52	35,814.48
2018 Sep	2,499,368	Drift_STL	2,477,679.11	21,688.89
2018 Oct	1,956,693	Drift_STL	1,871,557.02	85,135.98
2018 Nov	732,141	Drift_STL	934,568.77	-202,427.77
2018 Dec	554,803	Drift_STL	635,603.51	-80,800.51
2019 Jan	548,686	Drift_STL	607,859.59	-59,173.59
2019 Feb	739,981	Drift_STL	780,288.43	-40,307.43
2019 Mar	1,078,918	Drift_STL	1,095,093.59	-16,175.59
2019 Apr	1,795,494	Drift_STL	1,524,861.62	270,632.38
2019 May	1,990,529	Drift_STL	2,090,689.11	-100,160.11
2019 Jun	2,425,834	Drift_STL	2,395,158.99	30,675.01
2019 Jul	2,988,668	Drift_STL	2,977,037.21	11,630.79
2019 Aug	3,439,271	Drift_STL	3,359,517.02	79,753.98
2019 Sep	2,573,527	Drift_STL	2,546,800.58	26,726.42
2019 Oct	1,930,852	Drift_STL	1,958,221.06	-27,369.06
2019 Nov	785,875	Drift_STL	848,779.15	-62,904.15
2019 Dec	602,860	Drift_STL	663,327.32	-60,467.32
2020 Jan	560,368	Drift_STL	640,422.03	-80,054.03
2020 Feb	844,247	Drift_STL	791,293.12	52,953.88
2020 Mar	513,360	Drift_STL	1,196,304.33	-682,944.33
2020 Apr	25,614	Drift_STL	1,102,583.37	-1,076,969.37
2020 May	40,932	Drift_STL	523,063.25	-482,131.25
2020 Jun	330,393	Drift_STL	627,188.74	-296,795.74
2020 Jul	1,035,732	Drift_STL	1,015,969.47	19,762.53
2020 Aug	2,090,569	Drift_STL	1,476,043.17	614,525.83
2020 Sep	1,418,185	Drift_STL	1,139,429.58	278,755.42
2020 Oct	696,087	Drift_STL	702,719.98	-6,632.98
2020 Nov	181,873	Drift_STL	-510,199.24	692,072.24
2020 Dec	153,351	Drift_STL	-120,216.02	273,567.02
2021 Jan	105,336	Drift_STL	24,415.34	80,920.66
2021 Feb	66,194	Drift_STL	236,747.01	-170,553.01
2021 Mar	84,413	Drift_STL	266,581.05	-182,168.05
2021 Apr	138,661	Drift_STL	458,018.54	-319,357.54
2021 May	502,057	Drift_STL	500,410.11	1,646.89
2021 Jun	1,182,009	Drift_STL	991,428.60	190,580.40
2021 Jul	1,551,789	Drift_STL	1,826,069.04	-274,280.04
2021 Aug	2,762,537	Drift_STL	2,140,842.11	621,694.89
2021 Sep	1,869,194	Drift_STL	1,888,394.78	-19,200.78
2021 Oct	1,584,764	Drift_STL	1,221,821.90	362,942.10
2021 Nov	651,051	Drift_STL	492,656.14	158,394.86
2021 Dec	376,031	Drift_STL	446,979.34	-70,948.34
2022 Jan	344,634	Drift_STL	331,791.96	12,842.04
2022 Feb	590,122	Drift_STL	504,941.23	85,180.77
2022 Mar	873,841	Drift_STL	753,970.59	119,870.41
2022 Apr	1,629,377	Drift_STL	1,158,805.98	470,571.02
2022 May	1,867,744	Drift_STL	1,892,823.90	-25,079.90
2022 Jun	2,230,207	Drift_STL	2,343,919.10	-113,712.10
2010 Jan	366,296	Drift_STL_log	394,378.62	-28,082.62
2010 Feb	533,056	Drift_STL_log	518,234.92	14,821.08
2010 Mar	742,227	Drift_STL_log	727,735.68	14,491.32
2010 Apr	902,745	Drift_STL_log	907,832.48	-5,087.48
2010 May	1,107,303	Drift_STL_log	1,096,529.03	10,773.97
2010 Jun	1,464,695	Drift_STL_log	1,346,728.84	117,966.16
2010 Jul	2,050,478	Drift_STL_log	1,846,989.49	203,488.51
2010 Aug	2,468,924	Drift_STL_log	2,403,303.70	65,620.30
2010 Sep	1,696,356	Drift_STL_log	1,674,508.51	21,847.49
2010 Oct	1,104,659	Drift_STL_log	1,144,441.76	-39,782.76
2010 Nov	445,221	Drift_STL_log	522,939.65	-77,718.65
2010 Dec	365,490	Drift_STL_log	369,456.76	-3,966.76
2011 Jan	357,209	Drift_STL_log	385,844.56	-28,635.56
2011 Feb	503,831	Drift_STL_log	512,360.97	-8,529.97
2011 Mar	761,343	Drift_STL_log	700,866.42	60,476.58
2011 Apr	1,177,115	Drift_STL_log	932,690.65	244,424.35
2011 May	1,169,516	Drift_STL_log	1,390,595.56	-221,079.56
2011 Jun	1,576,730	Drift_STL_log	1,451,125.06	125,604.94
2011 Jul	2,208,160	Drift_STL_log	2,031,474.88	176,685.12
2011 Aug	2,572,404	Drift_STL_log	2,598,047.37	-25,643.37
2011 Sep	1,731,056	Drift_STL_log	1,753,570.15	-22,514.15
2011 Oct	1,161,751	Drift_STL_log	1,162,433.08	-682.08
2011 Nov	427,550	Drift_STL_log	534,377.63	-106,827.63
2011 Dec	333,201	Drift_STL_log	360,899.95	-27,698.95
2012 Jan	359,355	Drift_STL_log	351,459.92	7,895.08
2012 Feb	531,709	Drift_STL_log	515,219.55	16,489.45
2012 Mar	751,024	Drift_STL_log	748,337.10	2,686.90
2012 Apr	1,017,976	Drift_STL_log	963,611.14	54,364.86
2012 May	1,194,673	Drift_STL_log	1,181,127.66	13,545.34
2012 Jun	1,678,327	Drift_STL_log	1,494,925.28	183,401.72
2012 Jul	2,296,474	Drift_STL_log	2,168,440.36	128,033.64
2012 Aug	2,622,801	Drift_STL_log	2,662,993.14	-40,192.14
2012 Sep	1,829,252	Drift_STL_log	1,770,370.36	58,881.64
2012 Oct	1,244,751	Drift_STL_log	1,211,483.68	33,267.32
2012 Nov	453,958	Drift_STL_log	542,801.09	-88,843.09
2012 Dec	346,474	Drift_STL_log	378,206.20	-31,732.20
2013 Jan	369,969	Drift_STL_log	367,163.12	2,805.88
2013 Feb	520,055	Drift_STL_log	537,668.91	-17,613.91
2013 Mar	840,024	Drift_STL_log	745,040.88	94,983.12
2013 Apr	986,191	Drift_STL_log	1,088,572.72	-102,381.72
2013 May	1,382,234	Drift_STL_log	1,154,526.70	227,707.30
2013 Jun	1,814,108	Drift_STL_log	1,754,473.84	59,634.16
2013 Jul	2,387,304	Drift_STL_log	2,374,084.01	13,219.99
2013 Aug	2,764,686	Drift_STL_log	2,765,602.96	-916.96
2013 Sep	1,943,037	Drift_STL_log	1,875,073.02	67,963.98
2013 Oct	1,291,360	Drift_STL_log	1,286,134.75	5,225.25
2013 Nov	455,695	Drift_STL_log	539,427.33	-83,732.33
2013 Dec	358,062	Drift_STL_log	375,934.53	-17,872.53
2014 Jan	377,387	Drift_STL_log	380,662.36	-3,275.36
2014 Feb	543,470	Drift_STL_log	549,207.38	-5,737.38
2014 Mar	749,773	Drift_STL_log	798,919.44	-49,146.44
2014 Apr	1,337,145	Drift_STL_log	981,813.12	355,331.88
2014 May	1,538,342	Drift_STL_log	1,549,565.53	-11,223.53
2014 Jun	1,994,167	Drift_STL_log	1,969,890.25	24,276.75
2014 Jul	2,529,246	Drift_STL_log	2,619,842.48	-90,596.48
2014 Aug	3,069,865	Drift_STL_log	2,938,381.26	131,483.74
2014 Sep	2,089,656	Drift_STL_log	2,088,277.59	1,378.41
2014 Oct	1,477,481	Drift_STL_log	1,384,057.69	93,423.31
2014 Nov	502,473	Drift_STL_log	584,899.01	-82,426.01
2014 Dec	382,543	Drift_STL_log	410,169.47	-27,626.47
2015 Jan	381,607	Drift_STL_log	409,529.49	-27,922.49
2015 Feb	544,777	Drift_STL_log	562,990.62	-18,213.62
2015 Mar	827,071	Drift_STL_log	806,198.68	20,872.32
2015 Apr	1,242,844	Drift_STL_log	1,148,929.33	93,914.67
2015 May	1,654,526	Drift_STL_log	1,454,412.12	200,113.88
2015 Jun	2,079,484	Drift_STL_log	2,115,200.08	-35,716.08
2015 Jul	2,688,710	Drift_STL_log	2,710,123.78	-21,413.78
2015 Aug	3,108,357	Drift_STL_log	3,125,334.22	-16,977.22
2015 Sep	2,196,681	Drift_STL_log	2,115,827.88	80,853.12
2015 Oct	1,553,142	Drift_STL_log	1,462,691.44	90,450.56
2015 Nov	552,778	Drift_STL_log	582,051.77	-29,273.77
2015 Dec	426,419	Drift_STL_log	439,180.93	-12,761.93
2016 Jan	443,150	Drift_STL_log	447,893.66	-4,743.66
2016 Feb	664,278	Drift_STL_log	644,618.89	19,659.11
2016 Mar	1,089,392	Drift_STL_log	981,066.27	108,325.73
2016 Apr	1,335,308	Drift_STL_log	1,527,293.29	-191,985.29
2016 May	1,828,292	Drift_STL_log	1,623,814.65	204,477.35
2016 Jun	2,288,337	Drift_STL_log	2,356,239.09	-67,902.09
2016 Jul	2,848,570	Drift_STL_log	3,005,252.24	-156,682.24
2016 Aug	3,204,047	Drift_STL_log	3,351,062.68	-147,015.68
2016 Sep	2,378,618	Drift_STL_log	2,228,590.59	150,027.41
2016 Oct	1,793,822	Drift_STL_log	1,608,634.94	185,187.06
2016 Nov	653,514	Drift_STL_log	646,229.63	7,284.37
2016 Dec	478,510	Drift_STL_log	506,845.47	-28,335.47
2017 Jan	495,629	Drift_STL_log	499,726.32	-4,097.32
2017 Feb	704,532	Drift_STL_log	722,192.43	-17,660.43
2017 Mar	1,015,421	Drift_STL_log	1,066,480.78	-51,059.78
2017 Apr	1,765,170	Drift_STL_log	1,430,125.47	335,044.53
2017 May	1,970,072	Drift_STL_log	2,142,793.66	-172,721.66
2017 Jun	2,417,100	Drift_STL_log	2,528,860.86	-111,760.86
2017 Jul	2,968,641	Drift_STL_log	3,157,828.79	-189,187.79
2017 Aug	3,295,406	Drift_STL_log	3,493,955.07	-198,549.07
2017 Sep	2,470,298	Drift_STL_log	2,346,171.84	124,126.16
2017 Oct	1,911,961	Drift_STL_log	1,717,244.97	194,716.03
2017 Nov	680,373	Drift_STL_log	676,100.02	4,272.98
2017 Dec	512,548	Drift_STL_log	517,225.91	-4,677.91
2018 Jan	503,908	Drift_STL_log	530,155.07	-26,247.07
2018 Feb	731,090	Drift_STL_log	730,967.48	122.52
2018 Mar	1,151,455	Drift_STL_log	1,099,554.08	51,900.92
2018 Apr	1,575,078	Drift_STL_log	1,671,547.95	-96,469.95
2018 May	2,003,996	Drift_STL_log	1,936,887.73	67,108.27
2018 Jun	2,381,154	Drift_STL_log	2,540,075.60	-158,921.60
2018 Jul	2,981,643	Drift_STL_log	3,076,112.89	-94,469.89
2018 Aug	3,371,918	Drift_STL_log	3,475,025.84	-103,107.84
2018 Sep	2,499,368	Drift_STL_log	2,432,675.83	66,692.17
2018 Oct	1,956,693	Drift_STL_log	1,783,886.63	172,806.37
2018 Nov	732,141	Drift_STL_log	683,547.15	48,593.85
2018 Dec	554,803	Drift_STL_log	545,717.61	9,085.39
2019 Jan	548,686	Drift_STL_log	561,815.12	-13,129.12
2019 Feb	739,981	Drift_STL_log	790,266.91	-50,285.91
2019 Mar	1,078,918	Drift_STL_log	1,131,014.86	-52,096.86
2019 Apr	1,795,494	Drift_STL_log	1,580,732.60	214,761.40
2019 May	1,990,529	Drift_STL_log	2,209,486.22	-218,957.22
2019 Jun	2,425,834	Drift_STL_log	2,507,930.46	-82,096.46
2019 Jul	2,988,668	Drift_STL_log	3,119,785.84	-131,117.84
2019 Aug	3,439,271	Drift_STL_log	3,484,943.01	-45,672.01
2019 Sep	2,573,527	Drift_STL_log	2,519,603.98	53,923.02
2019 Oct	1,930,852	Drift_STL_log	1,889,616.57	41,235.43
2019 Nov	785,875	Drift_STL_log	684,128.73	101,746.27
2019 Dec	602,860	Drift_STL_log	578,706.41	24,153.59
2020 Jan	560,368	Drift_STL_log	599,012.98	-38,644.98
2020 Feb	844,247	Drift_STL_log	797,351.84	46,895.16
2020 Mar	513,360	Drift_STL_log	1,265,744.15	-752,384.15
2020 Apr	25,614	Drift_STL_log	859,678.68	-834,064.68
2020 May	40,932	Drift_STL_log	54,526.40	-13,594.40
2020 Jun	330,393	Drift_STL_log	73,737.12	256,655.88
2020 Jul	1,035,732	Drift_STL_log	426,364.37	609,367.63
2020 Aug	2,090,569	Drift_STL_log	1,051,532.80	1,039,036.20
2020 Sep	1,418,185	Drift_STL_log	1,277,375.91	140,809.09
2020 Oct	696,087	Drift_STL_log	920,427.26	-224,340.26
2020 Nov	181,873	Drift_STL_log	242,597.05	-60,724.05
2020 Dec	153,351	Drift_STL_log	138,851.42	14,499.58
2021 Jan	105,336	Drift_STL_log	153,339.88	-48,003.88
2021 Feb	66,194	Drift_STL_log	161,991.87	-95,797.87
2021 Mar	84,413	Drift_STL_log	101,170.02	-16,757.02
2021 Apr	138,661	Drift_STL_log	82,640.87	56,020.13
2021 May	502,057	Drift_STL_log	207,067.87	294,989.13
2021 Jun	1,182,009	Drift_STL_log	881,035.32	300,973.68
2021 Jul	1,551,789	Drift_STL_log	1,676,532.41	-124,743.41
2021 Aug	2,762,537	Drift_STL_log	1,941,875.41	820,661.59
2021 Sep	1,869,194	Drift_STL_log	1,922,607.98	-53,413.98
2021 Oct	1,584,764	Drift_STL_log	1,300,577.46	284,186.54
2021 Nov	651,051	Drift_STL_log	553,544.36	97,506.64
2021 Dec	376,031	Drift_STL_log	507,984.79	-131,953.79
2022 Jan	344,634	Drift_STL_log	375,426.42	-30,792.42
2022 Feb	590,122	Drift_STL_log	474,248.32	115,873.68
2022 Mar	873,841	Drift_STL_log	810,414.64	63,426.36
2022 Apr	1,629,377	Drift_STL_log	829,113.36	800,263.64
2022 May	1,867,744	Drift_STL_log	2,804,198.48	-936,454.48
2022 Jun	2,230,207	Drift_STL_log	4,135,760.94	-1,905,553.94
2010 Jan	366,296	ETS_auto	417,493.58	-51,197.58
2010 Feb	533,056	ETS_auto	563,256.14	-30,200.14
2010 Mar	742,227	ETS_auto	751,330.87	-9,103.87
2010 Apr	902,745	ETS_auto	909,359.12	-6,614.12
2010 May	1,107,303	ETS_auto	1,083,745.21	23,557.79
2010 Jun	1,464,695	ETS_auto	1,356,147.60	108,547.40
2010 Jul	2,050,478	ETS_auto	1,703,115.68	347,362.32
2010 Aug	2,468,924	ETS_auto	2,189,090.79	279,833.21
2010 Sep	1,696,356	ETS_auto	1,599,911.73	96,444.27
2010 Oct	1,104,659	ETS_auto	1,129,201.59	-24,542.59
2010 Nov	445,221	ETS_auto	540,960.23	-95,739.23
2010 Dec	365,490	ETS_auto	392,065.41	-26,575.41
2011 Jan	357,209	ETS_auto	413,149.61	-55,940.61
2011 Feb	503,831	ETS_auto	551,357.83	-47,526.83
2011 Mar	761,343	ETS_auto	713,371.22	47,971.78
2011 Apr	1,177,115	ETS_auto	931,020.48	246,094.52
2011 May	1,169,516	ETS_auto	1,199,382.78	-29,866.78
2011 Jun	1,576,730	ETS_auto	1,515,660.36	61,069.64
2011 Jul	2,208,160	ETS_auto	2,021,426.54	186,733.46
2011 Aug	2,572,404	ETS_auto	2,433,313.75	139,090.25
2011 Sep	1,731,056	ETS_auto	1,674,700.79	56,355.21
2011 Oct	1,161,751	ETS_auto	1,105,069.46	56,681.54
2011 Nov	427,550	ETS_auto	595,978.30	-168,428.30
2011 Dec	333,201	ETS_auto	387,904.36	-54,703.36
2012 Jan	359,355	ETS_auto	374,029.47	-14,674.47
2012 Feb	531,709	ETS_auto	512,226.55	19,482.45
2012 Mar	751,024	ETS_auto	778,827.99	-27,803.99
2012 Apr	1,017,976	ETS_auto	1,087,238.47	-69,262.47
2012 May	1,194,673	ETS_auto	1,134,942.50	59,730.50
2012 Jun	1,678,327	ETS_auto	1,513,951.71	164,375.29
2012 Jul	2,296,474	ETS_auto	2,111,285.52	185,188.48
2012 Aug	2,622,801	ETS_auto	2,505,204.03	117,596.97
2012 Sep	1,829,252	ETS_auto	1,699,095.29	130,156.71
2012 Oct	1,244,751	ETS_auto	1,138,557.65	106,193.35
2012 Nov	453,958	ETS_auto	560,452.73	-106,494.73
2012 Dec	346,474	ETS_auto	393,109.73	-46,635.73
2013 Jan	369,969	ETS_auto	374,205.97	-4,236.97
2013 Feb	520,055	ETS_auto	526,457.54	-6,402.54
2013 Mar	840,024	ETS_auto	714,698.16	125,325.84
2013 Apr	986,191	ETS_auto	1,104,941.74	-118,750.74
2013 May	1,382,234	ETS_auto	1,220,813.52	161,420.48
2013 Jun	1,814,108	ETS_auto	1,706,413.63	107,694.37
2013 Jul	2,387,304	ETS_auto	2,344,169.09	43,134.91
2013 Aug	2,764,686	ETS_auto	2,687,942.99	76,743.01
2013 Sep	1,943,037	ETS_auto	1,847,649.51	95,387.49
2013 Oct	1,291,360	ETS_auto	1,246,296.58	45,063.42
2013 Nov	455,695	ETS_auto	569,499.17	-113,804.17
2013 Dec	358,062	ETS_auto	387,247.27	-29,185.27
2014 Jan	377,387	ETS_auto	379,133.44	-1,746.44
2014 Feb	543,470	ETS_auto	531,743.69	11,726.31
2014 Mar	749,773	ETS_auto	755,327.75	-5,554.75
2014 Apr	1,337,145	ETS_auto	1,037,921.59	299,223.41
2014 May	1,538,342	ETS_auto	1,404,790.10	133,551.90
2014 Jun	1,994,167	ETS_auto	1,884,800.84	109,366.16
2014 Jul	2,529,246	ETS_auto	2,519,964.82	9,281.18
2014 Aug	3,069,865	ETS_auto	2,901,653.02	168,211.98
2014 Sep	2,089,656	ETS_auto	2,028,095.16	61,560.84
2014 Oct	1,477,481	ETS_auto	1,351,593.21	125,887.79
2014 Nov	502,473	ETS_auto	502,020.03	452.97
2014 Dec	382,543	ETS_auto	394,899.61	-12,356.61
2015 Jan	381,607	ETS_auto	405,512.88	-23,905.88
2015 Feb	544,777	ETS_auto	544,824.14	-47.14
2015 Mar	827,071	ETS_auto	854,993.25	-27,922.25
2015 Apr	1,242,844	ETS_auto	1,316,937.62	-74,093.62
2015 May	1,654,526	ETS_auto	1,521,971.25	132,554.75
2015 Jun	2,079,484	ETS_auto	1,995,913.45	83,570.55
2015 Jul	2,688,710	ETS_auto	2,575,852.83	112,857.17
2015 Aug	3,108,357	ETS_auto	3,089,554.92	18,802.08
2015 Sep	2,196,681	ETS_auto	2,105,834.37	90,846.63
2015 Oct	1,553,142	ETS_auto	1,459,336.81	93,805.19
2015 Nov	552,778	ETS_auto	506,892.64	45,885.36
2015 Dec	426,419	ETS_auto	464,949.30	-38,530.30
2016 Jan	443,150	ETS_auto	412,261.20	30,888.80
2016 Feb	664,278	ETS_auto	598,541.76	65,736.24
2016 Mar	1,089,392	ETS_auto	925,298.77	164,093.23
2016 Apr	1,335,308	ETS_auto	1,500,014.79	-164,706.79
2016 May	1,828,292	ETS_auto	1,846,920.02	-18,628.02
2016 Jun	2,288,337	ETS_auto	2,305,652.14	-17,315.14
2016 Jul	2,848,570	ETS_auto	2,948,352.07	-99,782.07
2016 Aug	3,204,047	ETS_auto	3,403,630.69	-199,583.69
2016 Sep	2,378,618	ETS_auto	2,329,657.11	48,960.89
2016 Oct	1,793,822	ETS_auto	1,655,728.84	138,093.16
2016 Nov	653,514	ETS_auto	575,438.26	78,075.74
2016 Dec	478,510	ETS_auto	525,474.81	-46,964.81
2017 Jan	495,629	ETS_auto	505,663.62	-10,034.62
2017 Feb	704,532	ETS_auto	694,075.46	10,456.54
2017 Mar	1,015,421	ETS_auto	1,120,495.91	-105,074.91
2017 Apr	1,765,170	ETS_auto	1,422,355.84	342,814.16
2017 May	1,970,072	ETS_auto	2,018,404.89	-48,332.89
2017 Jun	2,417,100	ETS_auto	2,539,480.82	-122,380.82
2017 Jul	2,968,641	ETS_auto	3,132,567.03	-163,926.03
2017 Aug	3,295,406	ETS_auto	3,554,910.95	-259,504.95
2017 Sep	2,470,298	ETS_auto	2,538,094.43	-67,796.43
2017 Oct	1,911,961	ETS_auto	1,836,694.58	75,266.42
2017 Nov	680,373	ETS_auto	713,031.57	-32,658.57
2017 Dec	512,548	ETS_auto	527,969.22	-15,421.22
2018 Jan	503,908	ETS_auto	531,120.50	-27,212.50
2018 Feb	731,090	ETS_auto	740,818.87	-9,728.87
2018 Mar	1,151,455	ETS_auto	1,113,103.61	38,351.39
2018 Apr	1,575,078	ETS_auto	1,588,490.23	-13,412.23
2018 May	2,003,996	ETS_auto	1,908,787.40	95,208.60
2018 Jun	2,381,154	ETS_auto	2,507,123.14	-125,969.14
2018 Jul	2,981,643	ETS_auto	3,130,545.34	-148,902.34
2018 Aug	3,371,918	ETS_auto	3,528,077.64	-156,159.64
2018 Sep	2,499,368	ETS_auto	2,366,314.31	133,053.69
2018 Oct	1,956,693	ETS_auto	1,867,851.71	88,841.29
2018 Nov	732,141	ETS_auto	695,639.32	36,501.68
2018 Dec	554,803	ETS_auto	556,450.50	-1,647.50
2019 Jan	548,686	ETS_auto	561,565.99	-12,879.99
2019 Feb	739,981	ETS_auto	799,060.11	-59,079.11
2019 Mar	1,078,918	ETS_auto	1,139,323.50	-60,405.50
2019 Apr	1,795,494	ETS_auto	1,657,910.05	137,583.95
2019 May	1,990,529	ETS_auto	1,986,030.38	4,498.62
2019 Jun	2,425,834	ETS_auto	2,552,861.39	-127,027.39
2019 Jul	2,988,668	ETS_auto	3,335,730.48	-347,062.48
2019 Aug	3,439,271	ETS_auto	3,722,938.59	-283,667.59
2019 Sep	2,573,527	ETS_auto	2,636,257.19	-62,730.19
2019 Oct	1,930,852	ETS_auto	1,990,527.06	-59,675.06
2019 Nov	785,875	ETS_auto	668,561.34	117,313.66
2019 Dec	602,860	ETS_auto	565,243.15	37,616.85
2020 Jan	560,368	ETS_auto	596,398.14	-36,030.14
2020 Feb	844,247	ETS_auto	810,177.53	34,069.47
2020 Mar	513,360	ETS_auto	1,182,658.49	-669,298.49
2020 Apr	25,614	ETS_auto	1,712,051.58	-1,686,437.58
2020 May	40,932	ETS_auto	396,067.70	-355,135.70
2020 Jun	330,393	ETS_auto	51,725.72	278,667.28
2020 Jul	1,035,732	ETS_auto	697,070.99	338,661.01
2020 Aug	2,090,569	ETS_auto	1,351,117.42	739,451.58
2020 Sep	1,418,185	ETS_auto	1,216,398.41	201,786.59
2020 Oct	696,087	ETS_auto	809,630.48	-113,543.48
2020 Nov	181,873	ETS_auto	-301,954.30	483,827.30
2020 Dec	153,351	ETS_auto	54,050.32	99,300.68
2021 Jan	105,336	ETS_auto	169,499.43	-64,163.43
2021 Feb	66,194	ETS_auto	309,736.63	-243,542.63
2021 Mar	84,413	ETS_auto	310,042.86	-225,629.86
2021 Apr	138,661	ETS_auto	428,048.51	-289,387.51
2021 May	502,057	ETS_auto	412,690.78	89,366.22
2021 Jun	1,182,009	ETS_auto	913,480.51	268,528.49
2021 Jul	1,551,789	ETS_auto	1,764,352.00	-212,563.00
2021 Aug	2,762,537	ETS_auto	2,022,719.37	739,817.63
2021 Sep	1,869,194	ETS_auto	1,912,607.86	-43,413.86
2021 Oct	1,584,764	ETS_auto	1,251,963.98	332,800.02
2021 Nov	651,051	ETS_auto	595,997.52	55,053.48
2021 Dec	376,031	ETS_auto	495,757.65	-119,726.65
2022 Jan	344,634	ETS_auto	358,849.78	-14,215.78
2022 Feb	590,122	ETS_auto	502,096.23	88,025.77
2022 Mar	873,841	ETS_auto	803,578.10	70,262.90
2022 Apr	1,629,377	ETS_auto	1,168,984.02	460,392.98
2022 May	1,867,744	ETS_auto	1,891,992.03	-24,248.03
2022 Jun	2,230,207	ETS_auto	2,281,945.61	-51,738.61
2010 Jan	366,296	ETS_auto_log	417,048.27	-50,752.27
2010 Feb	533,056	ETS_auto_log	571,119.00	-38,063.00
2010 Mar	742,227	ETS_auto_log	761,254.43	-19,027.43
2010 Apr	902,745	ETS_auto_log	902,504.40	240.60
2010 May	1,107,303	ETS_auto_log	1,083,964.30	23,338.70
2010 Jun	1,464,695	ETS_auto_log	1,352,833.86	111,861.14
2010 Jul	2,050,478	ETS_auto_log	1,720,713.43	329,764.57
2010 Aug	2,468,924	ETS_auto_log	2,169,043.45	299,880.55
2010 Sep	1,696,356	ETS_auto_log	1,640,291.15	56,064.85
2010 Oct	1,104,659	ETS_auto_log	1,145,056.31	-40,397.31
2010 Nov	445,221	ETS_auto_log	546,676.48	-101,455.48
2010 Dec	365,490	ETS_auto_log	394,710.52	-29,220.52
2011 Jan	357,209	ETS_auto_log	411,797.77	-54,588.77
2011 Feb	503,831	ETS_auto_log	557,745.75	-53,914.75
2011 Mar	761,343	ETS_auto_log	731,389.57	29,953.43
2011 Apr	1,177,115	ETS_auto_log	908,314.28	268,800.72
2011 May	1,169,516	ETS_auto_log	1,203,233.34	-33,717.34
2011 Jun	1,576,730	ETS_auto_log	1,497,229.15	79,500.85
2011 Jul	2,208,160	ETS_auto_log	1,979,762.45	228,397.55
2011 Aug	2,572,404	ETS_auto_log	2,445,925.81	126,478.19
2011 Sep	1,731,056	ETS_auto_log	1,679,735.15	51,320.85
2011 Oct	1,161,751	ETS_auto_log	1,105,398.34	56,352.66
2011 Nov	427,550	ETS_auto_log	537,696.14	-110,146.14
2011 Dec	333,201	ETS_auto_log	390,494.31	-57,293.31
2012 Jan	359,355	ETS_auto_log	374,449.74	-15,094.74
2012 Feb	531,709	ETS_auto_log	536,236.83	-4,527.83
2012 Mar	751,024	ETS_auto_log	777,410.64	-26,386.64
2012 Apr	1,017,976	ETS_auto_log	1,066,844.16	-48,868.16
2012 May	1,194,673	ETS_auto_log	1,134,475.99	60,197.01
2012 Jun	1,678,327	ETS_auto_log	1,509,876.91	168,450.09
2012 Jul	2,296,474	ETS_auto_log	2,114,136.26	182,337.74
2012 Aug	2,622,801	ETS_auto_log	2,498,315.43	124,485.57
2012 Sep	1,829,252	ETS_auto_log	1,701,534.36	127,717.64
2012 Oct	1,244,751	ETS_auto_log	1,133,421.43	111,329.57
2012 Nov	453,958	ETS_auto_log	458,063.54	-4,105.54
2012 Dec	346,474	ETS_auto_log	369,473.81	-22,999.81
2013 Jan	369,969	ETS_auto_log	388,048.43	-18,079.43
2013 Feb	520,055	ETS_auto_log	556,325.50	-36,270.50
2013 Mar	840,024	ETS_auto_log	789,946.86	50,077.14
2013 Apr	986,191	ETS_auto_log	1,100,050.62	-113,859.62
2013 May	1,382,234	ETS_auto_log	1,222,953.12	159,280.88
2013 Jun	1,814,108	ETS_auto_log	1,705,667.07	108,440.93
2013 Jul	2,387,304	ETS_auto_log	2,306,196.59	81,107.41
2013 Aug	2,764,686	ETS_auto_log	2,679,915.98	84,770.02
2013 Sep	1,943,037	ETS_auto_log	1,840,936.07	102,100.93
2013 Oct	1,291,360	ETS_auto_log	1,247,321.52	44,038.48
2013 Nov	455,695	ETS_auto_log	463,994.26	-8,299.26
2013 Dec	358,062	ETS_auto_log	359,202.39	-1,140.39
2014 Jan	377,387	ETS_auto_log	383,588.09	-6,201.09
2014 Feb	543,470	ETS_auto_log	555,145.54	-11,675.54
2014 Mar	749,773	ETS_auto_log	854,280.41	-104,507.41
2014 Apr	1,337,145	ETS_auto_log	1,036,568.19	300,576.81
2014 May	1,538,342	ETS_auto_log	1,422,929.77	115,412.23
2014 Jun	1,994,167	ETS_auto_log	1,893,309.64	100,857.36
2014 Jul	2,529,246	ETS_auto_log	2,527,579.75	1,666.25
2014 Aug	3,069,865	ETS_auto_log	2,904,218.62	165,646.38
2014 Sep	2,089,656	ETS_auto_log	2,035,618.28	54,037.72
2014 Oct	1,477,481	ETS_auto_log	1,342,018.32	135,462.68
2014 Nov	502,473	ETS_auto_log	492,037.15	10,435.85
2014 Dec	382,543	ETS_auto_log	389,338.39	-6,795.39
2015 Jan	381,607	ETS_auto_log	410,047.34	-28,440.34
2015 Feb	544,777	ETS_auto_log	585,491.60	-40,714.60
2015 Mar	827,071	ETS_auto_log	833,250.86	-6,179.86
2015 Apr	1,242,844	ETS_auto_log	1,316,963.60	-74,119.60
2015 May	1,654,526	ETS_auto_log	1,528,362.60	126,163.40
2015 Jun	2,079,484	ETS_auto_log	2,009,083.23	70,400.77
2015 Jul	2,688,710	ETS_auto_log	2,587,636.75	101,073.25
2015 Aug	3,108,357	ETS_auto_log	3,101,716.74	6,640.26
2015 Sep	2,196,681	ETS_auto_log	2,115,899.72	80,781.28
2015 Oct	1,553,142	ETS_auto_log	1,483,094.29	70,047.71
2015 Nov	552,778	ETS_auto_log	507,631.06	45,146.94
2015 Dec	426,419	ETS_auto_log	395,207.89	31,211.11
2016 Jan	443,150	ETS_auto_log	412,604.35	30,545.65
2016 Feb	664,278	ETS_auto_log	613,388.74	50,889.26
2016 Mar	1,089,392	ETS_auto_log	923,413.06	165,978.94
2016 Apr	1,335,308	ETS_auto_log	1,507,480.36	-172,172.36
2016 May	1,828,292	ETS_auto_log	1,844,808.43	-16,516.43
2016 Jun	2,288,337	ETS_auto_log	2,316,650.95	-28,313.95
2016 Jul	2,848,570	ETS_auto_log	2,958,371.19	-109,801.19
2016 Aug	3,204,047	ETS_auto_log	3,520,377.38	-316,330.38
2016 Sep	2,378,618	ETS_auto_log	2,427,280.12	-48,662.12
2016 Oct	1,793,822	ETS_auto_log	1,639,737.84	154,084.16
2016 Nov	653,514	ETS_auto_log	580,526.31	72,987.69
2016 Dec	478,510	ETS_auto_log	453,727.24	24,782.76
2017 Jan	495,629	ETS_auto_log	478,919.63	16,709.37
2017 Feb	704,532	ETS_auto_log	715,929.38	-11,397.38
2017 Mar	1,015,421	ETS_auto_log	1,125,481.82	-110,060.82
2017 Apr	1,765,170	ETS_auto_log	1,458,771.64	306,398.36
2017 May	1,970,072	ETS_auto_log	2,024,080.69	-54,008.69
2017 Jun	2,417,100	ETS_auto_log	2,544,409.46	-127,309.46
2017 Jul	2,968,641	ETS_auto_log	3,192,874.28	-224,233.28
2017 Aug	3,295,406	ETS_auto_log	3,642,929.53	-347,523.53
2017 Sep	2,470,298	ETS_auto_log	2,635,862.92	-165,564.92
2017 Oct	1,911,961	ETS_auto_log	1,819,992.27	91,968.73
2017 Nov	680,373	ETS_auto_log	686,092.85	-5,719.85
2017 Dec	512,548	ETS_auto_log	525,066.60	-12,518.60
2018 Jan	503,908	ETS_auto_log	524,696.71	-20,788.71
2018 Feb	731,090	ETS_auto_log	750,674.78	-19,584.78
2018 Mar	1,151,455	ETS_auto_log	1,122,965.62	28,489.38
2018 Apr	1,575,078	ETS_auto_log	1,752,802.84	-177,724.84
2018 May	2,003,996	ETS_auto_log	1,935,819.78	68,176.22
2018 Jun	2,381,154	ETS_auto_log	2,591,600.20	-210,446.20
2018 Jul	2,981,643	ETS_auto_log	3,204,733.91	-223,090.91
2018 Aug	3,371,918	ETS_auto_log	3,614,558.90	-242,640.90
2018 Sep	2,499,368	ETS_auto_log	2,551,899.12	-52,531.12
2018 Oct	1,956,693	ETS_auto_log	1,693,782.33	262,910.67
2018 Nov	732,141	ETS_auto_log	712,110.72	20,030.28
2018 Dec	554,803	ETS_auto_log	554,289.22	513.78
2019 Jan	548,686	ETS_auto_log	572,873.49	-24,187.49
2019 Feb	739,981	ETS_auto_log	767,014.82	-27,033.82
2019 Mar	1,078,918	ETS_auto_log	1,148,669.29	-69,751.29
2019 Apr	1,795,494	ETS_auto_log	1,586,199.23	209,294.77
2019 May	1,990,529	ETS_auto_log	2,020,668.13	-30,139.13
2019 Jun	2,425,834	ETS_auto_log	2,588,394.02	-162,560.02
2019 Jul	2,988,668	ETS_auto_log	3,212,523.69	-223,855.69
2019 Aug	3,439,271	ETS_auto_log	3,571,995.67	-132,724.67
2019 Sep	2,573,527	ETS_auto_log	2,519,828.34	53,698.66
2019 Oct	1,930,852	ETS_auto_log	2,000,591.24	-69,739.24
2019 Nov	785,875	ETS_auto_log	661,957.76	123,917.24
2019 Dec	602,860	ETS_auto_log	555,912.56	46,947.44
2020 Jan	560,368	ETS_auto_log	558,227.28	2,140.72
2020 Feb	844,247	ETS_auto_log	780,268.55	63,978.45
2020 Mar	513,360	ETS_auto_log	1,188,997.53	-675,637.53
2020 Apr	25,614	ETS_auto_log	1,733,580.18	-1,707,966.18
2020 May	40,932	ETS_auto_log	22,110.34	18,821.66
2020 Jun	330,393	ETS_auto_log	56,041.03	274,351.97
2020 Jul	1,035,732	ETS_auto_log	341,558.70	694,173.30
2020 Aug	2,090,569	ETS_auto_log	1,230,319.65	860,249.35
2020 Sep	1,418,185	ETS_auto_log	1,457,982.64	-39,797.64
2020 Oct	696,087	ETS_auto_log	1,083,500.20	-387,413.20
2020 Nov	181,873	ETS_auto_log	263,908.45	-82,035.45
2020 Dec	153,351	ETS_auto_log	131,185.62	22,165.38
2021 Jan	105,336	ETS_auto_log	147,685.32	-42,349.32
2021 Feb	66,194	ETS_auto_log	167,965.12	-101,771.12
2021 Mar	84,413	ETS_auto_log	97,273.67	-12,860.67
2021 Apr	138,661	ETS_auto_log	90,339.41	48,321.59
2021 May	502,057	ETS_auto_log	193,607.85	308,449.15
2021 Jun	1,182,009	ETS_auto_log	832,347.26	349,661.74
2021 Jul	1,551,789	ETS_auto_log	1,605,454.64	-53,665.64
2021 Aug	2,762,537	ETS_auto_log	1,971,226.93	791,310.07
2021 Sep	1,869,194	ETS_auto_log	2,036,278.80	-167,084.80
2021 Oct	1,584,764	ETS_auto_log	1,422,765.00	161,999.00
2021 Nov	651,051	ETS_auto_log	578,820.65	72,230.35
2021 Dec	376,031	ETS_auto_log	581,159.05	-205,128.05
2022 Jan	344,634	ETS_auto_log	394,567.43	-49,933.43
2022 Feb	590,122	ETS_auto_log	464,647.66	125,474.34
2022 Mar	873,841	ETS_auto_log	838,342.49	35,498.51
2022 Apr	1,629,377	ETS_auto_log	1,037,677.17	591,699.83
2022 May	1,867,744	ETS_auto_log	2,336,331.20	-468,587.20
2022 Jun	2,230,207	ETS_auto_log	3,372,492.21	-1,142,285.21
2010 Jan	366,296	HWA	379,162.29	-12,866.29
2010 Feb	533,056	HWA	568,769.53	-35,713.53
2010 Mar	742,227	HWA	782,719.76	-40,492.76
2010 Apr	902,745	HWA	949,006.37	-46,261.37
2010 May	1,107,303	HWA	1,157,080.79	-49,777.79
2010 Jun	1,464,695	HWA	1,424,631.32	40,063.68
2010 Jul	2,050,478	HWA	1,835,779.97	214,698.03
2010 Aug	2,468,924	HWA	2,230,222.87	238,701.13
2010 Sep	1,696,356	HWA	1,656,706.55	39,649.45
2010 Oct	1,104,659	HWA	1,172,783.52	-68,124.52
2010 Nov	445,221	HWA	551,237.33	-106,016.33
2010 Dec	365,490	HWA	392,412.87	-26,922.87
2011 Jan	357,209	HWA	414,702.67	-57,493.67
2011 Feb	503,831	HWA	580,540.24	-76,709.24
2011 Mar	761,343	HWA	779,678.82	-18,335.82
2011 Apr	1,177,115	HWA	936,983.64	240,131.36
2011 May	1,169,516	HWA	1,246,543.77	-77,027.77
2011 Jun	1,576,730	HWA	1,507,090.75	69,639.25
2011 Jul	2,208,160	HWA	1,958,163.94	249,996.06
2011 Aug	2,572,404	HWA	2,440,036.54	132,367.46
2011 Sep	1,731,056	HWA	1,767,976.70	-36,920.70
2011 Oct	1,161,751	HWA	1,222,533.44	-60,782.44
2011 Nov	427,550	HWA	597,813.57	-170,263.57
2011 Dec	333,201	HWA	410,817.82	-77,616.82
2012 Jan	359,355	HWA	394,498.36	-35,143.36
2012 Feb	531,709	HWA	544,649.74	-12,940.74
2012 Mar	751,024	HWA	764,586.09	-13,562.09
2012 Apr	1,017,976	HWA	962,983.40	54,992.60
2012 May	1,194,673	HWA	1,187,072.09	7,600.91
2012 Jun	1,678,327	HWA	1,490,792.73	187,534.27
2012 Jul	2,296,474	HWA	2,037,623.17	258,850.83
2012 Aug	2,622,801	HWA	2,571,271.66	51,529.34
2012 Sep	1,829,252	HWA	1,839,079.52	-9,827.52
2012 Oct	1,244,751	HWA	1,298,400.63	-53,649.63
2012 Nov	453,958	HWA	634,842.14	-180,884.14
2012 Dec	346,474	HWA	443,007.00	-96,533.00
2013 Jan	369,969	HWA	439,969.58	-70,000.58
2013 Feb	520,055	HWA	595,614.58	-75,559.58
2013 Mar	840,024	HWA	742,217.78	97,806.22
2013 Apr	986,191	HWA	1,027,574.11	-41,383.11
2013 May	1,382,234	HWA	1,185,471.72	196,762.28
2013 Jun	1,814,108	HWA	1,632,319.26	181,788.74
2013 Jul	2,387,304	HWA	2,232,223.40	155,080.60
2013 Aug	2,764,686	HWA	2,720,286.76	44,399.24
2013 Sep	1,943,037	HWA	1,983,846.86	-40,809.86
2013 Oct	1,291,360	HWA	1,395,308.57	-103,948.57
2013 Nov	455,695	HWA	672,277.39	-216,582.39
2013 Dec	358,062	HWA	427,144.20	-69,082.20
2014 Jan	377,387	HWA	445,511.83	-68,124.83
2014 Feb	543,470	HWA	540,718.74	2,751.26
2014 Mar	749,773	HWA	782,460.98	-32,687.98
2014 Apr	1,337,145	HWA	969,485.16	367,659.84
2014 May	1,538,342	HWA	1,413,673.41	124,668.59
2014 Jun	1,994,167	HWA	1,861,439.95	132,727.05
2014 Jul	2,529,246	HWA	2,460,434.17	68,811.83
2014 Aug	3,069,865	HWA	2,892,349.52	177,515.48
2014 Sep	2,089,656	HWA	2,033,301.86	56,354.14
2014 Oct	1,477,481	HWA	1,419,201.70	58,279.30
2014 Nov	502,473	HWA	625,517.41	-123,044.41
2014 Dec	382,543	HWA	512,070.14	-129,527.14
2015 Jan	381,607	HWA	502,013.23	-120,406.23
2015 Feb	544,777	HWA	656,741.11	-111,964.11
2015 Mar	827,071	HWA	885,173.63	-58,102.63
2015 Apr	1,242,844	HWA	1,368,012.93	-125,168.93
2015 May	1,654,526	HWA	1,545,549.19	108,976.81
2015 Jun	2,079,484	HWA	2,006,243.70	73,240.30
2015 Jul	2,688,710	HWA	2,551,230.42	137,479.58
2015 Aug	3,108,357	HWA	3,062,035.15	46,321.85
2015 Sep	2,196,681	HWA	2,087,680.52	109,000.48
2015 Oct	1,553,142	HWA	1,485,137.29	68,004.71
2015 Nov	552,778	HWA	548,588.72	4,189.28
2015 Dec	426,419	HWA	444,863.58	-18,444.58
2016 Jan	443,150	HWA	451,049.85	-7,899.85
2016 Feb	664,278	HWA	630,284.21	33,993.79
2016 Mar	1,089,392	HWA	934,085.08	155,306.92
2016 Apr	1,335,308	HWA	1,421,800.37	-86,492.37
2016 May	1,828,292	HWA	1,796,187.26	32,104.74
2016 Jun	2,288,337	HWA	2,216,079.61	72,257.39
2016 Jul	2,848,570	HWA	2,806,175.59	42,394.41
2016 Aug	3,204,047	HWA	3,215,383.22	-11,336.22
2016 Sep	2,378,618	HWA	2,315,410.56	63,207.44
2016 Oct	1,793,822	HWA	1,680,512.90	113,309.10
2016 Nov	653,514	HWA	699,686.44	-46,172.44
2016 Dec	478,510	HWA	572,637.46	-94,127.46
2017 Jan	495,629	HWA	579,861.03	-84,232.03
2017 Feb	704,532	HWA	783,494.76	-78,962.76
2017 Mar	1,015,421	HWA	1,172,088.07	-156,667.07
2017 Apr	1,765,170	HWA	1,404,024.67	361,145.33
2017 May	1,970,072	HWA	1,937,566.24	32,505.76
2017 Jun	2,417,100	HWA	2,391,463.65	25,636.35
2017 Jul	2,968,641	HWA	2,956,312.69	12,328.31
2017 Aug	3,295,406	HWA	3,326,726.37	-31,320.37
2017 Sep	2,470,298	HWA	2,485,593.32	-15,295.32
2017 Oct	1,911,961	HWA	1,882,098.90	29,862.10
2017 Nov	680,373	HWA	1,072,521.28	-392,148.28
2017 Dec	512,548	HWA	588,450.45	-75,902.45
2018 Jan	503,908	HWA	604,994.40	-101,086.40
2018 Feb	731,090	HWA	812,203.15	-81,113.15
2018 Mar	1,151,455	HWA	1,137,766.11	13,688.89
2018 Apr	1,575,078	HWA	1,822,847.73	-247,769.73
2018 May	2,003,996	HWA	2,034,729.22	-30,733.22
2018 Jun	2,381,154	HWA	2,489,775.37	-108,621.37
2018 Jul	2,981,643	HWA	3,010,195.85	-28,552.85
2018 Aug	3,371,918	HWA	3,338,707.61	33,210.39
2018 Sep	2,499,368	HWA	2,481,177.78	18,190.22
2018 Oct	1,956,693	HWA	1,876,186.75	80,506.25
2018 Nov	732,141	HWA	1,069,769.78	-337,628.78
2018 Dec	554,803	HWA	604,601.67	-49,798.67
2019 Jan	548,686	HWA	559,880.60	-11,194.60
2019 Feb	739,981	HWA	792,656.99	-52,675.99
2019 Mar	1,078,918	HWA	1,033,837.65	45,080.35
2019 Apr	1,795,494	HWA	1,460,361.47	335,132.53
2019 May	1,990,529	HWA	2,083,214.32	-92,685.32
2019 Jun	2,425,834	HWA	2,421,202.56	4,631.44
2019 Jul	2,988,668	HWA	2,983,035.89	5,632.11
2019 Aug	3,439,271	HWA	3,423,245.85	16,025.15
2019 Sep	2,573,527	HWA	2,553,148.17	20,378.83
2019 Oct	1,930,852	HWA	1,947,292.94	-16,440.94
2019 Nov	785,875	HWA	968,594.87	-182,719.87
2019 Dec	602,860	HWA	660,956.75	-58,096.75
2020 Jan	560,368	HWA	609,422.08	-49,054.08
2020 Feb	844,247	HWA	743,297.43	100,949.57
2020 Mar	513,360	HWA	1,146,696.09	-633,336.09
2020 Apr	25,614	HWA	1,018,732.90	-993,118.90
2020 May	40,932	HWA	98,858.18	-57,926.18
2020 Jun	330,393	HWA	258,311.96	72,081.04
2020 Jul	1,035,732	HWA	697,070.99	338,661.01
2020 Aug	2,090,569	HWA	1,309,415.01	781,153.99
2020 Sep	1,418,185	HWA	1,227,606.58	190,578.42
2020 Oct	696,087	HWA	830,221.73	-134,134.73
2020 Nov	181,873	HWA	-299,478.34	481,351.34
2020 Dec	153,351	HWA	66,788.90	86,562.10
2021 Jan	105,336	HWA	183,221.41	-77,885.41
2021 Feb	66,194	HWA	323,867.68	-257,673.68
2021 Mar	84,413	HWA	320,838.36	-236,425.36
2021 Apr	138,661	HWA	429,812.75	-291,151.75
2021 May	502,057	HWA	401,454.68	100,602.32
2021 Jun	1,182,009	HWA	909,505.18	272,503.82
2021 Jul	1,551,789	HWA	1,773,527.85	-221,738.85
2021 Aug	2,762,537	HWA	2,019,410.59	743,126.41
2021 Sep	1,869,194	HWA	1,900,680.34	-31,486.34
2021 Oct	1,584,764	HWA	1,250,610.82	334,153.18
2021 Nov	651,051	HWA	585,204.29	65,846.71
2021 Dec	376,031	HWA	500,929.19	-124,898.19
2022 Jan	344,634	HWA	371,391.26	-26,757.26
2022 Feb	590,122	HWA	512,635.19	77,486.81
2022 Mar	873,841	HWA	799,897.51	73,943.49
2022 Apr	1,629,377	HWA	1,156,375.06	473,001.94
2022 May	1,867,744	HWA	1,881,402.83	-13,658.83
2022 Jun	2,230,207	HWA	2,304,050.76	-73,843.76
2010 Jan	366,296	HWA_log	409,254.18	-42,958.18
2010 Feb	533,056	HWA_log	557,597.10	-24,541.10
2010 Mar	742,227	HWA_log	741,599.92	627.08
2010 Apr	902,745	HWA_log	926,277.80	-23,532.80
2010 May	1,107,303	HWA_log	1,119,398.42	-12,095.42
2010 Jun	1,464,695	HWA_log	1,382,547.85	82,147.15
2010 Jul	2,050,478	HWA_log	1,783,759.07	266,718.93
2010 Aug	2,468,924	HWA_log	2,193,508.01	275,415.99
2010 Sep	1,696,356	HWA_log	1,518,464.55	177,891.45
2010 Oct	1,104,659	HWA_log	1,045,705.23	58,953.77
2010 Nov	445,221	HWA_log	512,451.88	-67,230.88
2010 Dec	365,490	HWA_log	393,285.08	-27,795.08
2011 Jan	357,209	HWA_log	390,408.83	-33,199.83
2011 Feb	503,831	HWA_log	554,360.01	-50,529.01
2011 Mar	761,343	HWA_log	747,683.81	13,659.19
2011 Apr	1,177,115	HWA_log	927,005.30	250,109.70
2011 May	1,169,516	HWA_log	1,190,296.29	-20,780.29
2011 Jun	1,576,730	HWA_log	1,493,811.34	82,918.66
2011 Jul	2,208,160	HWA_log	2,024,499.16	183,660.84
2011 Aug	2,572,404	HWA_log	2,472,770.74	99,633.26
2011 Sep	1,731,056	HWA_log	1,679,735.15	51,320.85
2011 Oct	1,161,751	HWA_log	1,105,398.34	56,352.66
2011 Nov	427,550	HWA_log	496,395.06	-68,845.06
2011 Dec	333,201	HWA_log	390,494.31	-57,293.31
2012 Jan	359,355	HWA_log	374,449.74	-15,094.74
2012 Feb	531,709	HWA_log	533,036.43	-1,327.43
2012 Mar	751,024	HWA_log	774,687.29	-23,663.29
2012 Apr	1,017,976	HWA_log	1,084,890.27	-66,914.27
2012 May	1,194,673	HWA_log	1,145,240.05	49,432.95
2012 Jun	1,678,327	HWA_log	1,519,254.51	159,072.49
2012 Jul	2,296,474	HWA_log	2,114,136.26	182,337.74
2012 Aug	2,622,801	HWA_log	2,506,734.76	116,066.24
2012 Sep	1,829,252	HWA_log	1,694,532.65	134,719.35
2012 Oct	1,244,751	HWA_log	1,129,784.79	114,966.21
2012 Nov	453,958	HWA_log	453,647.26	310.74
2012 Dec	346,474	HWA_log	364,678.26	-18,204.26
2013 Jan	369,969	HWA_log	381,834.40	-11,865.40
2013 Feb	520,055	HWA_log	556,325.50	-36,270.50
2013 Mar	840,024	HWA_log	784,948.07	55,075.93
2013 Apr	986,191	HWA_log	1,099,741.01	-113,550.01
2013 May	1,382,234	HWA_log	1,218,830.92	163,403.08
2013 Jun	1,814,108	HWA_log	1,679,380.85	134,727.15
2013 Jul	2,387,304	HWA_log	2,317,757.31	69,546.69
2013 Aug	2,764,686	HWA_log	2,672,215.10	92,470.90
2013 Sep	1,943,037	HWA_log	1,851,325.65	91,711.35
2013 Oct	1,291,360	HWA_log	1,251,655.26	39,704.74
2013 Nov	455,695	HWA_log	467,131.01	-11,436.01
2013 Dec	358,062	HWA_log	362,290.01	-4,228.01
2014 Jan	377,387	HWA_log	388,715.19	-11,328.19
2014 Feb	543,470	HWA_log	555,053.20	-11,583.20
2014 Mar	749,773	HWA_log	851,197.24	-101,424.24
2014 Apr	1,337,145	HWA_log	1,047,508.94	289,636.06
2014 May	1,538,342	HWA_log	1,422,929.77	115,412.23
2014 Jun	1,994,167	HWA_log	1,922,477.61	71,689.39
2014 Jul	2,529,246	HWA_log	2,572,763.92	-43,517.92
2014 Aug	3,069,865	HWA_log	2,977,911.94	91,953.06
2014 Sep	2,089,656	HWA_log	2,074,843.34	14,812.66
2014 Oct	1,477,481	HWA_log	1,401,220.93	76,260.07
2014 Nov	502,473	HWA_log	510,433.63	-7,960.63
2014 Dec	382,543	HWA_log	401,383.98	-18,840.98
2015 Jan	381,607	HWA_log	423,487.54	-41,880.54
2015 Feb	544,777	HWA_log	589,991.39	-45,214.39
2015 Mar	827,071	HWA_log	878,956.89	-51,885.89
2015 Apr	1,242,844	HWA_log	1,358,702.84	-115,858.84
2015 May	1,654,526	HWA_log	1,524,767.70	129,758.30
2015 Jun	2,079,484	HWA_log	2,010,119.06	69,364.94
2015 Jul	2,688,710	HWA_log	2,597,956.38	90,753.62
2015 Aug	3,108,357	HWA_log	3,154,355.24	-45,998.24
2015 Sep	2,196,681	HWA_log	2,123,560.66	73,120.34
2015 Oct	1,553,142	HWA_log	1,483,094.29	70,047.71
2015 Nov	552,778	HWA_log	514,756.16	38,021.84
2015 Dec	426,419	HWA_log	400,375.37	26,043.63
2016 Jan	443,150	HWA_log	412,604.35	30,545.65
2016 Feb	664,278	HWA_log	605,852.74	58,425.26
2016 Mar	1,089,392	HWA_log	939,203.69	150,188.31
2016 Apr	1,335,308	HWA_log	1,507,480.36	-172,172.36
2016 May	1,828,292	HWA_log	1,868,391.85	-40,099.85
2016 Jun	2,288,337	HWA_log	2,381,624.99	-93,287.99
2016 Jul	2,848,570	HWA_log	3,045,521.80	-196,951.80
2016 Aug	3,204,047	HWA_log	3,520,377.38	-316,330.38
2016 Sep	2,378,618	HWA_log	2,427,280.12	-48,662.12
2016 Oct	1,793,822	HWA_log	1,679,313.57	114,508.43
2016 Nov	653,514	HWA_log	599,120.60	54,393.40
2016 Dec	478,510	HWA_log	469,951.40	8,558.60
2017 Jan	495,629	HWA_log	480,583.51	15,045.49
2017 Feb	704,532	HWA_log	715,929.38	-11,397.38
2017 Mar	1,015,421	HWA_log	1,125,481.82	-110,060.82
2017 Apr	1,765,170	HWA_log	1,458,771.64	306,398.36
2017 May	1,970,072	HWA_log	2,024,080.69	-54,008.69
2017 Jun	2,417,100	HWA_log	2,544,409.46	-127,309.46
2017 Jul	2,968,641	HWA_log	3,226,605.67	-257,964.67
2017 Aug	3,295,406	HWA_log	3,663,998.34	-368,592.34
2017 Sep	2,470,298	HWA_log	2,650,962.45	-180,664.45
2017 Oct	1,911,961	HWA_log	1,723,362.71	188,598.29
2017 Nov	680,373	HWA_log	688,688.54	-8,315.54
2017 Dec	512,548	HWA_log	510,483.66	2,064.34
2018 Jan	503,908	HWA_log	524,696.71	-20,788.71
2018 Feb	731,090	HWA_log	750,969.34	-19,879.34
2018 Mar	1,151,455	HWA_log	1,119,540.13	31,914.87
2018 Apr	1,575,078	HWA_log	1,737,566.52	-162,488.52
2018 May	2,003,996	HWA_log	2,061,039.34	-57,043.34
2018 Jun	2,381,154	HWA_log	2,575,916.71	-194,762.71
2018 Jul	2,981,643	HWA_log	3,182,216.99	-200,573.99
2018 Aug	3,371,918	HWA_log	3,460,419.97	-88,501.97
2018 Sep	2,499,368	HWA_log	2,563,486.69	-64,118.69
2018 Oct	1,956,693	HWA_log	1,950,504.67	6,188.33
2018 Nov	732,141	HWA_log	657,229.41	74,911.59
2018 Dec	554,803	HWA_log	521,217.18	33,585.82
2019 Jan	548,686	HWA_log	527,166.83	21,519.17
2019 Feb	739,981	HWA_log	767,014.82	-27,033.82
2019 Mar	1,078,918	HWA_log	1,176,828.36	-97,910.36
2019 Apr	1,795,494	HWA_log	1,690,397.72	105,096.28
2019 May	1,990,529	HWA_log	2,112,855.35	-122,326.35
2019 Jun	2,425,834	HWA_log	2,578,055.63	-152,221.63
2019 Jul	2,988,668	HWA_log	3,179,044.89	-190,376.89
2019 Aug	3,439,271	HWA_log	3,571,995.67	-132,724.67
2019 Sep	2,573,527	HWA_log	2,656,649.73	-83,122.73
2019 Oct	1,930,852	HWA_log	2,000,591.24	-69,739.24
2019 Nov	785,875	HWA_log	725,016.15	60,858.85
2019 Dec	602,860	HWA_log	546,675.28	56,184.72
2020 Jan	560,368	HWA_log	558,484.23	1,883.77
2020 Feb	844,247	HWA_log	780,268.55	63,978.45
2020 Mar	513,360	HWA_log	1,188,997.53	-675,637.53
2020 Apr	25,614	HWA_log	1,733,580.18	-1,707,966.18
2020 May	40,932	HWA_log	22,110.34	18,821.66
2020 Jun	330,393	HWA_log	29,466.23	300,926.77
2020 Jul	1,035,732	HWA_log	429,452.38	606,279.62
2020 Aug	2,090,569	HWA_log	1,328,993.65	761,575.35
2020 Sep	1,418,185	HWA_log	1,690,542.82	-272,357.82
2020 Oct	696,087	HWA_log	1,083,500.20	-387,413.20
2020 Nov	181,873	HWA_log	277,600.72	-95,727.72
2020 Dec	153,351	HWA_log	153,612.68	-261.68
2021 Jan	105,336	HWA_log	165,733.51	-60,397.51
2021 Feb	66,194	HWA_log	156,596.35	-90,402.35
2021 Mar	84,413	HWA_log	91,681.59	-7,268.59
2021 Apr	138,661	HWA_log	91,921.97	46,739.03
2021 May	502,057	HWA_log	187,642.23	314,414.77
2021 Jun	1,182,009	HWA_log	828,663.72	353,345.28
2021 Jul	1,551,789	HWA_log	1,727,748.09	-175,959.09
2021 Aug	2,762,537	HWA_log	2,173,608.73	588,928.27
2021 Sep	1,869,194	HWA_log	1,947,406.31	-78,212.31
2021 Oct	1,584,764	HWA_log	1,412,739.50	172,024.50
2021 Nov	651,051	HWA_log	607,133.40	43,917.60
2021 Dec	376,031	HWA_log	503,073.00	-127,042.00
2022 Jan	344,634	HWA_log	394,567.43	-49,933.43
2022 Feb	590,122	HWA_log	487,203.61	102,918.39
2022 Mar	873,841	HWA_log	891,514.57	-17,673.57
2022 Apr	1,629,377	HWA_log	933,942.28	695,434.72
2022 May	1,867,744	HWA_log	2,598,735.39	-730,991.39
2022 Jun	2,230,207	HWA_log	3,492,624.03	-1,262,417.03
2010 Jan	366,296	Naive	370,417.00	-4,121.00
2010 Feb	533,056	Naive	366,296.00	166,760.00
2010 Mar	742,227	Naive	533,056.00	209,171.00
2010 Apr	902,745	Naive	742,227.00	160,518.00
2010 May	1,107,303	Naive	902,745.00	204,558.00
2010 Jun	1,464,695	Naive	1,107,303.00	357,392.00
2010 Jul	2,050,478	Naive	1,464,695.00	585,783.00
2010 Aug	2,468,924	Naive	2,050,478.00	418,446.00
2010 Sep	1,696,356	Naive	2,468,924.00	-772,568.00
2010 Oct	1,104,659	Naive	1,696,356.00	-591,697.00
2010 Nov	445,221	Naive	1,104,659.00	-659,438.00
2010 Dec	365,490	Naive	445,221.00	-79,731.00
2011 Jan	357,209	Naive	365,490.00	-8,281.00
2011 Feb	503,831	Naive	357,209.00	146,622.00
2011 Mar	761,343	Naive	503,831.00	257,512.00
2011 Apr	1,177,115	Naive	761,343.00	415,772.00
2011 May	1,169,516	Naive	1,177,115.00	-7,599.00
2011 Jun	1,576,730	Naive	1,169,516.00	407,214.00
2011 Jul	2,208,160	Naive	1,576,730.00	631,430.00
2011 Aug	2,572,404	Naive	2,208,160.00	364,244.00
2011 Sep	1,731,056	Naive	2,572,404.00	-841,348.00
2011 Oct	1,161,751	Naive	1,731,056.00	-569,305.00
2011 Nov	427,550	Naive	1,161,751.00	-734,201.00
2011 Dec	333,201	Naive	427,550.00	-94,349.00
2012 Jan	359,355	Naive	333,201.00	26,154.00
2012 Feb	531,709	Naive	359,355.00	172,354.00
2012 Mar	751,024	Naive	531,709.00	219,315.00
2012 Apr	1,017,976	Naive	751,024.00	266,952.00
2012 May	1,194,673	Naive	1,017,976.00	176,697.00
2012 Jun	1,678,327	Naive	1,194,673.00	483,654.00
2012 Jul	2,296,474	Naive	1,678,327.00	618,147.00
2012 Aug	2,622,801	Naive	2,296,474.00	326,327.00
2012 Sep	1,829,252	Naive	2,622,801.00	-793,549.00
2012 Oct	1,244,751	Naive	1,829,252.00	-584,501.00
2012 Nov	453,958	Naive	1,244,751.00	-790,793.00
2012 Dec	346,474	Naive	453,958.00	-107,484.00
2013 Jan	369,969	Naive	346,474.00	23,495.00
2013 Feb	520,055	Naive	369,969.00	150,086.00
2013 Mar	840,024	Naive	520,055.00	319,969.00
2013 Apr	986,191	Naive	840,024.00	146,167.00
2013 May	1,382,234	Naive	986,191.00	396,043.00
2013 Jun	1,814,108	Naive	1,382,234.00	431,874.00
2013 Jul	2,387,304	Naive	1,814,108.00	573,196.00
2013 Aug	2,764,686	Naive	2,387,304.00	377,382.00
2013 Sep	1,943,037	Naive	2,764,686.00	-821,649.00
2013 Oct	1,291,360	Naive	1,943,037.00	-651,677.00
2013 Nov	455,695	Naive	1,291,360.00	-835,665.00
2013 Dec	358,062	Naive	455,695.00	-97,633.00
2014 Jan	377,387	Naive	358,062.00	19,325.00
2014 Feb	543,470	Naive	377,387.00	166,083.00
2014 Mar	749,773	Naive	543,470.00	206,303.00
2014 Apr	1,337,145	Naive	749,773.00	587,372.00
2014 May	1,538,342	Naive	1,337,145.00	201,197.00
2014 Jun	1,994,167	Naive	1,538,342.00	455,825.00
2014 Jul	2,529,246	Naive	1,994,167.00	535,079.00
2014 Aug	3,069,865	Naive	2,529,246.00	540,619.00
2014 Sep	2,089,656	Naive	3,069,865.00	-980,209.00
2014 Oct	1,477,481	Naive	2,089,656.00	-612,175.00
2014 Nov	502,473	Naive	1,477,481.00	-975,008.00
2014 Dec	382,543	Naive	502,473.00	-119,930.00
2015 Jan	381,607	Naive	382,543.00	-936.00
2015 Feb	544,777	Naive	381,607.00	163,170.00
2015 Mar	827,071	Naive	544,777.00	282,294.00
2015 Apr	1,242,844	Naive	827,071.00	415,773.00
2015 May	1,654,526	Naive	1,242,844.00	411,682.00
2015 Jun	2,079,484	Naive	1,654,526.00	424,958.00
2015 Jul	2,688,710	Naive	2,079,484.00	609,226.00
2015 Aug	3,108,357	Naive	2,688,710.00	419,647.00
2015 Sep	2,196,681	Naive	3,108,357.00	-911,676.00
2015 Oct	1,553,142	Naive	2,196,681.00	-643,539.00
2015 Nov	552,778	Naive	1,553,142.00	-1,000,364.00
2015 Dec	426,419	Naive	552,778.00	-126,359.00
2016 Jan	443,150	Naive	426,419.00	16,731.00
2016 Feb	664,278	Naive	443,150.00	221,128.00
2016 Mar	1,089,392	Naive	664,278.00	425,114.00
2016 Apr	1,335,308	Naive	1,089,392.00	245,916.00
2016 May	1,828,292	Naive	1,335,308.00	492,984.00
2016 Jun	2,288,337	Naive	1,828,292.00	460,045.00
2016 Jul	2,848,570	Naive	2,288,337.00	560,233.00
2016 Aug	3,204,047	Naive	2,848,570.00	355,477.00
2016 Sep	2,378,618	Naive	3,204,047.00	-825,429.00
2016 Oct	1,793,822	Naive	2,378,618.00	-584,796.00
2016 Nov	653,514	Naive	1,793,822.00	-1,140,308.00
2016 Dec	478,510	Naive	653,514.00	-175,004.00
2017 Jan	495,629	Naive	478,510.00	17,119.00
2017 Feb	704,532	Naive	495,629.00	208,903.00
2017 Mar	1,015,421	Naive	704,532.00	310,889.00
2017 Apr	1,765,170	Naive	1,015,421.00	749,749.00
2017 May	1,970,072	Naive	1,765,170.00	204,902.00
2017 Jun	2,417,100	Naive	1,970,072.00	447,028.00
2017 Jul	2,968,641	Naive	2,417,100.00	551,541.00
2017 Aug	3,295,406	Naive	2,968,641.00	326,765.00
2017 Sep	2,470,298	Naive	3,295,406.00	-825,108.00
2017 Oct	1,911,961	Naive	2,470,298.00	-558,337.00
2017 Nov	680,373	Naive	1,911,961.00	-1,231,588.00
2017 Dec	512,548	Naive	680,373.00	-167,825.00
2018 Jan	503,908	Naive	512,548.00	-8,640.00
2018 Feb	731,090	Naive	503,908.00	227,182.00
2018 Mar	1,151,455	Naive	731,090.00	420,365.00
2018 Apr	1,575,078	Naive	1,151,455.00	423,623.00
2018 May	2,003,996	Naive	1,575,078.00	428,918.00
2018 Jun	2,381,154	Naive	2,003,996.00	377,158.00
2018 Jul	2,981,643	Naive	2,381,154.00	600,489.00
2018 Aug	3,371,918	Naive	2,981,643.00	390,275.00
2018 Sep	2,499,368	Naive	3,371,918.00	-872,550.00
2018 Oct	1,956,693	Naive	2,499,368.00	-542,675.00
2018 Nov	732,141	Naive	1,956,693.00	-1,224,552.00
2018 Dec	554,803	Naive	732,141.00	-177,338.00
2019 Jan	548,686	Naive	554,803.00	-6,117.00
2019 Feb	739,981	Naive	548,686.00	191,295.00
2019 Mar	1,078,918	Naive	739,981.00	338,937.00
2019 Apr	1,795,494	Naive	1,078,918.00	716,576.00
2019 May	1,990,529	Naive	1,795,494.00	195,035.00
2019 Jun	2,425,834	Naive	1,990,529.00	435,305.00
2019 Jul	2,988,668	Naive	2,425,834.00	562,834.00
2019 Aug	3,439,271	Naive	2,988,668.00	450,603.00
2019 Sep	2,573,527	Naive	3,439,271.00	-865,744.00
2019 Oct	1,930,852	Naive	2,573,527.00	-642,675.00
2019 Nov	785,875	Naive	1,930,852.00	-1,144,977.00
2019 Dec	602,860	Naive	785,875.00	-183,015.00
2020 Jan	560,368	Naive	602,860.00	-42,492.00
2020 Feb	844,247	Naive	560,368.00	283,879.00
2020 Mar	513,360	Naive	844,247.00	-330,887.00
2020 Apr	25,614	Naive	513,360.00	-487,746.00
2020 May	40,932	Naive	25,614.00	15,318.00
2020 Jun	330,393	Naive	40,932.00	289,461.00
2020 Jul	1,035,732	Naive	330,393.00	705,339.00
2020 Aug	2,090,569	Naive	1,035,732.00	1,054,837.00
2020 Sep	1,418,185	Naive	2,090,569.00	-672,384.00
2020 Oct	696,087	Naive	1,418,185.00	-722,098.00
2020 Nov	181,873	Naive	696,087.00	-514,214.00
2020 Dec	153,351	Naive	181,873.00	-28,522.00
2021 Jan	105,336	Naive	153,351.00	-48,015.00
2021 Feb	66,194	Naive	105,336.00	-39,142.00
2021 Mar	84,413	Naive	66,194.00	18,219.00
2021 Apr	138,661	Naive	84,413.00	54,248.00
2021 May	502,057	Naive	138,661.00	363,396.00
2021 Jun	1,182,009	Naive	502,057.00	679,952.00
2021 Jul	1,551,789	Naive	1,182,009.00	369,780.00
2021 Aug	2,762,537	Naive	1,551,789.00	1,210,748.00
2021 Sep	1,869,194	Naive	2,762,537.00	-893,343.00
2021 Oct	1,584,764	Naive	1,869,194.00	-284,430.00
2021 Nov	651,051	Naive	1,584,764.00	-933,713.00
2021 Dec	376,031	Naive	651,051.00	-275,020.00
2022 Jan	344,634	Naive	376,031.00	-31,397.00
2022 Feb	590,122	Naive	344,634.00	245,488.00
2022 Mar	873,841	Naive	590,122.00	283,719.00
2022 Apr	1,629,377	Naive	873,841.00	755,536.00
2022 May	1,867,744	Naive	1,629,377.00	238,367.00
2022 Jun	2,230,207	Naive	1,867,744.00	362,463.00
2010 Jan	366,296	Naive_log	390,892.35	-24,596.35
2010 Feb	533,056	Naive_log	386,379.45	146,676.55
2010 Mar	742,227	Naive_log	562,336.86	179,890.14
2010 Apr	902,745	Naive_log	783,148.68	119,596.32
2010 May	1,107,303	Naive_log	952,599.10	154,703.90
2010 Jun	1,464,695	Naive_log	1,168,502.31	296,192.69
2010 Jul	2,050,478	Naive_log	1,545,886.22	504,591.78
2010 Aug	2,468,924	Naive_log	2,165,063.37	303,860.63
2010 Sep	1,696,356	Naive_log	2,606,748.74	-910,392.74
2010 Oct	1,104,659	Naive_log	1,791,499.85	-686,840.85
2010 Nov	445,221	Naive_log	1,165,023.04	-719,802.04
2010 Dec	365,490	Naive_log	470,872.24	-105,382.24
2011 Jan	357,209	Naive_log	386,591.62	-29,382.62
2011 Feb	503,831	Naive_log	377,606.87	126,224.13
2011 Mar	761,343	Naive_log	532,761.55	228,581.45
2011 Apr	1,177,115	Naive_log	805,403.61	371,711.39
2011 May	1,169,516	Naive_log	1,246,122.77	-76,606.77
2011 Jun	1,576,730	Naive_log	1,237,856.76	338,873.24
2011 Jul	2,208,160	Naive_log	1,669,194.12	538,965.88
2011 Aug	2,572,404	Naive_log	2,338,665.62	233,738.38
2011 Sep	1,731,056	Naive_log	2,724,059.76	-993,003.76
2011 Oct	1,161,751	Naive_log	1,833,444.53	-671,693.53
2011 Nov	427,550	Naive_log	1,228,628.68	-801,078.68
2011 Dec	333,201	Naive_log	453,741.38	-120,540.38
2012 Jan	359,355	Naive_log	353,667.19	5,687.81
2012 Feb	531,709	Naive_log	381,174.08	150,534.92
2012 Mar	751,024	Naive_log	563,971.91	187,052.09
2012 Apr	1,017,976	Naive_log	796,962.38	221,013.62
2012 May	1,194,673	Naive_log	1,080,310.36	114,362.64
2012 Jun	1,678,327	Naive_log	1,267,719.63	410,607.37
2012 Jul	2,296,474	Naive_log	1,781,460.29	515,013.71
2012 Aug	2,622,801	Naive_log	2,438,325.78	184,475.22
2012 Sep	1,829,252	Naive_log	2,783,899.58	-954,647.58
2012 Oct	1,244,751	Naive_log	1,941,405.76	-696,654.76
2012 Nov	453,958	Naive_log	1,319,465.14	-865,507.14
2012 Dec	346,474	Naive_log	482,886.84	-136,412.84
2013 Jan	369,969	Naive_log	368,626.19	1,342.81
2013 Feb	520,055	Naive_log	393,401.88	126,653.12
2013 Mar	840,024	Naive_log	553,079.51	286,944.49
2013 Apr	986,191	Naive_log	894,012.66	92,178.34
2013 May	1,382,234	Naive_log	1,049,541.17	332,692.83
2013 Jun	1,814,108	Naive_log	1,471,453.27	342,654.73
2013 Jul	2,387,304	Naive_log	1,931,534.95	455,769.05
2013 Aug	2,764,686	Naive_log	2,542,330.03	222,355.97
2013 Sep	1,943,037	Naive_log	2,942,670.47	-999,633.47
2013 Oct	1,291,360	Naive_log	2,068,082.44	-776,722.44
2013 Nov	455,695	Naive_log	1,372,605.89	-916,910.89
2013 Dec	358,062	Naive_log	486,280.69	-128,218.69
2014 Jan	377,387	Naive_log	382,146.15	-4,759.15
2014 Feb	543,470	Naive_log	402,553.13	140,916.87
2014 Mar	749,773	Naive_log	579,911.44	169,861.56
2014 Apr	1,337,145	Naive_log	800,211.49	536,933.51
2014 May	1,538,342	Naive_log	1,428,918.32	109,423.68
2014 Jun	1,994,167	Naive_log	1,643,812.68	350,354.32
2014 Jul	2,529,246	Naive_log	2,130,990.21	398,255.79
2014 Aug	3,069,865	Naive_log	2,702,777.99	367,087.01
2014 Sep	2,089,656	Naive_log	3,279,137.88	-1,189,481.88
2014 Oct	1,477,481	Naive_log	2,232,469.13	-754,988.13
2014 Nov	502,473	Naive_log	1,575,294.23	-1,072,821.23
2014 Dec	382,543	Naive_log	538,145.66	-155,602.66
2015 Jan	381,607	Naive_log	409,810.33	-28,203.33
2015 Feb	544,777	Naive_log	408,614.67	136,162.33
2015 Mar	827,071	Naive_log	583,416.03	243,654.97
2015 Apr	1,242,844	Naive_log	886,336.54	356,507.46
2015 May	1,654,526	Naive_log	1,332,121.43	322,404.57
2015 Jun	2,079,484	Naive_log	1,773,764.89	305,719.11
2015 Jul	2,688,710	Naive_log	2,229,365.77	459,344.23
2015 Aug	3,108,357	Naive_log	2,882,798.24	225,558.76
2015 Sep	2,196,681	Naive_log	3,331,283.04	-1,134,602.04
2015 Oct	1,553,142	Naive_log	2,354,212.79	-801,070.79
2015 Nov	552,778	Naive_log	1,661,571.16	-1,108,793.16
2015 Dec	426,419	Naive_log	593,715.96	-167,296.96
2016 Jan	443,150	Naive_log	458,100.46	-14,950.46
2016 Feb	664,278	Naive_log	475,918.96	188,359.04
2016 Mar	1,089,392	Naive_log	713,698.22	375,693.78
2016 Apr	1,335,308	Naive_log	1,170,916.70	164,391.30
2016 May	1,828,292	Naive_log	1,435,447.26	392,844.74
2016 Jun	2,288,337	Naive_log	1,965,741.81	322,595.19
2016 Jul	2,848,570	Naive_log	2,460,182.77	388,387.23
2016 Aug	3,204,047	Naive_log	3,062,708.41	141,338.59
2016 Sep	2,378,618	Naive_log	3,443,259.36	-1,064,641.36
2016 Oct	1,793,822	Naive_log	2,555,595.41	-761,773.41
2016 Nov	653,514	Naive_log	1,923,867.16	-1,270,353.16
2016 Dec	478,510	Naive_log	703,643.85	-225,133.85
2017 Jan	495,629	Naive_log	515,409.71	-19,780.71
2017 Feb	704,532	Naive_log	533,704.88	170,827.12
2017 Mar	1,015,421	Naive_log	758,664.07	256,756.93
2017 Apr	1,765,170	Naive_log	1,093,731.62	671,438.38
2017 May	1,970,072	Naive_log	1,903,437.52	66,634.48
2017 Jun	2,417,100	Naive_log	2,124,178.85	292,921.15
2017 Jul	2,968,641	Naive_log	2,605,901.55	362,739.45
2017 Aug	3,295,406	Naive_log	3,200,797.86	94,608.14
2017 Sep	2,470,298	Naive_log	3,551,697.03	-1,081,399.03
2017 Oct	1,911,961	Naive_log	2,661,747.37	-749,786.37
2017 Nov	680,373	Naive_log	2,056,212.08	-1,375,839.08
2017 Dec	512,548	Naive_log	734,674.76	-222,126.76
2018 Jan	503,908	Naive_log	553,627.93	-49,719.93
2018 Feb	731,090	Naive_log	544,023.60	187,066.40
2018 Mar	1,151,455	Naive_log	789,258.18	362,196.82
2018 Apr	1,575,078	Naive_log	1,244,056.80	331,021.20
2018 May	2,003,996	Naive_log	1,701,453.75	302,542.25
2018 Jun	2,381,154	Naive_log	2,165,151.30	216,002.70
2018 Jul	2,981,643	Naive_log	2,572,242.92	409,400.08
2018 Aug	3,371,918	Naive_log	3,221,135.24	150,782.76
2018 Sep	2,499,368	Naive_log	3,641,102.05	-1,141,734.05
2018 Oct	1,956,693	Naive_log	2,698,191.14	-741,498.14
2018 Nov	732,141	Naive_log	2,108,033.97	-1,375,892.97
2018 Dec	554,803	Naive_log	791,539.87	-236,736.87
2019 Jan	548,686	Naive_log	599,993.69	-51,307.69
2019 Feb	739,981	Naive_log	593,166.79	146,814.21
2019 Mar	1,078,918	Naive_log	800,064.69	278,853.31
2019 Apr	1,795,494	Naive_log	1,166,581.15	628,912.85
2019 May	1,990,529	Naive_log	1,943,242.52	47,286.48
2019 Jun	2,425,834	Naive_log	2,153,811.03	272,022.97
2019 Jul	2,988,668	Naive_log	2,624,640.35	364,027.65
2019 Aug	3,439,271	Naive_log	3,233,632.64	205,638.36
2019 Sep	2,573,527	Naive_log	3,719,049.08	-1,145,522.08
2019 Oct	1,930,852	Naive_log	2,781,866.77	-851,014.77
2019 Nov	785,875	Naive_log	2,083,233.70	-1,297,358.70
2019 Dec	602,860	Naive_log	850,357.04	-247,497.04
2020 Jan	560,368	Naive_log	652,503.14	-92,135.14
2020 Feb	844,247	Naive_log	606,193.25	238,053.75
2020 Mar	513,360	Naive_log	913,494.19	-400,134.19
2020 Apr	25,614	Naive_log	555,918.15	-530,304.15
2020 May	40,932	Naive_log	28,700.14	12,231.86
2020 Jun	330,393	Naive_log	45,888.09	284,504.91
2020 Jul	1,035,732	Naive_log	376,294.60	659,437.40
2020 Aug	2,090,569	Naive_log	1,185,157.74	905,411.26
2020 Sep	1,418,185	Naive_log	2,395,272.35	-977,087.35
2020 Oct	696,087	Naive_log	1,624,688.39	-928,601.39
2020 Nov	181,873	Naive_log	796,511.04	-614,638.04
2020 Dec	153,351	Naive_log	209,458.53	-56,107.53
2021 Jan	105,336	Naive_log	176,628.88	-71,292.88
2021 Feb	66,194	Naive_log	121,335.53	-55,141.53
2021 Mar	84,413	Naive_log	76,260.86	8,152.14
2021 Apr	138,661	Naive_log	97,204.25	41,456.75
2021 May	502,057	Naive_log	159,816.03	342,240.97
2021 Jun	1,182,009	Naive_log	581,958.16	600,050.84
2021 Jul	1,551,789	Naive_log	1,373,200.77	178,588.23
2021 Aug	2,762,537	Naive_log	1,803,124.33	959,412.67
2021 Sep	1,869,194	Naive_log	3,212,010.71	-1,342,816.71
2021 Oct	1,584,764	Naive_log	2,173,267.31	-588,503.31
2021 Nov	651,051	Naive_log	1,836,095.26	-1,185,044.26
2021 Dec	376,031	Naive_log	756,297.45	-380,266.45
2022 Jan	344,634	Naive_log	437,285.79	-92,651.79
2022 Feb	590,122	Naive_log	400,563.01	189,558.99
2022 Mar	873,841	Naive_log	686,311.65	187,529.35
2022 Apr	1,629,377	Naive_log	1,016,502.95	612,874.05
2022 May	1,867,744	Naive_log	1,897,868.87	-30,124.87
2022 Jun	2,230,207	Naive_log	2,174,753.94	55,453.06
2010 Jan	366,296	Prophet	377,106.46	-10,810.46
2010 Feb	533,056	Prophet	571,293.69	-38,237.69
2010 Mar	742,227	Prophet	784,461.43	-42,234.43
2010 Apr	902,745	Prophet	967,768.00	-65,023.00
2010 May	1,107,303	Prophet	1,151,565.07	-44,262.07
2010 Jun	1,464,695	Prophet	1,433,698.44	30,996.56
2010 Jul	2,050,478	Prophet	1,839,987.68	210,490.32
2010 Aug	2,468,924	Prophet	2,202,855.28	266,068.72
2010 Sep	1,696,356	Prophet	1,547,391.17	148,964.83
2010 Oct	1,104,659	Prophet	1,052,557.60	52,101.40
2010 Nov	445,221	Prophet	474,612.67	-29,391.67
2010 Dec	365,490	Prophet	351,032.15	14,457.85
2011 Jan	357,209	Prophet	383,037.22	-25,828.22
2011 Feb	503,831	Prophet	569,190.87	-65,359.87
2011 Mar	761,343	Prophet	760,078.26	1,264.74
2011 Apr	1,177,115	Prophet	964,057.36	213,057.64
2011 May	1,169,516	Prophet	1,140,781.71	28,734.29
2011 Jun	1,576,730	Prophet	1,475,757.82	100,972.18
2011 Jul	2,208,160	Prophet	1,916,597.46	291,562.54
2011 Aug	2,572,404	Prophet	2,282,638.56	289,765.44
2011 Sep	1,731,056	Prophet	1,618,092.47	112,963.53
2011 Oct	1,161,751	Prophet	1,119,915.51	41,835.49
2011 Nov	427,550	Prophet	550,531.50	-122,981.50
2011 Dec	333,201	Prophet	429,558.99	-96,357.99
2012 Jan	359,355	Prophet	465,282.78	-105,927.78
2012 Feb	531,709	Prophet	635,525.94	-103,816.94
2012 Mar	751,024	Prophet	869,522.73	-118,498.73
2012 Apr	1,017,976	Prophet	962,112.28	55,863.72
2012 May	1,194,673	Prophet	1,278,040.73	-83,367.73
2012 Jun	1,678,327	Prophet	1,528,555.09	149,771.91
2012 Jul	2,296,474	Prophet	1,938,172.26	358,301.74
2012 Aug	2,622,801	Prophet	2,390,348.77	232,452.23
2012 Sep	1,829,252	Prophet	1,668,565.21	160,686.79
2012 Oct	1,244,751	Prophet	1,165,179.03	79,571.97
2012 Nov	453,958	Prophet	572,642.45	-118,684.45
2012 Dec	346,474	Prophet	467,929.16	-121,455.16
2013 Jan	369,969	Prophet	494,097.18	-124,128.18
2013 Feb	520,055	Prophet	662,912.23	-142,857.23
2013 Mar	840,024	Prophet	875,445.44	-35,421.44
2013 Apr	986,191	Prophet	1,072,816.96	-86,625.96
2013 May	1,382,234	Prophet	1,279,766.34	102,467.66
2013 Jun	1,814,108	Prophet	1,594,686.74	219,421.26
2013 Jul	2,387,304	Prophet	2,086,148.84	301,155.16
2013 Aug	2,764,686	Prophet	2,504,404.18	260,281.82
2013 Sep	1,943,037	Prophet	1,777,372.78	165,664.22
2013 Oct	1,291,360	Prophet	1,267,856.87	23,503.13
2013 Nov	455,695	Prophet	636,862.77	-181,167.77
2013 Dec	358,062	Prophet	520,006.10	-161,944.10
2014 Jan	377,387	Prophet	533,197.09	-155,810.09
2014 Feb	543,470	Prophet	694,357.43	-150,887.43
2014 Mar	749,773	Prophet	908,947.77	-159,174.77
2014 Apr	1,337,145	Prophet	1,138,455.96	198,689.04
2014 May	1,538,342	Prophet	1,324,936.58	213,405.42
2014 Jun	1,994,167	Prophet	1,678,089.16	316,077.84
2014 Jul	2,529,246	Prophet	2,224,507.61	304,738.39
2014 Aug	3,069,865	Prophet	2,636,582.06	433,282.94
2014 Sep	2,089,656	Prophet	1,921,530.47	168,125.53
2014 Oct	1,477,481	Prophet	1,383,523.99	93,957.01
2014 Nov	502,473	Prophet	748,600.31	-246,127.31
2014 Dec	382,543	Prophet	631,316.81	-248,773.81
2015 Jan	381,607	Prophet	618,539.41	-236,932.41
2015 Feb	544,777	Prophet	772,496.56	-227,719.56
2015 Mar	827,071	Prophet	942,072.42	-115,001.42
2015 Apr	1,242,844	Prophet	1,320,089.35	-77,245.35
2015 May	1,654,526	Prophet	1,411,591.36	242,934.64
2015 Jun	2,079,484	Prophet	1,795,586.88	283,897.12
2015 Jul	2,688,710	Prophet	2,358,614.04	330,095.96
2015 Aug	3,108,357	Prophet	2,778,266.27	330,090.73
2015 Sep	2,196,681	Prophet	2,010,613.07	186,067.93
2015 Oct	1,553,142	Prophet	1,465,463.59	87,678.41
2015 Nov	552,778	Prophet	790,089.34	-237,311.34
2015 Dec	426,419	Prophet	687,301.29	-260,882.29
2016 Jan	443,150	Prophet	691,131.73	-247,981.73
2016 Feb	664,278	Prophet	847,054.08	-182,776.08
2016 Mar	1,089,392	Prophet	1,105,355.83	-15,963.83
2016 Apr	1,335,308	Prophet	1,315,330.20	19,977.80
2016 May	1,828,292	Prophet	1,598,798.61	229,493.39
2016 Jun	2,288,337	Prophet	1,965,940.82	322,396.18
2016 Jul	2,848,570	Prophet	2,492,447.83	356,122.17
2016 Aug	3,204,047	Prophet	2,902,824.76	301,222.24
2016 Sep	2,378,618	Prophet	2,128,714.90	249,903.10
2016 Oct	1,793,822	Prophet	1,553,608.43	240,213.57
2016 Nov	653,514	Prophet	882,193.89	-228,679.89
2016 Dec	478,510	Prophet	771,375.70	-292,865.70
2017 Jan	495,629	Prophet	772,793.79	-277,164.79
2017 Feb	704,532	Prophet	916,535.39	-212,003.39
2017 Mar	1,015,421	Prophet	1,194,965.81	-179,544.81
2017 Apr	1,765,170	Prophet	1,432,237.24	332,932.76
2017 May	1,970,072	Prophet	1,733,635.23	236,436.77
2017 Jun	2,417,100	Prophet	2,134,579.41	282,520.59
2017 Jul	2,968,641	Prophet	2,695,487.78	273,153.22
2017 Aug	3,295,406	Prophet	3,113,983.72	181,422.28
2017 Sep	2,470,298	Prophet	2,320,026.23	150,271.77
2017 Oct	1,911,961	Prophet	1,746,368.89	165,592.11
2017 Nov	680,373	Prophet	972,338.15	-291,965.15
2017 Dec	512,548	Prophet	838,306.39	-325,758.39
2018 Jan	503,908	Prophet	832,815.47	-328,907.47
2018 Feb	731,090	Prophet	989,934.25	-258,844.25
2018 Mar	1,151,455	Prophet	1,243,791.88	-92,336.88
2018 Apr	1,575,078	Prophet	1,608,605.71	-33,527.71
2018 May	2,003,996	Prophet	1,842,415.30	161,580.70
2018 Jun	2,381,154	Prophet	2,258,275.00	122,879.00
2018 Jul	2,981,643	Prophet	2,834,646.31	146,996.69
2018 Aug	3,371,918	Prophet	3,244,198.28	127,719.72
2018 Sep	2,499,368	Prophet	2,414,463.46	84,904.54
2018 Oct	1,956,693	Prophet	1,835,305.23	121,387.77
2018 Nov	732,141	Prophet	991,510.16	-259,369.16
2018 Dec	554,803	Prophet	868,370.53	-313,567.53
2019 Jan	548,686	Prophet	862,305.47	-313,619.47
2019 Feb	739,981	Prophet	1,027,560.79	-287,579.79
2019 Mar	1,078,918	Prophet	1,278,485.59	-199,567.59
2019 Apr	1,795,494	Prophet	1,672,871.20	122,622.80
2019 May	1,990,529	Prophet	1,927,638.09	62,890.91
2019 Jun	2,425,834	Prophet	2,334,140.39	91,693.61
2019 Jul	2,988,668	Prophet	2,936,008.24	52,659.76
2019 Aug	3,439,271	Prophet	3,346,303.23	92,967.77
2019 Sep	2,573,527	Prophet	2,482,956.83	90,570.17
2019 Oct	1,930,852	Prophet	1,894,624.63	36,227.37
2019 Nov	785,875	Prophet	997,547.68	-211,672.68
2019 Dec	602,860	Prophet	876,386.62	-273,526.62
2020 Jan	560,368	Prophet	866,893.54	-306,525.54
2020 Feb	844,247	Prophet	1,030,328.01	-186,081.01
2020 Mar	513,360	Prophet	1,348,145.64	-834,785.64
2020 Apr	25,614	Prophet	1,647,639.15	-1,622,025.15
2020 May	40,932	Prophet	1,885,997.42	-1,845,065.42
2020 Jun	330,393	Prophet	2,170,940.21	-1,840,547.21
2020 Jul	1,035,732	Prophet	2,625,786.18	-1,590,054.18
2020 Aug	2,090,569	Prophet	2,860,839.03	-770,270.03
2020 Sep	1,418,185	Prophet	1,965,280.85	-547,095.85
2020 Oct	696,087	Prophet	1,303,064.10	-606,977.10
2020 Nov	181,873	Prophet	223,898.70	-42,025.70
2020 Dec	153,351	Prophet	-13,342.83	166,693.83
2021 Jan	105,336	Prophet	60,190.21	45,145.79
2021 Feb	66,194	Prophet	238,683.88	-172,489.88
2021 Mar	84,413	Prophet	404,992.51	-320,579.51
2021 Apr	138,661	Prophet	649,583.49	-510,922.49
2021 May	502,057	Prophet	817,370.38	-315,313.38
2021 Jun	1,182,009	Prophet	1,174,287.41	7,721.59
2021 Jul	1,551,789	Prophet	1,750,844.92	-199,055.92
2021 Aug	2,762,537	Prophet	2,118,484.31	644,052.69
2021 Sep	1,869,194	Prophet	1,315,653.29	553,540.71
2021 Oct	1,584,764	Prophet	786,701.18	798,062.82
2021 Nov	651,051	Prophet	-105,998.26	757,049.26
2021 Dec	376,031	Prophet	-197,729.28	573,760.28
2022 Jan	344,634	Prophet	-178,766.76	523,400.76
2022 Feb	590,122	Prophet	53,698.64	536,423.36
2022 Mar	873,841	Prophet	267,587.18	606,253.82
2022 Apr	1,629,377	Prophet	632,360.20	997,016.80
2022 May	1,867,744	Prophet	998,245.33	869,498.67
2022 Jun	2,230,207	Prophet	1,489,626.63	740,580.37
2010 Jan	366,296	Prophet_log	405,827.58	-39,531.58
2010 Feb	533,056	Prophet_log	564,306.73	-31,250.73
2010 Mar	742,227	Prophet_log	738,536.00	3,691.00
2010 Apr	902,745	Prophet_log	894,549.69	8,195.31
2010 May	1,107,303	Prophet_log	1,055,632.88	51,670.12
2010 Jun	1,464,695	Prophet_log	1,296,921.00	167,774.00
2010 Jul	2,050,478	Prophet_log	1,648,370.76	402,107.24
2010 Aug	2,468,924	Prophet_log	1,974,881.97	494,042.03
2010 Sep	1,696,356	Prophet_log	1,421,244.96	275,111.04
2010 Oct	1,104,659	Prophet_log	1,002,684.25	101,974.75
2010 Nov	445,221	Prophet_log	492,240.41	-47,019.41
2010 Dec	365,490	Prophet_log	379,732.05	-14,242.05
2011 Jan	357,209	Prophet_log	408,542.56	-51,333.56
2011 Feb	503,831	Prophet_log	571,738.04	-67,907.04
2011 Mar	761,343	Prophet_log	735,174.18	26,168.82
2011 Apr	1,177,115	Prophet_log	929,415.98	247,699.02
2011 May	1,169,516	Prophet_log	1,107,165.71	62,350.29
2011 Jun	1,576,730	Prophet_log	1,414,960.68	161,769.32
2011 Jul	2,208,160	Prophet_log	1,840,716.99	367,443.01
2011 Aug	2,572,404	Prophet_log	2,208,723.24	363,680.76
2011 Sep	1,731,056	Prophet_log	1,597,024.64	134,031.36
2011 Oct	1,161,751	Prophet_log	1,109,700.21	52,050.79
2011 Nov	427,550	Prophet_log	540,211.67	-112,661.67
2011 Dec	333,201	Prophet_log	416,360.17	-83,159.17
2012 Jan	359,355	Prophet_log	434,981.25	-75,626.25
2012 Feb	531,709	Prophet_log	604,897.47	-73,188.47
2012 Mar	751,024	Prophet_log	832,054.45	-81,030.45
2012 Apr	1,017,976	Prophet_log	926,172.51	91,803.49
2012 May	1,194,673	Prophet_log	1,227,969.16	-33,296.16
2012 Jun	1,678,327	Prophet_log	1,469,592.63	208,734.37
2012 Jul	2,296,474	Prophet_log	1,883,227.10	413,246.90
2012 Aug	2,622,801	Prophet_log	2,343,661.06	279,139.94
2012 Sep	1,829,252	Prophet_log	1,605,396.45	223,855.55
2012 Oct	1,244,751	Prophet_log	1,103,100.49	141,650.51
2012 Nov	453,958	Prophet_log	519,781.97	-65,823.97
2012 Dec	346,474	Prophet_log	420,263.38	-73,789.38
2013 Jan	369,969	Prophet_log	437,591.44	-67,622.44
2013 Feb	520,055	Prophet_log	607,872.96	-87,817.96
2013 Mar	840,024	Prophet_log	820,600.32	19,423.68
2013 Apr	986,191	Prophet_log	1,018,315.60	-32,124.60
2013 May	1,382,234	Prophet_log	1,223,386.75	158,847.25
2013 Jun	1,814,108	Prophet_log	1,552,457.75	261,650.25
2013 Jul	2,387,304	Prophet_log	2,053,176.42	334,127.58
2013 Aug	2,764,686	Prophet_log	2,496,380.60	268,305.40
2013 Sep	1,943,037	Prophet_log	1,737,708.09	205,328.91
2013 Oct	1,291,360	Prophet_log	1,213,852.24	77,507.76
2013 Nov	455,695	Prophet_log	543,295.95	-87,600.95
2013 Dec	358,062	Prophet_log	429,994.32	-71,932.32
2014 Jan	377,387	Prophet_log	443,905.50	-66,518.50
2014 Feb	543,470	Prophet_log	611,318.52	-67,848.52
2014 Mar	749,773	Prophet_log	835,138.73	-85,365.73
2014 Apr	1,337,145	Prophet_log	1,090,080.13	247,064.87
2014 May	1,538,342	Prophet_log	1,276,640.47	261,701.53
2014 Jun	1,994,167	Prophet_log	1,670,131.00	324,036.00
2014 Jul	2,529,246	Prophet_log	2,270,247.21	258,998.79
2014 Aug	3,069,865	Prophet_log	2,734,672.56	335,192.44
2014 Sep	2,089,656	Prophet_log	1,932,798.70	156,857.30
2014 Oct	1,477,481	Prophet_log	1,324,256.30	153,224.70
2014 Nov	502,473	Prophet_log	579,656.47	-77,183.47
2014 Dec	382,543	Prophet_log	467,251.26	-84,708.26
2015 Jan	381,607	Prophet_log	471,841.66	-90,234.66
2015 Feb	544,777	Prophet_log	648,133.76	-103,356.76
2015 Mar	827,071	Prophet_log	853,305.49	-26,234.49
2015 Apr	1,242,844	Prophet_log	1,273,954.59	-31,110.59
2015 May	1,654,526	Prophet_log	1,375,664.71	278,861.29
2015 Jun	2,079,484	Prophet_log	1,810,395.29	269,088.71
2015 Jul	2,688,710	Prophet_log	2,467,173.00	221,537.00
2015 Aug	3,108,357	Prophet_log	2,973,215.32	135,141.68
2015 Sep	2,196,681	Prophet_log	2,068,057.21	128,623.79
2015 Oct	1,553,142	Prophet_log	1,415,696.88	137,445.12
2015 Nov	552,778	Prophet_log	590,832.14	-38,054.14
2015 Dec	426,419	Prophet_log	485,698.13	-59,279.13
2016 Jan	443,150	Prophet_log	484,745.57	-41,595.57
2016 Feb	664,278	Prophet_log	681,721.25	-17,443.25
2016 Mar	1,089,392	Prophet_log	1,036,204.79	53,187.21
2016 Apr	1,335,308	Prophet_log	1,235,669.27	99,638.73
2016 May	1,828,292	Prophet_log	1,621,183.68	207,108.32
2016 Jun	2,288,337	Prophet_log	2,107,717.40	180,619.60
2016 Jul	2,848,570	Prophet_log	2,787,985.09	60,584.91
2016 Aug	3,204,047	Prophet_log	3,307,273.56	-103,226.56
2016 Sep	2,378,618	Prophet_log	2,281,749.11	96,868.89
2016 Oct	1,793,822	Prophet_log	1,534,497.14	259,324.86
2016 Nov	653,514	Prophet_log	647,908.45	5,605.55
2016 Dec	478,510	Prophet_log	511,949.55	-33,439.55
2017 Jan	495,629	Prophet_log	530,440.72	-34,811.72
2017 Feb	704,532	Prophet_log	746,588.07	-42,056.07
2017 Mar	1,015,421	Prophet_log	1,131,828.19	-116,407.19
2017 Apr	1,765,170	Prophet_log	1,439,509.74	325,660.26
2017 May	1,970,072	Prophet_log	1,872,236.81	97,835.19
2017 Jun	2,417,100	Prophet_log	2,434,725.34	-17,625.34
2017 Jul	2,968,641	Prophet_log	3,195,256.94	-226,615.94
2017 Aug	3,295,406	Prophet_log	3,733,912.80	-438,506.80
2017 Sep	2,470,298	Prophet_log	2,578,757.63	-108,459.63
2017 Oct	1,911,961	Prophet_log	1,764,687.10	147,273.90
2017 Nov	680,373	Prophet_log	702,508.17	-22,135.17
2017 Dec	512,548	Prophet_log	543,641.00	-31,093.00
2018 Jan	503,908	Prophet_log	558,195.17	-54,287.17
2018 Feb	731,090	Prophet_log	793,362.94	-62,272.94
2018 Mar	1,151,455	Prophet_log	1,145,411.51	6,043.49
2018 Apr	1,575,078	Prophet_log	1,646,069.68	-70,991.68
2018 May	2,003,996	Prophet_log	1,934,497.87	69,498.13
2018 Jun	2,381,154	Prophet_log	2,507,393.34	-126,239.34
2018 Jul	2,981,643	Prophet_log	3,298,735.10	-317,092.10
2018 Aug	3,371,918	Prophet_log	3,837,622.86	-465,704.86
2018 Sep	2,499,368	Prophet_log	2,627,039.32	-127,671.32
2018 Oct	1,956,693	Prophet_log	1,795,149.57	161,543.43
2018 Nov	732,141	Prophet_log	676,434.45	55,706.55
2018 Dec	554,803	Prophet_log	530,611.36	24,191.64
2019 Jan	548,686	Prophet_log	546,045.27	2,640.73
2019 Feb	739,981	Prophet_log	793,236.24	-53,255.24
2019 Mar	1,078,918	Prophet_log	1,116,599.35	-37,681.35
2019 Apr	1,795,494	Prophet_log	1,687,336.49	108,157.51
2019 May	1,990,529	Prophet_log	1,960,344.04	30,184.96
2019 Jun	2,425,834	Prophet_log	2,507,112.76	-81,278.76
2019 Jul	2,988,668	Prophet_log	3,338,278.55	-349,610.55
2019 Aug	3,439,271	Prophet_log	3,904,274.79	-465,003.79
2019 Sep	2,573,527	Prophet_log	2,677,370.15	-103,843.15
2019 Oct	1,930,852	Prophet_log	1,853,129.35	77,722.65
2019 Nov	785,875	Prophet_log	681,593.65	104,281.35
2019 Dec	602,860	Prophet_log	537,790.00	65,070.00
2020 Jan	560,368	Prophet_log	547,738.40	12,629.60
2020 Feb	844,247	Prophet_log	791,199.83	53,047.17
2020 Mar	513,360	Prophet_log	1,276,293.59	-762,933.59
2020 Apr	25,614	Prophet_log	1,564,101.58	-1,538,487.58
2020 May	40,932	Prophet_log	1,684,844.52	-1,643,912.52
2020 Jun	330,393	Prophet_log	1,725,692.48	-1,395,299.48
2020 Jul	1,035,732	Prophet_log	1,831,161.03	-795,429.03
2020 Aug	2,090,569	Prophet_log	1,457,879.71	632,689.29
2020 Sep	1,418,185	Prophet_log	1,031,673.30	386,511.70
2020 Oct	696,087	Prophet_log	672,518.30	23,568.70
2020 Nov	181,873	Prophet_log	236,948.46	-55,075.46
2020 Dec	153,351	Prophet_log	169,680.12	-16,329.12
2021 Jan	105,336	Prophet_log	164,233.30	-58,897.30
2021 Feb	66,194	Prophet_log	246,284.21	-180,090.21
2021 Mar	84,413	Prophet_log	290,822.81	-206,409.81
2021 Apr	138,661	Prophet_log	198,196.34	-59,535.34
2021 May	502,057	Prophet_log	218,930.72	283,126.28
2021 Jun	1,182,009	Prophet_log	378,993.20	803,015.80
2021 Jul	1,551,789	Prophet_log	588,571.97	963,217.03
2021 Aug	2,762,537	Prophet_log	772,974.09	1,989,562.91
2021 Sep	1,869,194	Prophet_log	600,001.98	1,269,192.02
2021 Oct	1,584,764	Prophet_log	447,108.94	1,137,655.06
2021 Nov	651,051	Prophet_log	170,558.14	480,492.86
2021 Dec	376,031	Prophet_log	153,119.50	222,911.50
2022 Jan	344,634	Prophet_log	161,521.17	183,112.83
2022 Feb	590,122	Prophet_log	225,426.26	364,695.74
2022 Mar	873,841	Prophet_log	286,001.94	587,839.06
2022 Apr	1,629,377	Prophet_log	418,662.33	1,210,714.67
2022 May	1,867,744	Prophet_log	653,927.39	1,213,816.61
2022 Jun	2,230,207	Prophet_log	1,057,135.29	1,173,071.71
2010 Jan	366,296	SNaive	411,615.00	-45,319.00
2010 Feb	533,056	SNaive	557,401.00	-24,345.00
2010 Mar	742,227	SNaive	710,502.00	31,725.00
2010 Apr	902,745	SNaive	1,017,779.00	-115,034.00
2010 May	1,107,303	SNaive	1,138,068.00	-30,765.00
2010 Jun	1,464,695	SNaive	1,489,130.00	-24,435.00
2010 Jul	2,050,478	SNaive	1,891,157.00	159,321.00
2010 Aug	2,468,924	SNaive	2,315,586.00	153,338.00
2010 Sep	1,696,356	SNaive	1,539,886.00	156,470.00
2010 Oct	1,104,659	SNaive	1,010,273.00	94,386.00
2010 Nov	445,221	SNaive	475,789.00	-30,568.00
2010 Dec	365,490	SNaive	370,417.00	-4,927.00
2011 Jan	357,209	SNaive	366,296.00	-9,087.00
2011 Feb	503,831	SNaive	533,056.00	-29,225.00
2011 Mar	761,343	SNaive	742,227.00	19,116.00
2011 Apr	1,177,115	SNaive	902,745.00	274,370.00
2011 May	1,169,516	SNaive	1,107,303.00	62,213.00
2011 Jun	1,576,730	SNaive	1,464,695.00	112,035.00
2011 Jul	2,208,160	SNaive	2,050,478.00	157,682.00
2011 Aug	2,572,404	SNaive	2,468,924.00	103,480.00
2011 Sep	1,731,056	SNaive	1,696,356.00	34,700.00
2011 Oct	1,161,751	SNaive	1,104,659.00	57,092.00
2011 Nov	427,550	SNaive	445,221.00	-17,671.00
2011 Dec	333,201	SNaive	365,490.00	-32,289.00
2012 Jan	359,355	SNaive	357,209.00	2,146.00
2012 Feb	531,709	SNaive	503,831.00	27,878.00
2012 Mar	751,024	SNaive	761,343.00	-10,319.00
2012 Apr	1,017,976	SNaive	1,177,115.00	-159,139.00
2012 May	1,194,673	SNaive	1,169,516.00	25,157.00
2012 Jun	1,678,327	SNaive	1,576,730.00	101,597.00
2012 Jul	2,296,474	SNaive	2,208,160.00	88,314.00
2012 Aug	2,622,801	SNaive	2,572,404.00	50,397.00
2012 Sep	1,829,252	SNaive	1,731,056.00	98,196.00
2012 Oct	1,244,751	SNaive	1,161,751.00	83,000.00
2012 Nov	453,958	SNaive	427,550.00	26,408.00
2012 Dec	346,474	SNaive	333,201.00	13,273.00
2013 Jan	369,969	SNaive	359,355.00	10,614.00
2013 Feb	520,055	SNaive	531,709.00	-11,654.00
2013 Mar	840,024	SNaive	751,024.00	89,000.00
2013 Apr	986,191	SNaive	1,017,976.00	-31,785.00
2013 May	1,382,234	SNaive	1,194,673.00	187,561.00
2013 Jun	1,814,108	SNaive	1,678,327.00	135,781.00
2013 Jul	2,387,304	SNaive	2,296,474.00	90,830.00
2013 Aug	2,764,686	SNaive	2,622,801.00	141,885.00
2013 Sep	1,943,037	SNaive	1,829,252.00	113,785.00
2013 Oct	1,291,360	SNaive	1,244,751.00	46,609.00
2013 Nov	455,695	SNaive	453,958.00	1,737.00
2013 Dec	358,062	SNaive	346,474.00	11,588.00
2014 Jan	377,387	SNaive	369,969.00	7,418.00
2014 Feb	543,470	SNaive	520,055.00	23,415.00
2014 Mar	749,773	SNaive	840,024.00	-90,251.00
2014 Apr	1,337,145	SNaive	986,191.00	350,954.00
2014 May	1,538,342	SNaive	1,382,234.00	156,108.00
2014 Jun	1,994,167	SNaive	1,814,108.00	180,059.00
2014 Jul	2,529,246	SNaive	2,387,304.00	141,942.00
2014 Aug	3,069,865	SNaive	2,764,686.00	305,179.00
2014 Sep	2,089,656	SNaive	1,943,037.00	146,619.00
2014 Oct	1,477,481	SNaive	1,291,360.00	186,121.00
2014 Nov	502,473	SNaive	455,695.00	46,778.00
2014 Dec	382,543	SNaive	358,062.00	24,481.00
2015 Jan	381,607	SNaive	377,387.00	4,220.00
2015 Feb	544,777	SNaive	543,470.00	1,307.00
2015 Mar	827,071	SNaive	749,773.00	77,298.00
2015 Apr	1,242,844	SNaive	1,337,145.00	-94,301.00
2015 May	1,654,526	SNaive	1,538,342.00	116,184.00
2015 Jun	2,079,484	SNaive	1,994,167.00	85,317.00
2015 Jul	2,688,710	SNaive	2,529,246.00	159,464.00
2015 Aug	3,108,357	SNaive	3,069,865.00	38,492.00
2015 Sep	2,196,681	SNaive	2,089,656.00	107,025.00
2015 Oct	1,553,142	SNaive	1,477,481.00	75,661.00
2015 Nov	552,778	SNaive	502,473.00	50,305.00
2015 Dec	426,419	SNaive	382,543.00	43,876.00
2016 Jan	443,150	SNaive	381,607.00	61,543.00
2016 Feb	664,278	SNaive	544,777.00	119,501.00
2016 Mar	1,089,392	SNaive	827,071.00	262,321.00
2016 Apr	1,335,308	SNaive	1,242,844.00	92,464.00
2016 May	1,828,292	SNaive	1,654,526.00	173,766.00
2016 Jun	2,288,337	SNaive	2,079,484.00	208,853.00
2016 Jul	2,848,570	SNaive	2,688,710.00	159,860.00
2016 Aug	3,204,047	SNaive	3,108,357.00	95,690.00
2016 Sep	2,378,618	SNaive	2,196,681.00	181,937.00
2016 Oct	1,793,822	SNaive	1,553,142.00	240,680.00
2016 Nov	653,514	SNaive	552,778.00	100,736.00
2016 Dec	478,510	SNaive	426,419.00	52,091.00
2017 Jan	495,629	SNaive	443,150.00	52,479.00
2017 Feb	704,532	SNaive	664,278.00	40,254.00
2017 Mar	1,015,421	SNaive	1,089,392.00	-73,971.00
2017 Apr	1,765,170	SNaive	1,335,308.00	429,862.00
2017 May	1,970,072	SNaive	1,828,292.00	141,780.00
2017 Jun	2,417,100	SNaive	2,288,337.00	128,763.00
2017 Jul	2,968,641	SNaive	2,848,570.00	120,071.00
2017 Aug	3,295,406	SNaive	3,204,047.00	91,359.00
2017 Sep	2,470,298	SNaive	2,378,618.00	91,680.00
2017 Oct	1,911,961	SNaive	1,793,822.00	118,139.00
2017 Nov	680,373	SNaive	653,514.00	26,859.00
2017 Dec	512,548	SNaive	478,510.00	34,038.00
2018 Jan	503,908	SNaive	495,629.00	8,279.00
2018 Feb	731,090	SNaive	704,532.00	26,558.00
2018 Mar	1,151,455	SNaive	1,015,421.00	136,034.00
2018 Apr	1,575,078	SNaive	1,765,170.00	-190,092.00
2018 May	2,003,996	SNaive	1,970,072.00	33,924.00
2018 Jun	2,381,154	SNaive	2,417,100.00	-35,946.00
2018 Jul	2,981,643	SNaive	2,968,641.00	13,002.00
2018 Aug	3,371,918	SNaive	3,295,406.00	76,512.00
2018 Sep	2,499,368	SNaive	2,470,298.00	29,070.00
2018 Oct	1,956,693	SNaive	1,911,961.00	44,732.00
2018 Nov	732,141	SNaive	680,373.00	51,768.00
2018 Dec	554,803	SNaive	512,548.00	42,255.00
2019 Jan	548,686	SNaive	503,908.00	44,778.00
2019 Feb	739,981	SNaive	731,090.00	8,891.00
2019 Mar	1,078,918	SNaive	1,151,455.00	-72,537.00
2019 Apr	1,795,494	SNaive	1,575,078.00	220,416.00
2019 May	1,990,529	SNaive	2,003,996.00	-13,467.00
2019 Jun	2,425,834	SNaive	2,381,154.00	44,680.00
2019 Jul	2,988,668	SNaive	2,981,643.00	7,025.00
2019 Aug	3,439,271	SNaive	3,371,918.00	67,353.00
2019 Sep	2,573,527	SNaive	2,499,368.00	74,159.00
2019 Oct	1,930,852	SNaive	1,956,693.00	-25,841.00
2019 Nov	785,875	SNaive	732,141.00	53,734.00
2019 Dec	602,860	SNaive	554,803.00	48,057.00
2020 Jan	560,368	SNaive	548,686.00	11,682.00
2020 Feb	844,247	SNaive	739,981.00	104,266.00
2020 Mar	513,360	SNaive	1,078,918.00	-565,558.00
2020 Apr	25,614	SNaive	1,795,494.00	-1,769,880.00
2020 May	40,932	SNaive	1,990,529.00	-1,949,597.00
2020 Jun	330,393	SNaive	2,425,834.00	-2,095,441.00
2020 Jul	1,035,732	SNaive	2,988,668.00	-1,952,936.00
2020 Aug	2,090,569	SNaive	3,439,271.00	-1,348,702.00
2020 Sep	1,418,185	SNaive	2,573,527.00	-1,155,342.00
2020 Oct	696,087	SNaive	1,930,852.00	-1,234,765.00
2020 Nov	181,873	SNaive	785,875.00	-604,002.00
2020 Dec	153,351	SNaive	602,860.00	-449,509.00
2021 Jan	105,336	SNaive	560,368.00	-455,032.00
2021 Feb	66,194	SNaive	844,247.00	-778,053.00
2021 Mar	84,413	SNaive	513,360.00	-428,947.00
2021 Apr	138,661	SNaive	25,614.00	113,047.00
2021 May	502,057	SNaive	40,932.00	461,125.00
2021 Jun	1,182,009	SNaive	330,393.00	851,616.00
2021 Jul	1,551,789	SNaive	1,035,732.00	516,057.00
2021 Aug	2,762,537	SNaive	2,090,569.00	671,968.00
2021 Sep	1,869,194	SNaive	1,418,185.00	451,009.00
2021 Oct	1,584,764	SNaive	696,087.00	888,677.00
2021 Nov	651,051	SNaive	181,873.00	469,178.00
2021 Dec	376,031	SNaive	153,351.00	222,680.00
2022 Jan	344,634	SNaive	105,336.00	239,298.00
2022 Feb	590,122	SNaive	66,194.00	523,928.00
2022 Mar	873,841	SNaive	84,413.00	789,428.00
2022 Apr	1,629,377	SNaive	138,661.00	1,490,716.00
2022 May	1,867,744	SNaive	502,057.00	1,365,687.00
2022 Jun	2,230,207	SNaive	1,182,009.00	1,048,198.00
2010 Jan	366,296	SNaive_log	413,177.50	-46,881.50
2010 Feb	533,056	SNaive_log	559,550.01	-26,494.01
2010 Mar	742,227	SNaive_log	713,221.41	29,005.59
2010 Apr	902,745	SNaive_log	1,021,673.86	-118,928.86
2010 May	1,107,303	SNaive_log	1,142,489.98	-35,186.98
2010 Jun	1,464,695	SNaive_log	1,494,891.13	-30,196.13
2010 Jul	2,050,478	SNaive_log	1,898,467.72	152,010.28
2010 Aug	2,468,924	SNaive_log	2,324,598.28	144,325.72
2010 Sep	1,696,356	SNaive_log	1,545,896.15	150,459.85
2010 Oct	1,104,659	SNaive_log	1,014,241.32	90,417.68
2010 Nov	445,221	SNaive_log	477,645.57	-32,424.57
2010 Dec	365,490	SNaive_log	371,844.38	-6,354.38
2011 Jan	357,209	SNaive_log	367,681.71	-10,472.71
2011 Feb	503,831	SNaive_log	535,060.97	-31,229.97
2011 Mar	761,343	SNaive_log	745,022.77	16,320.23
2011 Apr	1,177,115	SNaive_log	906,051.12	271,063.88
2011 May	1,169,516	SNaive_log	1,111,603.28	57,912.72
2011 Jun	1,576,730	SNaive_log	1,470,400.02	106,329.98
2011 Jul	2,208,160	SNaive_log	2,058,509.27	149,650.73
2011 Aug	2,572,404	SNaive_log	2,478,643.70	93,760.30
2011 Sep	1,731,056	SNaive_log	1,702,938.27	28,117.73
2011 Oct	1,161,751	SNaive_log	1,108,938.17	52,812.83
2011 Nov	427,550	SNaive_log	446,950.11	-19,400.11
2011 Dec	333,201	SNaive_log	366,909.82	-33,708.82
2012 Jan	359,355	SNaive_log	358,610.40	744.60
2012 Feb	531,709	SNaive_log	505,807.20	25,901.80
2012 Mar	751,024	SNaive_log	764,338.23	-13,314.23
2012 Apr	1,017,976	SNaive_log	1,181,631.78	-163,655.78
2012 May	1,194,673	SNaive_log	1,174,035.79	20,637.21
2012 Jun	1,678,327	SNaive_log	1,582,820.55	95,506.45
2012 Jul	2,296,474	SNaive_log	2,216,727.76	79,746.24
2012 Aug	2,622,801	SNaive_log	2,582,399.07	40,401.93
2012 Sep	1,829,252	SNaive_log	1,737,784.60	91,467.40
2012 Oct	1,244,751	SNaive_log	1,166,244.96	78,506.04
2012 Nov	453,958	SNaive_log	429,208.56	24,749.44
2012 Dec	346,474	SNaive_log	334,486.98	11,987.02
2013 Jan	369,969	SNaive_log	360,744.29	9,224.71
2013 Feb	520,055	SNaive_log	533,766.59	-13,711.59
2013 Mar	840,024	SNaive_log	753,931.14	86,092.86
2013 Apr	986,191	SNaive_log	1,021,945.62	-35,754.62
2013 May	1,382,234	SNaive_log	1,199,310.49	182,923.51
2013 Jun	1,814,108	SNaive_log	1,684,831.45	129,276.55
2013 Jul	2,387,304	SNaive_log	2,305,170.30	82,133.70
2013 Aug	2,764,686	SNaive_log	2,632,634.61	132,051.39
2013 Sep	1,943,037	SNaive_log	1,836,130.29	106,906.71
2013 Oct	1,291,360	SNaive_log	1,249,452.35	41,907.65
2013 Nov	455,695	SNaive_log	455,673.65	21.35
2013 Dec	358,062	SNaive_log	347,779.37	10,282.63
2014 Jan	377,387	SNaive_log	371,351.23	6,035.77
2014 Feb	543,470	SNaive_log	521,998.35	21,471.65
2014 Mar	749,773	SNaive_log	843,169.97	-93,396.97
2014 Apr	1,337,145	SNaive_log	989,917.59	347,227.41
2014 May	1,538,342	SNaive_log	1,387,938.07	150,403.93
2014 Jun	1,994,167	SNaive_log	1,821,575.13	172,591.87
2014 Jul	2,529,246	SNaive_log	2,397,147.74	132,098.26
2014 Aug	3,069,865	SNaive_log	2,776,056.37	293,808.63
2014 Sep	2,089,656	SNaive_log	1,951,114.97	138,541.03
2014 Oct	1,477,481	SNaive_log	1,296,745.68	180,735.32
2014 Nov	502,473	SNaive_log	457,632.14	44,840.86
2014 Dec	382,543	SNaive_log	359,593.08	22,949.92
2015 Jan	381,607	SNaive_log	379,007.47	2,599.53
2015 Feb	544,777	SNaive_log	545,803.92	-1,026.92
2015 Mar	827,071	SNaive_log	752,982.29	74,088.71
2015 Apr	1,242,844	SNaive_log	1,342,841.34	-99,997.34
2015 May	1,654,526	SNaive_log	1,544,534.11	109,991.89
2015 Jun	2,079,484	SNaive_log	2,002,215.84	77,268.16
2015 Jul	2,688,710	SNaive_log	2,539,471.10	149,238.90
2015 Aug	3,108,357	SNaive_log	3,082,279.57	26,077.43
2015 Sep	2,196,681	SNaive_log	2,098,098.83	98,582.17
2015 Oct	1,553,142	SNaive_log	1,483,463.02	69,678.98
2015 Nov	552,778	SNaive_log	504,512.85	48,265.15
2015 Dec	426,419	SNaive_log	384,111.77	42,307.23
2016 Jan	443,150	SNaive_log	383,166.81	59,983.19
2016 Feb	664,278	SNaive_log	547,055.62	117,222.38
2016 Mar	1,089,392	SNaive_log	830,679.98	258,712.02
2016 Apr	1,335,308	SNaive_log	1,248,611.79	86,696.21
2016 May	1,828,292	SNaive_log	1,662,243.37	166,048.63
2016 Jun	2,288,337	SNaive_log	2,089,218.53	199,118.47
2016 Jul	2,848,570	SNaive_log	2,701,390.59	147,179.41
2016 Aug	3,204,047	SNaive_log	3,123,044.65	81,002.35
2016 Sep	2,378,618	SNaive_log	2,207,069.48	171,548.52
2016 Oct	1,793,822	SNaive_log	1,560,520.85	233,301.15
2016 Nov	653,514	SNaive_log	555,452.60	98,061.40
2016 Dec	478,510	SNaive_log	428,535.90	49,974.10
2017 Jan	495,629	SNaive_log	445,377.02	50,251.98
2017 Feb	704,532	SNaive_log	667,648.82	36,883.18
2017 Mar	1,015,421	SNaive_log	1,094,925.19	-79,504.19
2017 Apr	1,765,170	SNaive_log	1,342,073.27	423,096.73
2017 May	1,970,072	SNaive_log	1,837,826.01	132,245.99
2017 Jun	2,417,100	SNaive_log	2,300,319.62	116,780.38
2017 Jul	2,968,641	SNaive_log	2,863,501.36	105,139.64
2017 Aug	3,295,406	SNaive_log	3,220,840.93	74,565.07
2017 Sep	2,470,298	SNaive_log	2,391,094.16	79,203.84
2017 Oct	1,911,961	SNaive_log	1,803,236.32	108,724.68
2017 Nov	680,373	SNaive_log	656,951.41	23,421.59
2017 Dec	512,548	SNaive_log	481,022.75	31,525.25
2018 Jan	503,908	SNaive_log	498,193.76	5,714.24
2018 Feb	731,090	SNaive_log	708,119.66	22,970.34
2018 Mar	1,151,455	SNaive_log	1,020,428.45	131,026.55
2018 Apr	1,575,078	SNaive_log	1,773,093.80	-198,015.80
2018 May	2,003,996	SNaive_log	1,978,986.60	25,009.40
2018 Jun	2,381,154	SNaive_log	2,427,620.07	-46,466.07
2018 Jul	2,981,643	SNaive_log	2,981,535.78	107.22
2018 Aug	3,371,918	SNaive_log	3,309,645.32	62,272.68
2018 Sep	2,499,368	SNaive_log	2,480,948.61	18,419.39
2018 Oct	1,956,693	SNaive_log	1,920,125.05	36,567.95
2018 Nov	732,141	SNaive_log	683,233.77	48,907.23
2018 Dec	554,803	SNaive_log	514,687.44	40,115.56
2019 Jan	548,686	SNaive_log	506,000.86	42,685.14
2019 Feb	739,981	SNaive_log	734,104.88	5,876.12
2019 Mar	1,078,918	SNaive_log	1,156,193.54	-77,275.54
2019 Apr	1,795,494	SNaive_log	1,581,576.81	213,917.19
2019 May	1,990,529	SNaive_log	2,012,290.23	-21,761.23
2019 Jun	2,425,834	SNaive_log	2,391,001.46	34,832.54
2019 Jul	2,988,668	SNaive_log	2,993,974.82	-5,306.82
2019 Aug	3,439,271	SNaive_log	3,385,761.92	53,509.08
2019 Sep	2,573,527	SNaive_log	2,509,586.49	63,940.51
2019 Oct	1,930,852	SNaive_log	1,964,615.71	-33,763.71
2019 Nov	785,875	SNaive_log	735,079.02	50,795.98
2019 Dec	602,860	SNaive_log	557,030.94	45,829.06
2020 Jan	560,368	SNaive_log	550,906.45	9,461.55
2020 Feb	844,247	SNaive_log	742,974.95	101,272.05
2020 Mar	513,360	SNaive_log	1,083,354.19	-569,994.19
2020 Apr	25,614	SNaive_log	1,807,456.80	-1,781,842.80
2020 May	40,932	SNaive_log	2,169,587.51	-2,128,655.51
2020 Jun	330,393	SNaive_log	2,813,458.59	-2,483,065.59
2020 Jul	1,035,732	SNaive_log	3,521,147.49	-2,485,415.49
2020 Aug	2,090,569	SNaive_log	4,069,826.41	-1,979,257.41
2020 Sep	1,418,185	SNaive_log	3,048,289.70	-1,630,104.70
2020 Oct	696,087	SNaive_log	2,290,224.99	-1,594,137.99
2020 Nov	181,873	SNaive_log	935,921.06	-754,048.06
2020 Dec	153,351	SNaive_log	723,936.47	-570,585.47
2021 Jan	105,336	SNaive_log	677,750.14	-572,414.14
2021 Feb	66,194	SNaive_log	1,032,013.41	-965,819.41
2021 Mar	84,413	SNaive_log	642,932.02	-558,519.02
2021 Apr	138,661	SNaive_log	32,465.41	106,195.59
2021 May	502,057	SNaive_log	52,417.29	449,639.71
2021 Jun	1,182,009	SNaive_log	432,710.83	749,298.17
2021 Jul	1,551,789	SNaive_log	1,364,255.35	187,533.65
2021 Aug	2,762,537	SNaive_log	2,755,242.76	7,294.24
2021 Sep	1,869,194	SNaive_log	1,869,589.11	-395.11
2021 Oct	1,584,764	SNaive_log	917,885.35	666,878.65
2021 Nov	651,051	SNaive_log	240,390.19	410,660.81
2021 Dec	376,031	SNaive_log	203,843.39	172,187.61
2022 Jan	344,634	SNaive_log	140,410.54	204,223.46
2022 Feb	590,122	SNaive_log	88,665.44	501,456.56
2022 Mar	873,841	SNaive_log	114,939.66	758,901.34
2022 Apr	1,629,377	SNaive_log	192,304.13	1,437,072.87
2022 May	1,867,744	SNaive_log	710,393.95	1,157,350.05
2022 Jun	2,230,207	SNaive_log	1,681,832.16	548,374.84
2010 Jan	366,296	TSLM	443,287.46	-76,991.46
2010 Feb	533,056	TSLM	635,457.34	-102,401.34
2010 Mar	742,227	TSLM	863,235.34	-121,008.34
2010 Apr	902,745	TSLM	1,041,757.46	-139,012.46
2010 May	1,107,303	TSLM	1,254,757.06	-147,454.06
2010 Jun	1,464,695	TSLM	1,532,887.21	-68,192.21
2010 Jul	2,050,478	TSLM	1,931,429.21	119,048.79
2010 Aug	2,468,924	TSLM	2,274,405.15	194,518.85
2010 Sep	1,696,356	TSLM	1,609,765.79	86,590.21
2010 Oct	1,104,659	TSLM	1,114,211.14	-9,552.14
2010 Nov	445,221	TSLM	520,946.29	-75,725.29
2010 Dec	365,490	TSLM	398,211.37	-32,721.37
2011 Jan	357,209	TSLM	430,716.99	-73,507.99
2011 Feb	503,831	TSLM	621,760.79	-117,929.79
2011 Mar	761,343	TSLM	845,184.52	-83,841.52
2011 Apr	1,177,115	TSLM	1,013,674.92	163,440.08
2011 May	1,169,516	TSLM	1,237,618.98	-68,102.98
2011 Jun	1,576,730	TSLM	1,525,311.63	51,418.37
2011 Jul	2,208,160	TSLM	1,948,788.58	259,371.42
2011 Aug	2,572,404	TSLM	2,319,327.74	253,076.26
2011 Sep	1,731,056	TSLM	1,618,160.26	112,895.74
2011 Oct	1,161,751	TSLM	1,103,458.42	58,292.58
2011 Nov	427,550	TSLM	509,937.98	-82,387.98
2011 Dec	333,201	TSLM	396,069.77	-62,868.77
2012 Jan	359,355	TSLM	421,025.76	-61,670.76
2012 Feb	531,709	TSLM	602,948.65	-71,239.65
2012 Mar	751,024	TSLM	836,324.79	-85,300.79
2012 Apr	1,017,976	TSLM	1,025,747.49	-7,771.49
2012 May	1,194,673	TSLM	1,227,225.63	-32,552.63
2012 Jun	1,678,327	TSLM	1,527,437.23	150,889.77
2012 Jul	2,296,474	TSLM	1,982,965.73	313,508.27
2012 Aug	2,622,801	TSLM	2,379,552.58	243,248.42
2012 Sep	1,829,252	TSLM	1,644,939.22	184,312.78
2012 Oct	1,244,751	TSLM	1,123,344.71	121,406.29
2012 Nov	453,958	TSLM	518,218.78	-64,260.78
2012 Dec	346,474	TSLM	413,385.86	-66,911.86
2013 Jan	369,969	TSLM	435,313.58	-65,344.58
2013 Feb	520,055	TSLM	611,676.73	-91,621.73
2013 Mar	840,024	TSLM	832,448.83	7,575.17
2013 Apr	986,191	TSLM	1,053,375.66	-67,184.66
2013 May	1,382,234	TSLM	1,243,822.52	138,411.48
2013 Jun	1,814,108	TSLM	1,567,156.91	246,951.09
2013 Jul	2,387,304	TSLM	2,050,906.54	336,397.46
2013 Aug	2,764,686	TSLM	2,447,326.67	317,359.33
2013 Sep	1,943,037	TSLM	1,697,874.94	245,162.06
2013 Oct	1,291,360	TSLM	1,171,097.32	120,262.68
2013 Nov	455,695	TSLM	541,812.43	-86,117.43
2013 Dec	358,062	TSLM	443,429.80	-85,367.80
2014 Jan	377,387	TSLM	461,602.94	-84,215.94
2014 Feb	543,470	TSLM	631,760.45	-88,290.45
2014 Mar	749,773	TSLM	863,796.47	-114,023.47
2014 Apr	1,337,145	TSLM	1,073,398.03	263,746.97
2014 May	1,538,342	TSLM	1,288,047.13	250,294.87
2014 Jun	1,994,167	TSLM	1,622,531.85	371,635.15
2014 Jul	2,529,246	TSLM	2,128,313.48	400,932.52
2014 Aug	3,069,865	TSLM	2,523,726.70	546,138.30
2014 Sep	2,089,656	TSLM	1,770,887.38	318,768.62
2014 Oct	1,477,481	TSLM	1,227,379.97	250,101.03
2014 Nov	502,473	TSLM	574,495.14	-72,022.14
2014 Dec	382,543	TSLM	480,569.51	-98,026.51
2015 Jan	381,607	TSLM	495,980.01	-114,373.01
2015 Feb	544,777	TSLM	662,453.46	-117,676.46
2015 Mar	827,071	TSLM	899,587.12	-72,516.12
2015 Apr	1,242,844	TSLM	1,151,015.72	91,828.28
2015 May	1,654,526	TSLM	1,366,525.30	288,000.70
2015 Jun	2,079,484	TSLM	1,727,203.31	352,280.69
2015 Jul	2,688,710	TSLM	2,251,875.30	436,834.70
2015 Aug	3,108,357	TSLM	2,657,435.19	450,921.81
2015 Sep	2,196,681	TSLM	1,876,686.48	319,994.52
2015 Oct	1,553,142	TSLM	1,317,305.55	235,836.45
2015 Nov	552,778	TSLM	629,060.44	-76,282.44
2015 Dec	426,419	TSLM	532,553.62	-106,134.62
2016 Jan	443,150	TSLM	545,293.58	-102,143.58
2016 Feb	664,278	TSLM	710,563.13	-46,285.13
2016 Mar	1,089,392	TSLM	955,097.46	134,294.54
2016 Apr	1,335,308	TSLM	1,250,219.87	85,088.13
2016 May	1,828,292	TSLM	1,476,125.12	352,166.88
2016 Jun	2,288,337	TSLM	1,856,790.16	431,546.84
2016 Jul	2,848,570	TSLM	2,406,843.11	441,726.89
2016 Aug	3,204,047	TSLM	2,815,210.53	388,836.47
2016 Sep	2,378,618	TSLM	2,015,261.99	363,356.01
2016 Oct	1,793,822	TSLM	1,442,224.02	351,597.98
2016 Nov	653,514	TSLM	718,337.05	-64,823.05
2016 Dec	478,510	TSLM	623,309.24	-144,799.24
2017 Jan	495,629	TSLM	636,052.81	-140,423.81
2017 Feb	704,532	TSLM	809,559.50	-105,027.50
2017 Mar	1,015,421	TSLM	1,080,810.47	-65,389.47
2017 Apr	1,765,170	TSLM	1,363,971.31	401,198.69
2017 May	1,970,072	TSLM	1,641,881.76	328,190.24
2017 Jun	2,417,100	TSLM	2,039,403.06	377,696.94
2017 Jul	2,968,641	TSLM	2,599,210.56	369,430.44
2017 Aug	3,295,406	TSLM	3,005,823.84	289,582.16
2017 Sep	2,470,298	TSLM	2,196,546.91	273,751.09
2017 Oct	1,911,961	TSLM	1,619,167.65	292,793.35
2017 Nov	680,373	TSLM	840,952.29	-160,579.29
2017 Dec	512,548	TSLM	735,703.27	-223,155.27
2018 Jan	503,908	TSLM	749,674.00	-245,766.00
2018 Feb	731,090	TSLM	928,661.33	-197,571.33
2018 Mar	1,151,455	TSLM	1,205,597.35	-54,142.35
2018 Apr	1,575,078	TSLM	1,542,640.74	32,437.26
2018 May	2,003,996	TSLM	1,809,322.43	194,673.57
2018 Jun	2,381,154	TSLM	2,221,480.03	159,673.97
2018 Jul	2,981,643	TSLM	2,780,270.05	201,372.95
2018 Aug	3,371,918	TSLM	3,180,121.20	191,796.80
2018 Sep	2,499,368	TSLM	2,355,148.84	144,219.16
2018 Oct	1,956,693	TSLM	1,772,734.38	183,958.62
2018 Nov	732,141	TSLM	929,317.08	-197,176.08
2018 Dec	554,803	TSLM	815,716.63	-260,913.63
2019 Jan	548,686	TSLM	828,157.64	-279,471.64
2019 Feb	739,981	TSLM	1,008,669.74	-268,688.74
2019 Mar	1,078,918	TSLM	1,292,192.04	-213,274.04
2019 Apr	1,795,494	TSLM	1,664,796.50	130,697.50
2019 May	1,990,529	TSLM	1,935,097.80	55,431.20
2019 Jun	2,425,834	TSLM	2,355,995.09	69,838.91
2019 Jul	2,988,668	TSLM	2,922,283.72	66,384.28
2019 Aug	3,439,271	TSLM	3,311,089.19	128,181.81
2019 Sep	2,573,527	TSLM	2,465,879.75	107,647.25
2019 Oct	1,930,852	TSLM	1,877,248.46	53,603.54
2019 Nov	785,875	TSLM	963,160.81	-177,285.81
2019 Dec	602,860	TSLM	842,357.12	-239,497.12
2020 Jan	560,368	TSLM	853,283.89	-292,915.89
2020 Feb	844,247	TSLM	1,036,492.68	-192,245.68
2020 Mar	513,360	TSLM	1,339,447.02	-826,087.02
2020 Apr	25,614	TSLM	1,737,765.05	-1,712,151.05
2020 May	40,932	TSLM	1,963,458.39	-1,922,526.39
2020 Jun	330,393	TSLM	2,338,364.12	-2,007,971.12
2020 Jul	1,035,732	TSLM	2,862,396.89	-1,826,664.89
2020 Aug	2,090,569	TSLM	3,203,767.22	-1,113,198.22
2020 Sep	1,418,185	TSLM	2,314,278.46	-896,093.46
2020 Oct	696,087	TSLM	1,684,495.99	-988,408.99
2020 Nov	181,873	TSLM	676,259.61	-494,386.61
2020 Dec	153,351	TSLM	529,934.84	-376,583.84
2021 Jan	105,336	TSLM	524,344.89	-419,008.89
2021 Feb	66,194	TSLM	706,533.94	-640,339.94
2021 Mar	84,413	TSLM	933,409.34	-848,996.34
2021 Apr	138,661	TSLM	1,258,032.87	-1,119,371.87
2021 May	502,057	TSLM	1,480,884.86	-978,827.86
2021 Jun	1,182,009	TSLM	1,868,350.86	-686,341.86
2021 Jul	1,551,789	TSLM	2,435,354.60	-883,565.60
2021 Aug	2,762,537	TSLM	2,863,720.99	-101,183.99
2021 Sep	1,869,194	TSLM	2,006,313.69	-137,119.69
2021 Oct	1,584,764	TSLM	1,377,372.02	207,391.98
2021 Nov	651,051	TSLM	409,889.29	241,161.71
2021 Dec	376,031	TSLM	281,337.97	94,693.03
2022 Jan	344,634	TSLM	277,533.56	67,100.44
2022 Feb	590,122	TSLM	448,593.53	141,528.47
2022 Mar	873,841	TSLM	667,920.97	205,920.03
2022 Apr	1,629,377	TSLM	979,573.22	649,803.78
2022 May	1,867,744	TSLM	1,277,699.22	590,044.78
2022 Jun	2,230,207	TSLM	1,731,057.98	499,149.02
2010 Jan	366,296	TSLM_log	451,085.59	-84,789.59
2010 Feb	533,056	TSLM_log	634,031.31	-100,975.31
2010 Mar	742,227	TSLM_log	847,973.36	-105,746.36
2010 Apr	902,745	TSLM_log	1,017,868.52	-115,123.52
2010 May	1,107,303	TSLM_log	1,221,755.90	-114,452.90
2010 Jun	1,464,695	TSLM_log	1,486,153.33	-21,458.33
2010 Jul	2,050,478	TSLM_log	1,863,746.02	186,731.98
2010 Aug	2,468,924	TSLM_log	2,188,638.29	280,285.71
2010 Sep	1,696,356	TSLM_log	1,558,879.09	137,476.91
2010 Oct	1,104,659	TSLM_log	1,086,742.58	17,916.42
2010 Nov	445,221	TSLM_log	520,772.60	-75,551.60
2010 Dec	365,490	TSLM_log	403,441.78	-37,951.78
2011 Jan	357,209	TSLM_log	434,065.03	-76,856.03
2011 Feb	503,831	TSLM_log	614,121.42	-110,290.42
2011 Mar	761,343	TSLM_log	822,614.32	-61,271.32
2011 Apr	1,177,115	TSLM_log	982,867.20	194,247.80
2011 May	1,169,516	TSLM_log	1,197,145.30	-27,629.30
2011 Jun	1,576,730	TSLM_log	1,471,990.96	104,739.04
2011 Jul	2,208,160	TSLM_log	1,874,529.46	333,630.54
2011 Aug	2,572,404	TSLM_log	2,227,091.52	345,312.48
2011 Sep	1,731,056	TSLM_log	1,560,159.75	170,896.25
2011 Oct	1,161,751	TSLM_log	1,070,105.24	91,645.76
2011 Nov	427,550	TSLM_log	502,877.38	-75,327.38
2011 Dec	333,201	TSLM_log	394,303.37	-61,102.37
2012 Jan	359,355	TSLM_log	416,941.79	-57,586.79
2012 Feb	531,709	TSLM_log	587,092.03	-55,383.03
2012 Mar	751,024	TSLM_log	804,353.38	-53,329.38
2012 Apr	1,017,976	TSLM_log	983,946.61	34,029.39
2012 May	1,194,673	TSLM_log	1,175,222.13	19,450.87
2012 Jun	1,678,327	TSLM_log	1,460,104.06	218,222.94
2012 Jul	2,296,474	TSLM_log	1,889,819.54	406,654.46
2012 Aug	2,622,801	TSLM_log	2,267,973.29	354,827.71
2012 Sep	1,829,252	TSLM_log	1,569,116.86	260,135.14
2012 Oct	1,244,751	TSLM_log	1,071,772.22	172,978.78
2012 Nov	453,958	TSLM_log	490,941.52	-36,983.52
2012 Dec	346,474	TSLM_log	390,281.31	-43,807.31
2013 Jan	369,969	TSLM_log	410,505.54	-40,536.54
2013 Feb	520,055	TSLM_log	578,031.53	-57,976.53
2013 Mar	840,024	TSLM_log	787,637.82	52,386.18
2013 Apr	986,191	TSLM_log	998,730.91	-12,539.91
2013 May	1,382,234	TSLM_log	1,182,402.37	199,831.63
2013 Jun	1,814,108	TSLM_log	1,494,923.47	319,184.53
2013 Jul	2,387,304	TSLM_log	1,960,165.04	427,138.96
2013 Aug	2,764,686	TSLM_log	2,347,623.11	417,062.89
2013 Sep	1,943,037	TSLM_log	1,617,867.40	325,169.60
2013 Oct	1,291,360	TSLM_log	1,104,560.17	186,799.83
2013 Nov	455,695	TSLM_log	488,798.13	-33,103.13
2013 Dec	358,062	TSLM_log	391,969.67	-33,907.67
2014 Jan	377,387	TSLM_log	409,294.04	-31,907.04
2014 Feb	543,470	TSLM_log	574,761.69	-31,291.69
2014 Mar	749,773	TSLM_log	800,870.41	-51,097.41
2014 Apr	1,337,145	TSLM_log	1,004,903.41	332,241.59
2014 May	1,538,342	TSLM_log	1,216,217.12	322,124.88
2014 Jun	1,994,167	TSLM_log	1,545,676.71	448,490.29
2014 Jul	2,529,246	TSLM_log	2,040,982.02	488,263.98
2014 Aug	3,069,865	TSLM_log	2,434,242.24	635,622.76
2014 Sep	2,089,656	TSLM_log	1,686,242.91	403,413.09
2014 Oct	1,477,481	TSLM_log	1,146,251.38	331,229.62
2014 Nov	502,473	TSLM_log	492,620.56	9,852.44
2014 Dec	382,543	TSLM_log	397,694.46	-15,151.46
2015 Jan	381,607	TSLM_log	413,064.34	-31,457.34
2015 Feb	544,777	TSLM_log	580,548.22	-35,771.22
2015 Mar	827,071	TSLM_log	818,462.29	8,608.71
2015 Apr	1,242,844	TSLM_log	1,069,331.50	173,512.50
2015 May	1,654,526	TSLM_log	1,289,215.05	365,310.95
2015 Jun	2,079,484	TSLM_log	1,656,036.47	423,447.53
2015 Jul	2,688,710	TSLM_log	2,191,135.38	497,574.62
2015 Aug	3,108,357	TSLM_log	2,606,804.27	501,552.73
2015 Sep	2,196,681	TSLM_log	1,803,820.76	392,860.24
2015 Oct	1,553,142	TSLM_log	1,225,128.79	328,013.21
2015 Nov	552,778	TSLM_log	511,987.81	40,790.19
2015 Dec	426,419	TSLM_log	410,121.77	16,297.23
2016 Jan	443,150	TSLM_log	423,584.17	19,565.83
2016 Feb	664,278	TSLM_log	598,745.74	65,532.26
2016 Mar	1,089,392	TSLM_log	857,849.95	231,542.05
2016 Apr	1,335,308	TSLM_log	1,169,875.48	165,432.52
2016 May	1,828,292	TSLM_log	1,411,537.49	416,754.51
2016 Jun	2,288,337	TSLM_log	1,824,672.83	463,664.17
2016 Jul	2,848,570	TSLM_log	2,425,266.61	423,303.39
2016 Aug	3,204,047	TSLM_log	2,873,559.84	330,487.16
2016 Sep	2,378,618	TSLM_log	1,991,903.49	386,714.51
2016 Oct	1,793,822	TSLM_log	1,354,656.23	439,165.77
2016 Nov	653,514	TSLM_log	551,603.04	101,910.96
2016 Dec	478,510	TSLM_log	442,893.96	35,616.04
2017 Jan	495,629	TSLM_log	457,277.63	38,351.37
2017 Feb	704,532	TSLM_log	656,438.30	48,093.70
2017 Mar	1,015,421	TSLM_log	966,420.55	49,000.45
2017 Apr	1,765,170	TSLM_log	1,295,415.74	469,754.26
2017 May	1,970,072	TSLM_log	1,613,878.92	356,193.08
2017 Jun	2,417,100	TSLM_log	2,088,400.26	328,699.74
2017 Jul	2,968,641	TSLM_log	2,763,951.52	204,689.48
2017 Aug	3,295,406	TSLM_log	3,257,792.39	37,613.61
2017 Sep	2,470,298	TSLM_log	2,272,833.86	197,464.14
2017 Oct	1,911,961	TSLM_log	1,562,086.19	349,874.81
2017 Nov	680,373	TSLM_log	618,645.70	61,727.30
2017 Dec	512,548	TSLM_log	488,087.21	24,460.79
2018 Jan	503,908	TSLM_log	505,036.57	-1,128.57
2018 Feb	731,090	TSLM_log	730,434.81	655.19
2018 Mar	1,151,455	TSLM_log	1,078,803.76	72,651.24
2018 Apr	1,575,078	TSLM_log	1,496,706.96	78,371.04
2018 May	2,003,996	TSLM_log	1,838,127.98	165,868.02
2018 Jun	2,381,154	TSLM_log	2,378,543.66	2,610.34
2018 Jul	2,981,643	TSLM_log	3,117,663.95	-136,020.95
2018 Aug	3,371,918	TSLM_log	3,649,521.37	-277,603.37
2018 Sep	2,499,368	TSLM_log	2,555,590.68	-56,222.68
2018 Oct	1,956,693	TSLM_log	1,774,543.10	182,149.90
2018 Nov	732,141	TSLM_log	680,459.82	51,681.18
2018 Dec	554,803	TSLM_log	530,242.14	24,560.86
2019 Jan	548,686	TSLM_log	546,846.77	1,839.23
2019 Feb	739,981	TSLM_log	790,327.16	-50,346.16
2019 Mar	1,078,918	TSLM_log	1,168,782.07	-89,864.07
2019 Apr	1,795,494	TSLM_log	1,661,048.96	134,445.04
2019 May	1,990,529	TSLM_log	2,017,534.47	-27,005.47
2019 Jun	2,425,834	TSLM_log	2,603,332.77	-177,498.77
2019 Jul	2,988,668	TSLM_log	3,388,209.67	-399,541.67
2019 Aug	3,439,271	TSLM_log	3,926,215.31	-486,944.31
2019 Sep	2,573,527	TSLM_log	2,759,321.03	-185,794.03
2019 Oct	1,930,852	TSLM_log	1,936,884.66	-6,032.66
2019 Nov	785,875	TSLM_log	721,517.77	64,357.23
2019 Dec	602,860	TSLM_log	559,317.10	43,542.90
2020 Jan	560,368	TSLM_log	574,691.73	-14,323.73
2020 Feb	844,247	TSLM_log	826,643.60	17,603.40
2020 Mar	513,360	TSLM_log	1,239,632.41	-726,272.41
2020 Apr	25,614	TSLM_log	1,759,821.73	-1,734,207.73
2020 May	40,932	TSLM_log	2,065,057.62	-2,024,125.62
2020 Jun	330,393	TSLM_log	2,542,357.94	-2,211,964.94
2020 Jul	1,035,732	TSLM_log	3,173,467.84	-2,137,735.84
2020 Aug	2,090,569	TSLM_log	3,571,320.86	-1,480,751.86
2020 Sep	1,418,185	TSLM_log	2,508,630.47	-1,090,445.47
2020 Oct	696,087	TSLM_log	1,759,277.33	-1,063,190.33
2020 Nov	181,873	TSLM_log	630,287.65	-448,414.65
2020 Dec	153,351	TSLM_log	470,188.17	-316,837.17
2021 Jan	105,336	TSLM_log	464,174.40	-358,838.40
2021 Feb	66,194	TSLM_log	644,819.12	-578,625.12
2021 Mar	84,413	TSLM_log	845,820.18	-761,407.18
2021 Apr	138,661	TSLM_log	847,529.75	-708,868.75
2021 May	502,057	TSLM_log	1,021,306.62	-519,249.62
2021 Jun	1,182,009	TSLM_log	1,540,502.85	-358,493.85
2021 Jul	1,551,789	TSLM_log	2,142,460.71	-590,671.71
2021 Aug	2,762,537	TSLM_log	2,569,598.57	192,938.43
2021 Sep	1,869,194	TSLM_log	1,817,391.13	51,802.87
2021 Oct	1,584,764	TSLM_log	1,247,847.76	336,916.24
2021 Nov	651,051	TSLM_log	437,671.63	213,379.37
2021 Dec	376,031	TSLM_log	337,809.39	38,221.61
2022 Jan	344,634	TSLM_log	328,529.00	16,105.00
2022 Feb	590,122	TSLM_log	433,601.30	156,520.70
2022 Mar	873,841	TSLM_log	588,716.83	285,124.17
2022 Apr	1,629,377	TSLM_log	626,785.11	1,002,591.89
2022 May	1,867,744	TSLM_log	917,099.55	950,644.45
2022 Jun	2,230,207	TSLM_log	1,523,192.69	707,014.31

# Show Point Forecasts in Plot: 2000-2022
error_fc_algarve_slide %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_until2022, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2000-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2010-2022
error_fc_algarve_slide %>%
  filter(year(Month) >= 2010) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_from2010, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2010-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2019-2022
error_fc_algarve_slide %>%
  filter(year(Month) >= 2019) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_from2019, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2019-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2020-2022
error_fc_algarve_slide %>%
  filter(year(Month) >= 2020) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_algarve_from2020, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2020-2022") +
  ylab("Overnight_Stays")

2.2.2.4 Change of RMSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_slide, tourism_algarve_until2019) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_slide, tourism_algarve_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
HWA	13	122,389.91	1	191,442.2
Drift_STL	9	113,320.35	2	193,122.8
ARIMA_d1D1	3	93,811.73	3	215,791.6
ARIMA_auto	1	91,912.66	4	217,384.8
ARIMA_d0D1	2	93,792.07	5	219,343.2
ETS_auto	12	116,099.46	6	220,659.7
ETS_auto_log	14	122,511.93	7	251,552.7
HWA_log	11	115,502.73	8	252,256.1
Drift_STL_log	7	106,580.12	9	263,040.9
ARIMA_d1D1_log	6	104,162.72	10	292,584.2
ARIMA_auto_log	5	103,514.04	11	315,121.1
ARIMA_d0D1_log	4	96,736.60	12	315,334.7
Prophet	16	198,915.77	13	406,925.0
Prophet_log	15	178,871.59	14	418,992.3
TSLM	17	212,112.29	15	444,227.3
SNaive	10	114,889.37	16	464,522.7
TSLM_log	18	233,576.19	17	472,326.3
SNaive_log	8	110,733.92	18	512,938.3
Naive	19	517,678.97	19	519,314.1
Naive_log	20	548,521.02	20	552,221.8

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Save best models according to the RMSE of Forecasts from 2010-2022
best_models_fc_algarve_slide <- c("ARIMA_d0D1", "Drift_STL", "ARIMA_d1D1", "ARIMA_auto", "HWA", "ETS_auto", "Naive", "Prophet", "TSLM", "SNaive")

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_slide, tourism_algarve_until2019) %>%
  filter(.model %in% best_models_fc_algarve_slide) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_slide, tourism_algarve_until2022) %>%
  filter(.model %in% best_models_fc_algarve_slide) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
HWA	7	122,389.91	1	191,442.2
Drift_STL	4	113,320.35	2	193,122.8
ARIMA_d1D1	3	93,811.73	3	215,791.6
ARIMA_auto	1	91,912.66	4	217,384.8
ARIMA_d0D1	2	93,792.07	5	219,343.2
ETS_auto	6	116,099.46	6	220,659.7
Prophet	8	198,915.77	7	406,925.0
TSLM	9	212,112.29	8	444,227.3
SNaive	5	114,889.37	9	464,522.7
Naive	10	517,678.97	10	519,314.1

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.2.2.5 RMSE Development by including more Years in Time Series

# Compute RMSE and RMSSE for 2010 and create tibble
tourism_until_i <- tourism_algarve_until2022 %>%
    filter(year(Month) <= 2010)

accuracy_algarve_slide <- accuracy(fc_algarve_slide, tourism_until_i) %>%
  select(c(.model, RMSE, RMSSE)) %>%
  mutate(Until_Year = 2010)

# Create tsibble of summarized RMSE and RMSSE, beginning in 2010 and including more years
for (i in 2011:2022){
  tourism_until_i <- tourism_algarve_until2022 %>%
    filter(year(Month) <= i)

  accuracy_next_year <- accuracy(fc_algarve_slide, tourism_until_i) %>%
    select(c(.model, RMSE, RMSSE)) %>%
    mutate(Until_Year = i)

  accuracy_algarve_slide <- rbind(accuracy_algarve_slide, accuracy_next_year)
}

rm(accuracy_next_year, tourism_until_i) # remove variables from R environment

accuracy_algarve_slide <- accuracy_algarve_slide %>%
  rename(Model = .model) %>%
  select(c(Until_Year, Model, RMSE, RMSSE)) %>%
  as_tsibble(key = Model, index = Until_Year)

# Show table
accuracy_algarve_slide %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	71,467.63	0.76
2011	ARIMA_auto	87,941.58	0.92
2012	ARIMA_auto	83,677.97	0.89
2013	ARIMA_auto	84,794.16	0.90
2014	ARIMA_auto	98,226.19	0.97
2015	ARIMA_auto	93,853.38	0.93
2016	ARIMA_auto	93,303.20	0.89
2017	ARIMA_auto	96,371.35	0.89
2018	ARIMA_auto	93,083.70	0.87
2019	ARIMA_auto	91,912.66	0.87
2020	ARIMA_auto	205,825.86	0.66
2021	ARIMA_auto	216,470.69	0.66
2022	ARIMA_auto	217,384.75	0.61
2010	ARIMA_auto_log	102,271.01	1.08
2011	ARIMA_auto_log	99,337.75	1.04
2012	ARIMA_auto_log	89,240.30	0.95
2013	ARIMA_auto_log	88,930.92	0.95
2014	ARIMA_auto_log	97,325.08	0.96
2015	ARIMA_auto_log	90,733.85	0.90
2016	ARIMA_auto_log	98,526.96	0.94
2017	ARIMA_auto_log	106,595.99	0.98
2018	ARIMA_auto_log	104,063.57	0.97
2019	ARIMA_auto_log	103,514.04	0.98
2020	ARIMA_auto_log	287,515.64	0.92
2021	ARIMA_auto_log	286,498.15	0.87
2022	ARIMA_auto_log	315,121.07	0.89
2010	ARIMA_d0D1	71,467.63	0.76
2011	ARIMA_d0D1	87,941.58	0.92
2012	ARIMA_d0D1	83,677.97	0.89
2013	ARIMA_d0D1	84,794.16	0.90
2014	ARIMA_d0D1	95,809.09	0.94
2015	ARIMA_d0D1	91,232.20	0.91
2016	ARIMA_d0D1	92,970.15	0.88
2017	ARIMA_d0D1	99,058.12	0.91
2018	ARIMA_d0D1	95,143.94	0.89
2019	ARIMA_d0D1	93,792.07	0.89
2020	ARIMA_d0D1	207,749.61	0.67
2021	ARIMA_d0D1	218,518.93	0.67
2022	ARIMA_d0D1	219,343.24	0.62
2010	ARIMA_d0D1_log	102,271.01	1.08
2011	ARIMA_d0D1_log	99,337.75	1.04
2012	ARIMA_d0D1_log	89,240.30	0.95
2013	ARIMA_d0D1_log	88,930.92	0.95
2014	ARIMA_d0D1_log	97,319.77	0.96
2015	ARIMA_d0D1_log	91,024.20	0.90
2016	ARIMA_d0D1_log	95,308.59	0.90
2017	ARIMA_d0D1_log	100,072.40	0.92
2018	ARIMA_d0D1_log	96,548.59	0.90
2019	ARIMA_d0D1_log	96,736.60	0.91
2020	ARIMA_d0D1_log	285,563.02	0.92
2021	ARIMA_d0D1_log	286,742.91	0.87
2022	ARIMA_d0D1_log	315,334.72	0.89
2010	ARIMA_d1D1	78,216.64	0.83
2011	ARIMA_d1D1	94,067.88	0.98
2012	ARIMA_d1D1	89,706.70	0.95
2013	ARIMA_d1D1	90,334.79	0.96
2014	ARIMA_d1D1	101,472.12	1.00
2015	ARIMA_d1D1	96,688.32	0.96
2016	ARIMA_d1D1	95,752.25	0.91
2017	ARIMA_d1D1	98,450.84	0.91
2018	ARIMA_d1D1	94,687.05	0.88
2019	ARIMA_d1D1	93,811.73	0.89
2020	ARIMA_d1D1	200,183.04	0.64
2021	ARIMA_d1D1	211,166.39	0.64
2022	ARIMA_d1D1	215,791.57	0.61
2010	ARIMA_d1D1_log	120,629.62	1.28
2011	ARIMA_d1D1_log	111,365.76	1.16
2012	ARIMA_d1D1_log	98,983.05	1.05
2013	ARIMA_d1D1_log	95,228.42	1.01
2014	ARIMA_d1D1_log	101,470.68	1.00
2015	ARIMA_d1D1_log	94,442.61	0.94
2016	ARIMA_d1D1_log	101,470.32	0.96
2017	ARIMA_d1D1_log	108,985.25	1.00
2018	ARIMA_d1D1_log	106,240.65	0.99
2019	ARIMA_d1D1_log	104,162.72	0.98
2020	ARIMA_d1D1_log	212,503.09	0.68
2021	ARIMA_d1D1_log	234,439.67	0.71
2022	ARIMA_d1D1_log	292,584.19	0.83
2010	Drift_STL	62,249.26	0.66
2011	Drift_STL	93,531.76	0.98
2012	Drift_STL	89,870.98	0.96
2013	Drift_STL	92,514.50	0.98
2014	Drift_STL	107,012.21	1.05
2015	Drift_STL	107,670.19	1.07
2016	Drift_STL	111,905.54	1.06
2017	Drift_STL	117,991.35	1.09
2018	Drift_STL	115,301.73	1.08
2019	Drift_STL	113,320.35	1.07
2020	Drift_STL	184,772.41	0.59
2021	Drift_STL	192,528.46	0.59
2022	Drift_STL	193,122.83	0.55
2010	Drift_STL_log	75,886.85	0.80
2011	Drift_STL_log	100,543.09	1.05
2012	Drift_STL_log	92,977.35	0.99
2013	Drift_STL_log	91,126.48	0.97
2014	Drift_STL_log	97,451.83	0.96
2015	Drift_STL_log	94,132.36	0.94
2016	Drift_STL_log	99,834.97	0.95
2017	Drift_STL_log	108,172.28	1.00
2018	Drift_STL_log	106,374.49	0.99
2019	Drift_STL_log	106,580.12	1.01
2020	Drift_STL_log	178,792.09	0.57
2021	Drift_STL_log	190,242.50	0.58
2022	Drift_STL_log	263,040.94	0.74
2010	ETS_auto	139,863.23	1.48
2011	ETS_auto	129,031.47	1.35
2012	ETS_auto	120,898.12	1.29
2013	ETS_auto	114,236.00	1.22
2014	ETS_auto	115,041.17	1.13
2015	ETS_auto	109,239.60	1.09
2016	ETS_auto	109,039.78	1.03
2017	ETS_auto	114,136.17	1.05
2018	ETS_auto	111,865.74	1.04
2019	ETS_auto	116,099.46	1.10
2020	ETS_auto	214,525.50	0.69
2021	ETS_auto	221,665.01	0.67
2022	ETS_auto	220,659.74	0.62
2010	ETS_auto_log	139,056.22	1.47
2011	ETS_auto_log	130,371.41	1.36
2012	ETS_auto_log	120,329.22	1.28
2013	ETS_auto_log	111,960.83	1.19
2014	ETS_auto_log	113,687.65	1.12
2015	ETS_auto_log	107,307.28	1.07
2016	ETS_auto_log	111,003.61	1.05
2017	ETS_auto_log	119,359.01	1.10
2018	ETS_auto_log	122,880.07	1.15
2019	ETS_auto_log	122,511.93	1.16
2020	ETS_auto_log	224,203.23	0.72
2021	ETS_auto_log	229,701.17	0.70
2022	ETS_auto_log	251,552.70	0.71
2010	HWA	104,305.04	1.10
2011	HWA	117,014.49	1.22
2012	HWA	115,845.50	1.23
2013	HWA	117,876.11	1.25
2014	HWA	123,540.49	1.21
2015	HWA	118,846.41	1.18
2016	HWA	113,692.60	1.08
2017	HWA	121,518.14	1.12
2018	HWA	122,999.58	1.15
2019	HWA	122,389.91	1.16
2020	HWA	178,895.18	0.57
2021	HWA	191,048.96	0.58
2022	HWA	191,442.17	0.54
2010	HWA_log	128,225.95	1.36
2011	HWA_log	116,992.99	1.22
2012	HWA_log	110,545.09	1.18
2013	HWA_log	104,650.89	1.11
2014	HWA_log	104,513.72	1.03
2015	HWA_log	99,977.69	0.99
2016	HWA_log	106,004.43	1.01
2017	HWA_log	118,148.28	1.09
2018	HWA_log	116,605.23	1.09
2019	HWA_log	115,502.73	1.09
2020	HWA_log	217,606.67	0.70
2021	HWA_log	219,214.11	0.67
2022	HWA_log	252,256.06	0.71
2010	Naive	425,572.00	4.50
2011	Naive	443,060.84	4.63
2012	Naive	447,928.19	4.77
2013	Naive	456,249.31	4.85
2014	Naive	474,952.55	4.67
2015	Naive	485,530.92	4.82
2016	Naive	494,166.22	4.69
2017	Naive	504,209.78	4.64
2018	Naive	511,349.21	4.77
2019	Naive	517,678.97	4.89
2020	Naive	518,752.28	1.67
2021	Naive	524,088.42	1.60
2022	Naive	519,314.08	1.47
2010	Naive_log	443,205.75	4.69
2011	Naive_log	462,046.98	4.83
2012	Naive_log	467,723.95	4.98
2013	Naive_log	477,131.98	5.08
2014	Naive_log	497,536.96	4.89
2015	Naive_log	509,685.52	5.06
2016	Naive_log	520,021.10	4.94
2017	Naive_log	531,961.98	4.89
2018	Naive_log	540,710.12	5.05
2019	Naive_log	548,521.02	5.18
2020	Naive_log	551,479.92	1.77
2021	Naive_log	560,772.43	1.71
2022	Naive_log	552,221.84	1.56
2010	Prophet	112,393.41	1.19
2011	Prophet	132,419.09	1.38
2012	Prophet	142,671.16	1.52
2013	Prophet	150,103.30	1.60
2014	Prophet	172,189.51	1.69
2015	Prophet	183,725.41	1.83
2016	Prophet	193,904.16	1.84
2017	Prophet	201,756.84	1.86
2018	Prophet	200,906.70	1.87
2019	Prophet	198,915.77	1.88
2020	Prophet	377,544.61	1.21
2021	Prophet	387,391.74	1.18
2022	Prophet	406,924.99	1.15
2010	Prophet_log	209,703.05	2.22
2011	Prophet_log	197,337.19	2.06
2012	Prophet_log	192,498.31	2.05
2013	Prophet_log	187,418.51	1.99
2014	Prophet_log	190,504.86	1.87
2015	Prophet_log	184,688.89	1.83
2016	Prophet_log	177,225.18	1.68
2017	Prophet_log	178,224.96	1.64
2018	Prophet_log	178,614.47	1.67
2019	Prophet_log	178,871.59	1.69
2020	Prophet_log	309,287.42	0.99
2021	Prophet_log	386,453.00	1.18
2022	Prophet_log	418,992.28	1.18
2010	SNaive	92,048.59	0.97
2011	SNaive	99,177.61	1.04
2012	SNaive	91,436.27	0.97
2013	SNaive	92,129.31	0.98
2014	SNaive	113,161.42	1.11
2015	SNaive	108,815.62	1.08
2016	SNaive	117,533.45	1.12
2017	SNaive	122,419.19	1.13
2018	SNaive	118,239.07	1.10
2019	SNaive	114,889.37	1.09
2020	SNaive	411,007.46	1.32
2021	SNaive	426,762.60	1.30
2022	SNaive	464,522.72	1.31
2010	SNaive_log	89,385.60	0.95
2011	SNaive_log	96,099.59	1.00
2012	SNaive_log	88,521.80	0.94
2013	SNaive_log	88,824.66	0.94
2014	SNaive_log	109,474.33	1.08
2015	SNaive_log	105,032.27	1.04
2016	SNaive_log	113,257.53	1.07
2017	SNaive_log	117,884.37	1.08
2018	SNaive_log	113,991.72	1.06
2019	SNaive_log	110,733.92	1.05
2020	SNaive_log	491,332.88	1.58
2021	SNaive_log	492,241.23	1.50
2022	SNaive_log	512,938.30	1.45
2010	TSLM	109,231.56	1.16
2011	TSLM	122,766.38	1.28
2012	TSLM	130,866.24	1.39
2013	TSLM	145,563.90	1.55
2014	TSLM	180,427.76	1.77
2015	TSLM	196,149.41	1.95
2016	TSLM	211,159.20	2.00
2017	TSLM	220,046.10	2.02
2018	TSLM	216,326.47	2.02
2019	TSLM	212,112.29	2.00
2020	TSLM	422,884.88	1.36
2021	TSLM	444,989.08	1.35
2022	TSLM	444,227.30	1.25
2010	TSLM_log	127,534.02	1.35
2011	TSLM_log	150,558.99	1.57
2012	TSLM_log	166,213.28	1.77
2013	TSLM_log	185,042.13	1.97
2014	TSLM_log	222,809.66	2.19
2015	TSLM_log	238,247.52	2.37
2016	TSLM_log	248,894.17	2.36
2017	TSLM_log	247,372.74	2.28
2018	TSLM_log	236,656.38	2.21
2019	TSLM_log	233,576.19	2.21
2020	TSLM_log	464,299.11	1.49
2021	TSLM_log	463,598.37	1.41
2022	TSLM_log	472,326.26	1.33

All Models

# Plot development of RMSE for period 2010-2022
accuracy_algarve_slide %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_algarve_slide %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_algarve_slide %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_algarve_slide %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_algarve_slide %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	517,678.97	518,752.3	1,073.31	0.0021
Naive_log	548,521.02	551,479.9	2,958.90	0.0054
HWA	122,389.91	178,895.2	56,505.27	0.4617
Drift_STL	113,320.35	184,772.4	71,452.06	0.6305
Drift_STL_log	106,580.12	178,792.1	72,211.97	0.6775
Prophet_log	178,871.59	309,287.4	130,415.83	0.7291
ETS_auto_log	122,511.93	224,203.2	101,691.30	0.8301
ETS_auto	116,099.46	214,525.5	98,426.05	0.8478
HWA_log	115,502.73	217,606.7	102,103.95	0.8840
Prophet	198,915.77	377,544.6	178,628.85	0.8980
TSLM_log	233,576.19	464,299.1	230,722.92	0.9878
TSLM	212,112.29	422,884.9	210,772.59	0.9937
ARIMA_d1D1_log	104,162.72	212,503.1	108,340.38	1.0401
ARIMA_d1D1	93,811.73	200,183.0	106,371.30	1.1339
ARIMA_d0D1	93,792.07	207,749.6	113,957.54	1.2150
ARIMA_auto	91,912.66	205,825.9	113,913.20	1.2394
ARIMA_auto_log	103,514.04	287,515.6	184,001.59	1.7776
ARIMA_d0D1_log	96,736.60	285,563.0	188,826.42	1.9520
SNaive	114,889.37	411,007.5	296,118.09	2.5774
SNaive_log	110,733.92	491,332.9	380,598.96	3.4371

# DELETE!
accuracy_algarve_slide %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	71,467.63	0.76
2011	ARIMA_auto	87,941.58	0.92
2012	ARIMA_auto	83,677.97	0.89
2013	ARIMA_auto	84,794.16	0.90
2014	ARIMA_auto	98,226.19	0.97
2015	ARIMA_auto	93,853.38	0.93
2016	ARIMA_auto	93,303.20	0.89
2017	ARIMA_auto	96,371.35	0.89
2018	ARIMA_auto	93,083.70	0.87
2019	ARIMA_auto	91,912.66	0.87
2020	ARIMA_auto	205,825.86	0.66
2021	ARIMA_auto	216,470.69	0.66
2022	ARIMA_auto	217,384.75	0.61
2010	ARIMA_auto_log	102,271.01	1.08
2011	ARIMA_auto_log	99,337.75	1.04
2012	ARIMA_auto_log	89,240.30	0.95
2013	ARIMA_auto_log	88,930.92	0.95
2014	ARIMA_auto_log	97,325.08	0.96
2015	ARIMA_auto_log	90,733.85	0.90
2016	ARIMA_auto_log	98,526.96	0.94
2017	ARIMA_auto_log	106,595.99	0.98
2018	ARIMA_auto_log	104,063.57	0.97
2019	ARIMA_auto_log	103,514.04	0.98
2020	ARIMA_auto_log	287,515.64	0.92
2021	ARIMA_auto_log	286,498.15	0.87
2022	ARIMA_auto_log	315,121.07	0.89
2010	ARIMA_d0D1	71,467.63	0.76
2011	ARIMA_d0D1	87,941.58	0.92
2012	ARIMA_d0D1	83,677.97	0.89
2013	ARIMA_d0D1	84,794.16	0.90
2014	ARIMA_d0D1	95,809.09	0.94
2015	ARIMA_d0D1	91,232.20	0.91
2016	ARIMA_d0D1	92,970.15	0.88
2017	ARIMA_d0D1	99,058.12	0.91
2018	ARIMA_d0D1	95,143.94	0.89
2019	ARIMA_d0D1	93,792.07	0.89
2020	ARIMA_d0D1	207,749.61	0.67
2021	ARIMA_d0D1	218,518.93	0.67
2022	ARIMA_d0D1	219,343.24	0.62
2010	ARIMA_d0D1_log	102,271.01	1.08
2011	ARIMA_d0D1_log	99,337.75	1.04
2012	ARIMA_d0D1_log	89,240.30	0.95
2013	ARIMA_d0D1_log	88,930.92	0.95
2014	ARIMA_d0D1_log	97,319.77	0.96
2015	ARIMA_d0D1_log	91,024.20	0.90
2016	ARIMA_d0D1_log	95,308.59	0.90
2017	ARIMA_d0D1_log	100,072.40	0.92
2018	ARIMA_d0D1_log	96,548.59	0.90
2019	ARIMA_d0D1_log	96,736.60	0.91
2020	ARIMA_d0D1_log	285,563.02	0.92
2021	ARIMA_d0D1_log	286,742.91	0.87
2022	ARIMA_d0D1_log	315,334.72	0.89
2010	ARIMA_d1D1	78,216.64	0.83
2011	ARIMA_d1D1	94,067.88	0.98
2012	ARIMA_d1D1	89,706.70	0.95
2013	ARIMA_d1D1	90,334.79	0.96
2014	ARIMA_d1D1	101,472.12	1.00
2015	ARIMA_d1D1	96,688.32	0.96
2016	ARIMA_d1D1	95,752.25	0.91
2017	ARIMA_d1D1	98,450.84	0.91
2018	ARIMA_d1D1	94,687.05	0.88
2019	ARIMA_d1D1	93,811.73	0.89
2020	ARIMA_d1D1	200,183.04	0.64
2021	ARIMA_d1D1	211,166.39	0.64
2022	ARIMA_d1D1	215,791.57	0.61
2010	ARIMA_d1D1_log	120,629.62	1.28
2011	ARIMA_d1D1_log	111,365.76	1.16
2012	ARIMA_d1D1_log	98,983.05	1.05
2013	ARIMA_d1D1_log	95,228.42	1.01
2014	ARIMA_d1D1_log	101,470.68	1.00
2015	ARIMA_d1D1_log	94,442.61	0.94
2016	ARIMA_d1D1_log	101,470.32	0.96
2017	ARIMA_d1D1_log	108,985.25	1.00
2018	ARIMA_d1D1_log	106,240.65	0.99
2019	ARIMA_d1D1_log	104,162.72	0.98
2020	ARIMA_d1D1_log	212,503.09	0.68
2021	ARIMA_d1D1_log	234,439.67	0.71
2022	ARIMA_d1D1_log	292,584.19	0.83
2010	Drift_STL	62,249.26	0.66
2011	Drift_STL	93,531.76	0.98
2012	Drift_STL	89,870.98	0.96
2013	Drift_STL	92,514.50	0.98
2014	Drift_STL	107,012.21	1.05
2015	Drift_STL	107,670.19	1.07
2016	Drift_STL	111,905.54	1.06
2017	Drift_STL	117,991.35	1.09
2018	Drift_STL	115,301.73	1.08
2019	Drift_STL	113,320.35	1.07
2020	Drift_STL	184,772.41	0.59
2021	Drift_STL	192,528.46	0.59
2022	Drift_STL	193,122.83	0.55
2010	Drift_STL_log	75,886.85	0.80
2011	Drift_STL_log	100,543.09	1.05
2012	Drift_STL_log	92,977.35	0.99
2013	Drift_STL_log	91,126.48	0.97
2014	Drift_STL_log	97,451.83	0.96
2015	Drift_STL_log	94,132.36	0.94
2016	Drift_STL_log	99,834.97	0.95
2017	Drift_STL_log	108,172.28	1.00
2018	Drift_STL_log	106,374.49	0.99
2019	Drift_STL_log	106,580.12	1.01
2020	Drift_STL_log	178,792.09	0.57
2021	Drift_STL_log	190,242.50	0.58
2022	Drift_STL_log	263,040.94	0.74
2010	ETS_auto	139,863.23	1.48
2011	ETS_auto	129,031.47	1.35
2012	ETS_auto	120,898.12	1.29
2013	ETS_auto	114,236.00	1.22
2014	ETS_auto	115,041.17	1.13
2015	ETS_auto	109,239.60	1.09
2016	ETS_auto	109,039.78	1.03
2017	ETS_auto	114,136.17	1.05
2018	ETS_auto	111,865.74	1.04
2019	ETS_auto	116,099.46	1.10
2020	ETS_auto	214,525.50	0.69
2021	ETS_auto	221,665.01	0.67
2022	ETS_auto	220,659.74	0.62
2010	ETS_auto_log	139,056.22	1.47
2011	ETS_auto_log	130,371.41	1.36
2012	ETS_auto_log	120,329.22	1.28
2013	ETS_auto_log	111,960.83	1.19
2014	ETS_auto_log	113,687.65	1.12
2015	ETS_auto_log	107,307.28	1.07
2016	ETS_auto_log	111,003.61	1.05
2017	ETS_auto_log	119,359.01	1.10
2018	ETS_auto_log	122,880.07	1.15
2019	ETS_auto_log	122,511.93	1.16
2020	ETS_auto_log	224,203.23	0.72
2021	ETS_auto_log	229,701.17	0.70
2022	ETS_auto_log	251,552.70	0.71
2010	HWA	104,305.04	1.10
2011	HWA	117,014.49	1.22
2012	HWA	115,845.50	1.23
2013	HWA	117,876.11	1.25
2014	HWA	123,540.49	1.21
2015	HWA	118,846.41	1.18
2016	HWA	113,692.60	1.08
2017	HWA	121,518.14	1.12
2018	HWA	122,999.58	1.15
2019	HWA	122,389.91	1.16
2020	HWA	178,895.18	0.57
2021	HWA	191,048.96	0.58
2022	HWA	191,442.17	0.54
2010	HWA_log	128,225.95	1.36
2011	HWA_log	116,992.99	1.22
2012	HWA_log	110,545.09	1.18
2013	HWA_log	104,650.89	1.11
2014	HWA_log	104,513.72	1.03
2015	HWA_log	99,977.69	0.99
2016	HWA_log	106,004.43	1.01
2017	HWA_log	118,148.28	1.09
2018	HWA_log	116,605.23	1.09
2019	HWA_log	115,502.73	1.09
2020	HWA_log	217,606.67	0.70
2021	HWA_log	219,214.11	0.67
2022	HWA_log	252,256.06	0.71
2010	Naive	425,572.00	4.50
2011	Naive	443,060.84	4.63
2012	Naive	447,928.19	4.77
2013	Naive	456,249.31	4.85
2014	Naive	474,952.55	4.67
2015	Naive	485,530.92	4.82
2016	Naive	494,166.22	4.69
2017	Naive	504,209.78	4.64
2018	Naive	511,349.21	4.77
2019	Naive	517,678.97	4.89
2020	Naive	518,752.28	1.67
2021	Naive	524,088.42	1.60
2022	Naive	519,314.08	1.47
2010	Naive_log	443,205.75	4.69
2011	Naive_log	462,046.98	4.83
2012	Naive_log	467,723.95	4.98
2013	Naive_log	477,131.98	5.08
2014	Naive_log	497,536.96	4.89
2015	Naive_log	509,685.52	5.06
2016	Naive_log	520,021.10	4.94
2017	Naive_log	531,961.98	4.89
2018	Naive_log	540,710.12	5.05
2019	Naive_log	548,521.02	5.18
2020	Naive_log	551,479.92	1.77
2021	Naive_log	560,772.43	1.71
2022	Naive_log	552,221.84	1.56
2010	Prophet	112,393.41	1.19
2011	Prophet	132,419.09	1.38
2012	Prophet	142,671.16	1.52
2013	Prophet	150,103.30	1.60
2014	Prophet	172,189.51	1.69
2015	Prophet	183,725.41	1.83
2016	Prophet	193,904.16	1.84
2017	Prophet	201,756.84	1.86
2018	Prophet	200,906.70	1.87
2019	Prophet	198,915.77	1.88
2020	Prophet	377,544.61	1.21
2021	Prophet	387,391.74	1.18
2022	Prophet	406,924.99	1.15
2010	Prophet_log	209,703.05	2.22
2011	Prophet_log	197,337.19	2.06
2012	Prophet_log	192,498.31	2.05
2013	Prophet_log	187,418.51	1.99
2014	Prophet_log	190,504.86	1.87
2015	Prophet_log	184,688.89	1.83
2016	Prophet_log	177,225.18	1.68
2017	Prophet_log	178,224.96	1.64
2018	Prophet_log	178,614.47	1.67
2019	Prophet_log	178,871.59	1.69
2020	Prophet_log	309,287.42	0.99
2021	Prophet_log	386,453.00	1.18
2022	Prophet_log	418,992.28	1.18
2010	SNaive	92,048.59	0.97
2011	SNaive	99,177.61	1.04
2012	SNaive	91,436.27	0.97
2013	SNaive	92,129.31	0.98
2014	SNaive	113,161.42	1.11
2015	SNaive	108,815.62	1.08
2016	SNaive	117,533.45	1.12
2017	SNaive	122,419.19	1.13
2018	SNaive	118,239.07	1.10
2019	SNaive	114,889.37	1.09
2020	SNaive	411,007.46	1.32
2021	SNaive	426,762.60	1.30
2022	SNaive	464,522.72	1.31
2010	SNaive_log	89,385.60	0.95
2011	SNaive_log	96,099.59	1.00
2012	SNaive_log	88,521.80	0.94
2013	SNaive_log	88,824.66	0.94
2014	SNaive_log	109,474.33	1.08
2015	SNaive_log	105,032.27	1.04
2016	SNaive_log	113,257.53	1.07
2017	SNaive_log	117,884.37	1.08
2018	SNaive_log	113,991.72	1.06
2019	SNaive_log	110,733.92	1.05
2020	SNaive_log	491,332.88	1.58
2021	SNaive_log	492,241.23	1.50
2022	SNaive_log	512,938.30	1.45
2010	TSLM	109,231.56	1.16
2011	TSLM	122,766.38	1.28
2012	TSLM	130,866.24	1.39
2013	TSLM	145,563.90	1.55
2014	TSLM	180,427.76	1.77
2015	TSLM	196,149.41	1.95
2016	TSLM	211,159.20	2.00
2017	TSLM	220,046.10	2.02
2018	TSLM	216,326.47	2.02
2019	TSLM	212,112.29	2.00
2020	TSLM	422,884.88	1.36
2021	TSLM	444,989.08	1.35
2022	TSLM	444,227.30	1.25
2010	TSLM_log	127,534.02	1.35
2011	TSLM_log	150,558.99	1.57
2012	TSLM_log	166,213.28	1.77
2013	TSLM_log	185,042.13	1.97
2014	TSLM_log	222,809.66	2.19
2015	TSLM_log	238,247.52	2.37
2016	TSLM_log	248,894.17	2.36
2017	TSLM_log	247,372.74	2.28
2018	TSLM_log	236,656.38	2.21
2019	TSLM_log	233,576.19	2.21
2020	TSLM_log	464,299.11	1.49
2021	TSLM_log	463,598.37	1.41
2022	TSLM_log	472,326.26	1.33

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

Each Model once

# Plot development of RMSE for period 2010-2022
accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	517,678.97	518,752.3	1,073.31	0.0021
HWA	122,389.91	178,895.2	56,505.27	0.4617
Drift_STL	113,320.35	184,772.4	71,452.06	0.6305
ETS_auto	116,099.46	214,525.5	98,426.05	0.8478
Prophet	198,915.77	377,544.6	178,628.85	0.8980
TSLM	212,112.29	422,884.9	210,772.59	0.9937
ARIMA_d1D1	93,811.73	200,183.0	106,371.30	1.1339
ARIMA_d0D1	93,792.07	207,749.6	113,957.54	1.2150
ARIMA_auto	91,912.66	205,825.9	113,913.20	1.2394
SNaive	114,889.37	411,007.5	296,118.09	2.5774

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

2.2.2.6 RMSE per Year

All Models

# Calculate RMSE per year and save as tsibble
rmse_pyear_algarve_slide <- error_fc_algarve_slide %>%
  mutate(Year = year(Month)) %>%
  index_by(Year) %>%
  group_by(Model) %>%
  summarise(RMSE = (mean(Forecast_Error**2))**0.5)

# Create Plot for 2010-2022
rmse_pyear_algarve_slide %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Create Plot for 2020-2022
rmse_pyear_algarve_slide %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_algarve_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	529,365.7	-42,134.88	-0.0737
Naive_log	580,239.6	-34,126.88	-0.0555
HWA	449,717.1	332,957.31	2.8516
ETS_auto	609,460.6	460,580.38	3.0936
Drift_STL_log	487,892.9	379,479.64	3.5003
Prophet_log	855,742.6	674,573.36	3.7234
Drift_STL	497,126.0	403,506.50	4.3101
ETS_auto_log	634,701.7	515,554.25	4.3270
HWA_log	622,471.3	517,410.44	4.9249
Prophet	1,082,711.6	902,702.49	5.0148
TSLM_log	1,351,196.5	1,147,426.57	5.6310
ARIMA_d1D1	593,969.1	508,437.40	5.9444
TSLM	1,231,759.6	1,062,224.98	6.2655
ARIMA_d1D1_log	623,084.7	539,927.97	6.4929
ARIMA_auto	617,679.3	537,067.95	6.6624
ARIMA_d0D1	621,923.9	541,312.56	6.7151
ARIMA_auto_log	895,637.2	797,206.92	8.0992
ARIMA_d0D1_log	896,342.0	797,929.40	8.1080
SNaive	1,313,850.4	1,235,292.24	15.7246
SNaive_log	1,591,498.6	1,516,179.45	20.1301

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_algarve_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_auto_log	275,057.5	-620,579.74	-0.6929
SNaive_log	502,124.7	-1,089,374.00	-0.6845
ARIMA_d0D1_log	299,415.0	-596,926.91	-0.6660
TSLM_log	455,819.0	-895,377.46	-0.6627
HWA_log	236,175.0	-386,296.31	-0.6206
SNaive	572,116.5	-741,733.82	-0.5645
Prophet	482,627.3	-600,084.33	-0.5542
ETS_auto_log	283,220.0	-351,481.72	-0.5538
ETS_auto	288,775.7	-320,684.93	-0.5262
ARIMA_auto	310,334.6	-307,344.76	-0.4976
ARIMA_d0D1	313,444.3	-308,479.61	-0.4960
ARIMA_d1D1	307,065.4	-286,903.68	-0.4830
TSLM	639,558.9	-592,200.69	-0.4808
Drift_STL	263,167.7	-233,958.30	-0.4706
Drift_STL_log	287,530.5	-200,362.46	-0.4107
ARIMA_d1D1_log	403,497.6	-219,587.07	-0.3524
HWA	293,186.1	-156,530.92	-0.3481
Prophet_log	860,177.5	4,434.92	0.0052
Naive	579,552.2	50,186.51	0.0948
Naive_log	654,337.4	74,097.82	0.1277

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_algarve_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive_log	276,671.1	-377,666.36	-0.5772
TSLM	425,535.6	-214,023.24	-0.3346
Naive	387,466.0	-192,086.23	-0.3314
ETS_auto	194,984.6	-93,791.07	-0.3248
HWA	200,648.1	-92,537.99	-0.3156
ARIMA_d0D1	238,272.6	-75,171.70	-0.2398
ARIMA_auto	238,272.6	-72,061.94	-0.2322
Drift_STL	206,876.0	-56,291.68	-0.2139
ARIMA_d1D1	306,529.3	-536.12	-0.0017
Prophet_log	896,973.2	36,795.76	0.0428
TSLM_log	647,410.0	191,591.00	0.4203
Prophet	733,458.9	250,831.62	0.5197
SNaive_log	873,159.9	371,035.29	0.7389
SNaive	1,011,683.0	439,566.46	0.7683
ETS_auto_log	561,841.5	278,621.54	0.9838
ARIMA_d1D1_log	906,118.5	502,620.88	1.2457
ARIMA_d0D1_log	715,949.4	416,534.39	1.3912
ARIMA_auto_log	715,949.4	440,891.93	1.6029
HWA_log	661,447.0	425,271.98	1.8007
Drift_STL_log	927,981.9	640,451.45	2.2274

Each Model once

# Create Plot for 2010-2022
rmse_pyear_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022")

# Create Plot for 2020-2022
rmse_pyear_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022")

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	529,365.7	-42,134.88	-0.0737
HWA	449,717.1	332,957.31	2.8516
ETS_auto	609,460.6	460,580.38	3.0936
Drift_STL	497,126.0	403,506.50	4.3101
Prophet	1,082,711.6	902,702.49	5.0148
ARIMA_d1D1	593,969.1	508,437.40	5.9444
TSLM	1,231,759.6	1,062,224.98	6.2655
ARIMA_auto	617,679.3	537,067.95	6.6624
ARIMA_d0D1	621,923.9	541,312.56	6.7151
SNaive	1,313,850.4	1,235,292.24	15.7246

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
SNaive	572,116.5	-741,733.82	-0.5645
Prophet	482,627.3	-600,084.33	-0.5542
ETS_auto	288,775.7	-320,684.93	-0.5262
ARIMA_auto	310,334.6	-307,344.76	-0.4976
ARIMA_d0D1	313,444.3	-308,479.61	-0.4960
ARIMA_d1D1	307,065.4	-286,903.68	-0.4830
TSLM	639,558.9	-592,200.69	-0.4808
Drift_STL	263,167.7	-233,958.30	-0.4706
HWA	293,186.1	-156,530.92	-0.3481
Naive	579,552.2	50,186.51	0.0948

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
TSLM	425,535.6	-214,023.24	-0.3346
Naive	387,466.0	-192,086.23	-0.3314
ETS_auto	194,984.6	-93,791.07	-0.3248
HWA	200,648.1	-92,537.99	-0.3156
ARIMA_d0D1	238,272.6	-75,171.70	-0.2398
ARIMA_auto	238,272.6	-72,061.94	-0.2322
Drift_STL	206,876.0	-56,291.68	-0.2139
ARIMA_d1D1	306,529.3	-536.12	-0.0017
Prophet	733,458.9	250,831.62	0.5197
SNaive	1,011,683.0	439,566.46	0.7683

2.2.2.7 Change of RMSSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_slide, tourism_algarve_until2019) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_slide, tourism_algarve_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
HWA	13	1.1561	1	0.5405
Drift_STL	9	1.0705	2	0.5453
ARIMA_d1D1	3	0.8862	3	0.6093
ARIMA_auto	1	0.8682	4	0.6138
ARIMA_d0D1	2	0.8860	5	0.6193
ETS_auto	12	1.0967	6	0.6230
ETS_auto_log	14	1.1573	7	0.7102
HWA_log	11	1.0911	8	0.7122
Drift_STL_log	7	1.0068	9	0.7427
ARIMA_d1D1_log	6	0.9839	10	0.8261
ARIMA_auto_log	5	0.9778	11	0.8897
ARIMA_d0D1_log	4	0.9138	12	0.8903
Prophet	16	1.8790	13	1.1489
Prophet_log	15	1.6897	14	1.1830
TSLM	17	2.0037	15	1.2542
SNaive	10	1.0853	16	1.3115
TSLM_log	18	2.2064	17	1.3336
SNaive_log	8	1.0460	18	1.4482
Naive	19	4.8901	19	1.4662
Naive_log	20	5.1815	20	1.5591

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_algarve_slide, tourism_algarve_until2019) %>%
  filter(.model %in% best_models_fc_algarve_slide) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_algarve_slide, tourism_algarve_until2022) %>%
  filter(.model %in% best_models_fc_algarve_slide) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
HWA	7	1.1561	1	0.5405
Drift_STL	4	1.0705	2	0.5453
ARIMA_d1D1	3	0.8862	3	0.6093
ARIMA_auto	1	0.8682	4	0.6138
ARIMA_d0D1	2	0.8860	5	0.6193
ETS_auto	6	1.0967	6	0.6230
Prophet	8	1.8790	7	1.1489
TSLM	9	2.0037	8	1.2542
SNaive	5	1.0853	9	1.3115
Naive	10	4.8901	10	1.4662

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.2.2.8 RMSSE Development by including more Years in Time Series

All Models

# Plot development of RMSSE for period 2010-2022
accuracy_algarve_slide %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_algarve_slide %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_algarve_slide %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

Each Model once

# Plot development of RMSSE for period 2010-2022
accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_algarve_slide %>%
  filter(Model %in% best_models_fc_algarve_slide) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSSE")

2.3 Alentejo

2.3.1 Recursive Window Cross-Validation

2.3.1.1 Time series Cross-Validation & Seasonal Strength Test

# Cross-Validation to create Training sets
data_stretch_alentejo <- tourism_alentejo_until2022 %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Testing for Seasonal Strength
data_stretch_alentejo %>%
  features(Overnight_Stays, unitroot_nsdiffs) %>%
  group_by(Region) %>%
  summarise(Mean_nsdiffs = (mean(nsdiffs))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Strength Test</span>", align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Strength Test

Region	Mean_nsdiffs
Alentejo	1

2.3.1.2 Fitting Models and one-step ahead Forecasts

# Fit models
fit_alentejo_stretch <- data_stretch_alentejo %>%
  model(
    SNaive = SNAIVE(Overnight_Stays),
    Drift_STL = decomposition_model(STL(Overnight_Stays),RW(season_adjust ~ drift())),
    Naive = NAIVE(Overnight_Stays),
    TSLM = TSLM(Overnight_Stays ~ trend() + season()),
    ETS_auto = ETS(Overnight_Stays),
    HWA = ETS(Overnight_Stays ~ error("A") + trend("A") + season("A")),
    ARIMA_auto = ARIMA(Overnight_Stays),
        ARIMA_d1D1 = ARIMA(Overnight_Stays ~ pdq(d=1) + PDQ(D=1)),
        ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)),
        Prophet = fable.prophet::prophet(Overnight_Stays ~ season(period = 12)),
        SNaive_log = SNAIVE(log(Overnight_Stays)),
    Drift_STL_log = decomposition_model(STL(log(Overnight_Stays)),RW(season_adjust ~ drift())),
    Naive_log = NAIVE(log(Overnight_Stays)),
    TSLM_log = TSLM(log(Overnight_Stays) ~ trend() + season()),
    ETS_auto_log = ETS(log(Overnight_Stays)),
        HWA_log = ETS(log(Overnight_Stays) ~ error("A") + trend("A") + season("A")),
    ARIMA_auto_log = ARIMA(log(Overnight_Stays)),
    ARIMA_d1D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)),
    Prophet_log = fable.prophet::prophet(log(Overnight_Stays) ~ season(period = 12))
    )

# Perform a one-step ahead Forecast
fc_alentejo_stretch <- fit_alentejo_stretch %>% forecast(h=1)

2.3.1.3 Forecast Errors

# Calculate forecast error per observation and model
error_fc_alentejo_stretch <- merge(tourism_alentejo_until2022, fc_alentejo_stretch, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# Show table
error_fc_alentejo_stretch %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Forecast Error per Observation and Model</span>", digits = 2, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Forecast Error per Observation and Model

Month	Overnight_Stays	Model	Point_Forecast	Forecast_Error
2010 Jan	53,653	ARIMA_auto	54,763.29	-1,110.29
2010 Feb	62,257	ARIMA_auto	65,393.22	-3,136.22
2010 Mar	77,588	ARIMA_auto	80,500.84	-2,912.84
2010 Apr	99,982	ARIMA_auto	96,719.35	3,262.65
2010 May	101,387	ARIMA_auto	98,995.10	2,391.90
2010 Jun	108,611	ARIMA_auto	101,385.35	7,225.65
2010 Jul	126,498	ARIMA_auto	116,414.65	10,083.35
2010 Aug	178,380	ARIMA_auto	168,455.15	9,924.85
2010 Sep	127,822	ARIMA_auto	118,766.68	9,055.32
2010 Oct	104,174	ARIMA_auto	100,799.98	3,374.02
2010 Nov	69,271	ARIMA_auto	75,692.82	-6,421.82
2010 Dec	62,935	ARIMA_auto	69,138.12	-6,203.12
2011 Jan	60,457	ARIMA_auto	55,680.01	4,776.99
2011 Feb	67,260	ARIMA_auto	68,122.90	-862.90
2011 Mar	83,464	ARIMA_auto	83,127.27	336.73
2011 Apr	102,958	ARIMA_auto	101,480.32	1,477.68
2011 May	101,223	ARIMA_auto	103,797.34	-2,574.34
2011 Jun	120,148	ARIMA_auto	106,314.61	13,833.39
2011 Jul	136,999	ARIMA_auto	123,776.95	13,222.05
2011 Aug	212,668	ARIMA_auto	179,875.86	32,792.14
2011 Sep	129,606	ARIMA_auto	130,796.31	-1,190.31
2011 Oct	101,185	ARIMA_auto	106,951.74	-5,766.74
2011 Nov	62,121	ARIMA_auto	78,776.90	-16,655.90
2011 Dec	65,563	ARIMA_auto	64,072.91	1,490.09
2012 Jan	49,716	ARIMA_auto	59,655.46	-9,939.46
2012 Feb	58,638	ARIMA_auto	61,145.68	-2,507.68
2012 Mar	72,210	ARIMA_auto	77,507.57	-5,297.57
2012 Apr	87,406	ARIMA_auto	100,128.83	-12,722.83
2012 May	96,946	ARIMA_auto	99,947.40	-3,001.40
2012 Jun	115,885	ARIMA_auto	111,871.82	4,013.18
2012 Jul	139,695	ARIMA_auto	131,919.38	7,775.62
2012 Aug	194,368	ARIMA_auto	198,395.01	-4,027.01
2012 Sep	127,610	ARIMA_auto	129,695.86	-2,085.86
2012 Oct	89,649	ARIMA_auto	102,863.00	-13,214.00
2012 Nov	58,900	ARIMA_auto	67,698.04	-8,798.04
2012 Dec	51,122	ARIMA_auto	63,415.05	-12,293.05
2013 Jan	50,313	ARIMA_auto	52,499.67	-2,186.67
2013 Feb	58,615	ARIMA_auto	62,995.09	-4,380.09
2013 Mar	92,426	ARIMA_auto	79,217.63	13,208.37
2013 Apr	100,996	ARIMA_auto	101,325.23	-329.23
2013 May	123,431	ARIMA_auto	107,050.99	16,380.01
2013 Jun	143,946	ARIMA_auto	122,708.43	21,237.57
2013 Jul	171,016	ARIMA_auto	149,118.97	21,897.03
2013 Aug	252,423	ARIMA_auto	220,249.36	32,173.64
2013 Sep	158,839	ARIMA_auto	152,227.69	6,611.31
2013 Oct	109,956	ARIMA_auto	117,429.15	-7,473.15
2013 Nov	82,040	ARIMA_auto	69,793.84	12,246.16
2013 Dec	72,692	ARIMA_auto	61,494.73	11,197.27
2014 Jan	56,872	ARIMA_auto	50,996.91	5,875.09
2014 Feb	64,346	ARIMA_auto	57,190.65	7,155.35
2014 Mar	102,852	ARIMA_auto	80,400.91	22,451.09
2014 Apr	151,151	ARIMA_auto	103,766.05	47,384.95
2014 May	148,593	ARIMA_auto	139,838.64	8,754.36
2014 Jun	154,231	ARIMA_auto	162,288.44	-8,057.44
2014 Jul	194,227	ARIMA_auto	176,896.82	17,330.18
2014 Aug	303,902	ARIMA_auto	254,175.59	49,726.41
2014 Sep	186,247	ARIMA_auto	194,681.11	-8,434.11
2014 Oct	133,884	ARIMA_auto	144,038.68	-10,154.68
2014 Nov	86,161	ARIMA_auto	111,367.16	-25,206.16
2014 Dec	81,830	ARIMA_auto	93,032.04	-11,202.04
2015 Jan	68,436	ARIMA_auto	77,770.26	-9,334.26
2015 Feb	84,417	ARIMA_auto	81,833.76	2,583.24
2015 Mar	116,291	ARIMA_auto	122,004.11	-5,713.11
2015 Apr	145,183	ARIMA_auto	152,841.31	-7,658.31
2015 May	172,016	ARIMA_auto	158,328.37	13,687.63
2015 Jun	182,765	ARIMA_auto	175,456.57	7,308.43
2015 Jul	238,708	ARIMA_auto	214,968.41	23,739.59
2015 Aug	358,044	ARIMA_auto	325,274.25	32,769.75
2015 Sep	216,474	ARIMA_auto	228,704.63	-12,230.63
2015 Oct	148,376	ARIMA_auto	168,079.86	-19,703.86
2015 Nov	99,794	ARIMA_auto	118,434.59	-18,640.59
2015 Dec	93,804	ARIMA_auto	101,888.21	-8,084.21
2016 Jan	74,572	ARIMA_auto	86,556.00	-11,984.00
2016 Feb	97,522	ARIMA_auto	96,774.87	747.13
2016 Mar	144,216	ARIMA_auto	136,083.88	8,132.12
2016 Apr	153,386	ARIMA_auto	182,329.03	-28,943.03
2016 May	168,235	ARIMA_auto	183,723.39	-15,488.39
2016 Jun	215,800	ARIMA_auto	184,821.50	30,978.50
2016 Jul	271,212	ARIMA_auto	257,805.18	13,406.82
2016 Aug	380,776	ARIMA_auto	383,487.12	-2,711.12
2016 Sep	249,098	ARIMA_auto	237,821.78	11,276.22
2016 Oct	175,862	ARIMA_auto	177,274.05	-1,412.05
2016 Nov	102,775	ARIMA_auto	125,550.25	-22,775.25
2016 Dec	100,859	ARIMA_auto	108,104.11	-7,245.11
2017 Jan	83,249	ARIMA_auto	89,773.97	-6,524.97
2017 Feb	105,210	ARIMA_auto	112,243.18	-7,033.18
2017 Mar	121,167	ARIMA_auto	153,088.14	-31,921.14
2017 Apr	217,906	ARIMA_auto	154,671.03	63,234.97
2017 May	196,622	ARIMA_auto	204,992.11	-8,370.11
2017 Jun	248,582	ARIMA_auto	233,162.56	15,419.44
2017 Jul	323,496	ARIMA_auto	303,088.81	20,407.19
2017 Aug	431,571	ARIMA_auto	438,799.49	-7,228.49
2017 Sep	287,242	ARIMA_auto	282,660.57	4,581.43
2017 Oct	212,357	ARIMA_auto	202,862.37	9,494.63
2017 Nov	127,745	ARIMA_auto	136,135.88	-8,390.88
2017 Dec	132,238	ARIMA_auto	130,150.54	2,087.46
2018 Jan	95,453	ARIMA_auto	109,150.74	-13,697.74
2018 Feb	120,303	ARIMA_auto	131,436.11	-11,133.11
2018 Mar	162,886	ARIMA_auto	158,840.71	4,045.29
2018 Apr	187,186	ARIMA_auto	231,674.48	-44,488.48
2018 May	239,851	ARIMA_auto	201,604.21	38,246.79
2018 Jun	264,588	ARIMA_auto	274,527.58	-9,939.58
2018 Jul	339,564	ARIMA_auto	341,002.20	-1,438.20
2018 Aug	446,375	ARIMA_auto	451,645.94	-5,270.94
2018 Sep	304,516	ARIMA_auto	303,501.36	1,014.64
2018 Oct	230,827	ARIMA_auto	227,839.98	2,987.02
2018 Nov	149,080	ARIMA_auto	144,480.51	4,599.49
2018 Dec	135,316	ARIMA_auto	149,493.01	-14,177.01
2019 Jan	114,710	ARIMA_auto	114,633.85	76.15
2019 Feb	122,635	ARIMA_auto	139,294.66	-16,659.66
2019 Mar	172,412	ARIMA_auto	162,971.75	9,440.25
2019 Apr	241,790	ARIMA_auto	228,210.59	13,579.41
2019 May	259,714	ARIMA_auto	250,936.52	8,777.48
2019 Jun	306,048	ARIMA_auto	299,218.37	6,829.63
2019 Jul	360,566	ARIMA_auto	377,759.90	-17,193.90
2019 Aug	484,403	ARIMA_auto	472,819.90	11,583.10
2019 Sep	327,937	ARIMA_auto	333,770.67	-5,833.67
2019 Oct	238,677	ARIMA_auto	257,861.02	-19,184.02
2019 Nov	171,296	ARIMA_auto	161,587.47	9,708.53
2019 Dec	138,642	ARIMA_auto	160,341.60	-21,699.60
2020 Jan	126,349	ARIMA_auto	125,563.76	785.24
2020 Feb	167,411	ARIMA_auto	141,851.82	25,559.18
2020 Mar	70,530	ARIMA_auto	196,919.09	-126,389.09
2020 Apr	13,892	ARIMA_auto	227,814.12	-213,922.12
2020 May	38,343	ARIMA_auto	40,416.69	-2,073.69
2020 Jun	159,738	ARIMA_auto	98,736.43	61,001.57
2020 Jul	272,786	ARIMA_auto	267,696.72	5,089.28
2020 Aug	407,020	ARIMA_auto	406,597.17	422.83
2020 Sep	258,651	ARIMA_auto	275,809.85	-17,158.85
2020 Oct	167,448	ARIMA_auto	191,917.18	-24,469.18
2020 Nov	73,734	ARIMA_auto	96,778.30	-23,044.30
2020 Dec	73,353	ARIMA_auto	71,329.73	2,023.27
2021 Jan	48,435	ARIMA_auto	63,639.00	-15,204.00
2021 Feb	40,443	ARIMA_auto	80,217.22	-39,774.22
2021 Mar	60,251	ARIMA_auto	60,441.40	-190.40
2021 Apr	85,179	ARIMA_auto	105,130.36	-19,951.36
2021 May	169,690	ARIMA_auto	126,144.86	43,545.14
2021 Jun	254,243	ARIMA_auto	245,070.34	9,172.66
2021 Jul	329,058	ARIMA_auto	334,528.70	-5,470.70
2021 Aug	461,844	ARIMA_auto	452,917.53	8,926.47
2021 Sep	308,273	ARIMA_auto	311,791.10	-3,518.10
2021 Oct	250,949	ARIMA_auto	221,064.53	29,884.47
2021 Nov	156,624	ARIMA_auto	170,644.85	-14,020.85
2021 Dec	115,100	ARIMA_auto	131,119.68	-16,019.68
2022 Jan	96,107	ARIMA_auto	97,181.03	-1,074.03
2022 Feb	141,508	ARIMA_auto	117,333.15	24,174.85
2022 Mar	167,854	ARIMA_auto	103,904.27	63,949.73
2022 Apr	248,959	ARIMA_auto	159,875.97	89,083.03
2022 May	258,413	ARIMA_auto	279,875.95	-21,462.95
2022 Jun	300,520	ARIMA_auto	320,482.87	-19,962.87
2010 Jan	53,653	ARIMA_auto_log	52,479.36	1,173.64
2010 Feb	62,257	ARIMA_auto_log	66,196.39	-3,939.39
2010 Mar	77,588	ARIMA_auto_log	81,017.06	-3,429.06
2010 Apr	99,982	ARIMA_auto_log	99,548.29	433.71
2010 May	101,387	ARIMA_auto_log	101,699.94	-312.94
2010 Jun	108,611	ARIMA_auto_log	102,888.79	5,722.21
2010 Jul	126,498	ARIMA_auto_log	120,468.70	6,029.30
2010 Aug	178,380	ARIMA_auto_log	177,001.32	1,378.68
2010 Sep	127,822	ARIMA_auto_log	123,273.47	4,548.53
2010 Oct	104,174	ARIMA_auto_log	96,986.25	7,187.75
2010 Nov	69,271	ARIMA_auto_log	77,454.89	-8,183.89
2010 Dec	62,935	ARIMA_auto_log	65,473.63	-2,538.63
2011 Jan	60,457	ARIMA_auto_log	54,838.89	5,618.11
2011 Feb	67,260	ARIMA_auto_log	64,545.07	2,714.93
2011 Mar	83,464	ARIMA_auto_log	84,109.26	-645.26
2011 Apr	102,958	ARIMA_auto_log	107,066.53	-4,108.53
2011 May	101,223	ARIMA_auto_log	108,810.21	-7,587.21
2011 Jun	120,148	ARIMA_auto_log	111,524.47	8,623.53
2011 Jul	136,999	ARIMA_auto_log	131,678.96	5,320.04
2011 Aug	212,668	ARIMA_auto_log	185,837.28	26,830.72
2011 Sep	129,606	ARIMA_auto_log	129,236.11	369.89
2011 Oct	101,185	ARIMA_auto_log	102,280.17	-1,095.17
2011 Nov	62,121	ARIMA_auto_log	76,374.07	-14,253.07
2011 Dec	65,563	ARIMA_auto_log	64,882.59	680.41
2012 Jan	49,716	ARIMA_auto_log	58,560.52	-8,844.52
2012 Feb	58,638	ARIMA_auto_log	66,969.51	-8,331.51
2012 Mar	72,210	ARIMA_auto_log	82,464.38	-10,254.38
2012 Apr	87,406	ARIMA_auto_log	104,200.45	-16,794.45
2012 May	96,946	ARIMA_auto_log	102,427.97	-5,481.97
2012 Jun	115,885	ARIMA_auto_log	110,315.14	5,569.86
2012 Jul	139,695	ARIMA_auto_log	133,899.66	5,795.34
2012 Aug	194,368	ARIMA_auto_log	201,366.50	-6,998.50
2012 Sep	127,610	ARIMA_auto_log	132,688.81	-5,078.81
2012 Oct	89,649	ARIMA_auto_log	104,453.60	-14,804.60
2012 Nov	58,900	ARIMA_auto_log	69,842.39	-10,942.39
2012 Dec	51,122	ARIMA_auto_log	63,382.09	-12,260.09
2013 Jan	50,313	ARIMA_auto_log	50,527.50	-214.50
2013 Feb	58,615	ARIMA_auto_log	60,986.15	-2,371.15
2013 Mar	92,426	ARIMA_auto_log	77,114.56	15,311.44
2013 Apr	100,996	ARIMA_auto_log	102,346.70	-1,350.70
2013 May	123,431	ARIMA_auto_log	108,104.63	15,326.37
2013 Jun	143,946	ARIMA_auto_log	135,385.13	8,560.87
2013 Jul	171,016	ARIMA_auto_log	159,385.09	11,630.91
2013 Aug	252,423	ARIMA_auto_log	224,660.03	27,762.97
2013 Sep	158,839	ARIMA_auto_log	149,393.98	9,445.02
2013 Oct	109,956	ARIMA_auto_log	112,843.17	-2,887.17
2013 Nov	82,040	ARIMA_auto_log	72,562.12	9,477.88
2013 Dec	72,692	ARIMA_auto_log	68,233.14	4,458.86
2014 Jan	56,872	ARIMA_auto_log	61,464.23	-4,592.23
2014 Feb	64,346	ARIMA_auto_log	68,396.63	-4,050.63
2014 Mar	102,852	ARIMA_auto_log	88,875.26	13,976.74
2014 Apr	151,151	ARIMA_auto_log	109,626.70	41,524.30
2014 May	148,593	ARIMA_auto_log	137,123.43	11,469.57
2014 Jun	154,231	ARIMA_auto_log	157,556.68	-3,325.68
2014 Jul	194,227	ARIMA_auto_log	174,141.27	20,085.73
2014 Aug	303,902	ARIMA_auto_log	263,475.04	40,426.96
2014 Sep	186,247	ARIMA_auto_log	176,393.76	9,853.24
2014 Oct	133,884	ARIMA_auto_log	128,130.81	5,753.19
2014 Nov	86,161	ARIMA_auto_log	89,376.69	-3,215.69
2014 Dec	81,830	ARIMA_auto_log	78,003.64	3,826.36
2015 Jan	68,436	ARIMA_auto_log	66,096.68	2,339.32
2015 Feb	84,417	ARIMA_auto_log	76,060.49	8,356.51
2015 Mar	116,291	ARIMA_auto_log	114,480.84	1,810.16
2015 Apr	145,183	ARIMA_auto_log	146,571.43	-1,388.43
2015 May	172,016	ARIMA_auto_log	152,363.95	19,652.05
2015 Jun	182,765	ARIMA_auto_log	174,253.99	8,511.01
2015 Jul	238,708	ARIMA_auto_log	212,820.92	25,887.08
2015 Aug	358,044	ARIMA_auto_log	331,813.58	26,230.42
2015 Sep	216,474	ARIMA_auto_log	211,773.93	4,700.07
2015 Oct	148,376	ARIMA_auto_log	153,510.30	-5,134.30
2015 Nov	99,794	ARIMA_auto_log	104,442.05	-4,648.05
2015 Dec	93,804	ARIMA_auto_log	91,248.16	2,555.84
2016 Jan	74,572	ARIMA_auto_log	80,867.02	-6,295.02
2016 Feb	97,522	ARIMA_auto_log	93,145.69	4,376.31
2016 Mar	144,216	ARIMA_auto_log	145,135.51	-919.51
2016 Apr	153,386	ARIMA_auto_log	184,250.89	-30,864.89
2016 May	168,235	ARIMA_auto_log	193,411.49	-25,176.49
2016 Jun	215,800	ARIMA_auto_log	196,272.05	19,527.95
2016 Jul	271,212	ARIMA_auto_log	264,973.31	6,238.69
2016 Aug	380,776	ARIMA_auto_log	404,746.71	-23,970.71
2016 Sep	249,098	ARIMA_auto_log	240,346.01	8,751.99
2016 Oct	175,862	ARIMA_auto_log	171,330.69	4,531.31
2016 Nov	102,775	ARIMA_auto_log	118,809.35	-16,034.35
2016 Dec	100,859	ARIMA_auto_log	103,451.11	-2,592.11
2017 Jan	83,249	ARIMA_auto_log	83,548.77	-299.77
2017 Feb	105,210	ARIMA_auto_log	103,339.08	1,870.92
2017 Mar	121,167	ARIMA_auto_log	154,750.10	-33,583.10
2017 Apr	217,906	ARIMA_auto_log	171,794.93	46,111.07
2017 May	196,622	ARIMA_auto_log	207,279.31	-10,657.31
2017 Jun	248,582	ARIMA_auto_log	228,858.15	19,723.85
2017 Jul	323,496	ARIMA_auto_log	300,593.20	22,902.80
2017 Aug	431,571	ARIMA_auto_log	453,108.63	-21,537.63
2017 Sep	287,242	ARIMA_auto_log	281,500.84	5,741.16
2017 Oct	212,357	ARIMA_auto_log	199,939.94	12,417.06
2017 Nov	127,745	ARIMA_auto_log	125,161.32	2,583.68
2017 Dec	132,238	ARIMA_auto_log	121,738.48	10,499.52
2018 Jan	95,453	ARIMA_auto_log	103,815.49	-8,362.49
2018 Feb	120,303	ARIMA_auto_log	129,170.87	-8,867.87
2018 Mar	162,886	ARIMA_auto_log	161,788.00	1,098.00
2018 Apr	187,186	ARIMA_auto_log	226,639.62	-39,453.62
2018 May	239,851	ARIMA_auto_log	221,202.42	18,648.58
2018 Jun	264,588	ARIMA_auto_log	277,783.20	-13,195.20
2018 Jul	339,564	ARIMA_auto_log	353,418.79	-13,854.79
2018 Aug	446,375	ARIMA_auto_log	485,943.07	-39,568.07
2018 Sep	304,516	ARIMA_auto_log	305,813.88	-1,297.88
2018 Oct	230,827	ARIMA_auto_log	217,808.77	13,018.23
2018 Nov	149,080	ARIMA_auto_log	137,186.18	11,893.82
2018 Dec	135,316	ARIMA_auto_log	139,977.04	-4,661.04
2019 Jan	114,710	ARIMA_auto_log	105,999.58	8,710.42
2019 Feb	122,635	ARIMA_auto_log	138,899.51	-16,264.51
2019 Mar	172,412	ARIMA_auto_log	177,792.53	-5,380.53
2019 Apr	241,790	ARIMA_auto_log	226,320.83	15,469.17
2019 May	259,714	ARIMA_auto_log	253,270.16	6,443.84
2019 Jun	306,048	ARIMA_auto_log	309,120.62	-3,072.62
2019 Jul	360,566	ARIMA_auto_log	394,526.96	-33,960.96
2019 Aug	484,403	ARIMA_auto_log	513,616.63	-29,213.63
2019 Sep	327,937	ARIMA_auto_log	340,603.60	-12,666.60
2019 Oct	238,677	ARIMA_auto_log	250,135.94	-11,458.94
2019 Nov	171,296	ARIMA_auto_log	150,240.87	21,055.13
2019 Dec	138,642	ARIMA_auto_log	151,532.00	-12,890.00
2020 Jan	126,349	ARIMA_auto_log	118,975.91	7,373.09
2020 Feb	167,411	ARIMA_auto_log	141,424.14	25,986.86
2020 Mar	70,530	ARIMA_auto_log	193,445.08	-122,915.08
2020 Apr	13,892	ARIMA_auto_log	206,643.05	-192,751.05
2020 May	38,343	ARIMA_auto_log	11,815.60	26,527.40
2020 Jun	159,738	ARIMA_auto_log	103,537.93	56,200.07
2020 Jul	272,786	ARIMA_auto_log	292,735.43	-19,949.43
2020 Aug	407,020	ARIMA_auto_log	416,998.48	-9,978.48
2020 Sep	258,651	ARIMA_auto_log	290,084.30	-31,433.30
2020 Oct	167,448	ARIMA_auto_log	200,305.68	-32,857.68
2020 Nov	73,734	ARIMA_auto_log	120,792.95	-47,058.95
2020 Dec	73,353	ARIMA_auto_log	77,379.18	-4,026.18
2021 Jan	48,435	ARIMA_auto_log	81,027.30	-32,592.30
2021 Feb	40,443	ARIMA_auto_log	71,341.97	-30,898.97
2021 Mar	60,251	ARIMA_auto_log	56,939.22	3,311.78
2021 Apr	85,179	ARIMA_auto_log	77,656.93	7,522.07
2021 May	169,690	ARIMA_auto_log	137,040.34	32,649.66
2021 Jun	254,243	ARIMA_auto_log	277,374.18	-23,131.18
2021 Jul	329,058	ARIMA_auto_log	322,772.09	6,285.91
2021 Aug	461,844	ARIMA_auto_log	472,094.01	-10,250.01
2021 Sep	308,273	ARIMA_auto_log	301,682.10	6,590.90
2021 Oct	250,949	ARIMA_auto_log	222,683.36	28,265.64
2021 Nov	156,624	ARIMA_auto_log	152,439.49	4,184.51
2021 Dec	115,100	ARIMA_auto_log	138,136.48	-23,036.48
2022 Jan	96,107	ARIMA_auto_log	88,158.47	7,948.53
2022 Feb	141,508	ARIMA_auto_log	114,441.75	27,066.25
2022 Mar	167,854	ARIMA_auto_log	151,629.39	16,224.61
2022 Apr	248,959	ARIMA_auto_log	150,308.62	98,650.38
2022 May	258,413	ARIMA_auto_log	318,574.88	-60,161.88
2022 Jun	300,520	ARIMA_auto_log	292,140.37	8,379.63
2010 Jan	53,653	ARIMA_d0D1	54,763.29	-1,110.29
2010 Feb	62,257	ARIMA_d0D1	65,393.22	-3,136.22
2010 Mar	77,588	ARIMA_d0D1	80,500.84	-2,912.84
2010 Apr	99,982	ARIMA_d0D1	96,719.35	3,262.65
2010 May	101,387	ARIMA_d0D1	98,995.10	2,391.90
2010 Jun	108,611	ARIMA_d0D1	101,385.35	7,225.65
2010 Jul	126,498	ARIMA_d0D1	116,414.65	10,083.35
2010 Aug	178,380	ARIMA_d0D1	168,455.15	9,924.85
2010 Sep	127,822	ARIMA_d0D1	118,766.68	9,055.32
2010 Oct	104,174	ARIMA_d0D1	100,799.98	3,374.02
2010 Nov	69,271	ARIMA_d0D1	75,692.82	-6,421.82
2010 Dec	62,935	ARIMA_d0D1	69,138.12	-6,203.12
2011 Jan	60,457	ARIMA_d0D1	55,680.01	4,776.99
2011 Feb	67,260	ARIMA_d0D1	68,122.90	-862.90
2011 Mar	83,464	ARIMA_d0D1	83,127.27	336.73
2011 Apr	102,958	ARIMA_d0D1	101,480.32	1,477.68
2011 May	101,223	ARIMA_d0D1	103,797.34	-2,574.34
2011 Jun	120,148	ARIMA_d0D1	106,314.61	13,833.39
2011 Jul	136,999	ARIMA_d0D1	123,776.95	13,222.05
2011 Aug	212,668	ARIMA_d0D1	179,875.86	32,792.14
2011 Sep	129,606	ARIMA_d0D1	130,796.31	-1,190.31
2011 Oct	101,185	ARIMA_d0D1	106,951.74	-5,766.74
2011 Nov	62,121	ARIMA_d0D1	78,776.90	-16,655.90
2011 Dec	65,563	ARIMA_d0D1	64,072.91	1,490.09
2012 Jan	49,716	ARIMA_d0D1	59,655.46	-9,939.46
2012 Feb	58,638	ARIMA_d0D1	61,145.68	-2,507.68
2012 Mar	72,210	ARIMA_d0D1	77,507.57	-5,297.57
2012 Apr	87,406	ARIMA_d0D1	100,128.83	-12,722.83
2012 May	96,946	ARIMA_d0D1	99,947.40	-3,001.40
2012 Jun	115,885	ARIMA_d0D1	111,871.82	4,013.18
2012 Jul	139,695	ARIMA_d0D1	131,919.38	7,775.62
2012 Aug	194,368	ARIMA_d0D1	198,395.01	-4,027.01
2012 Sep	127,610	ARIMA_d0D1	129,695.86	-2,085.86
2012 Oct	89,649	ARIMA_d0D1	102,863.00	-13,214.00
2012 Nov	58,900	ARIMA_d0D1	67,698.04	-8,798.04
2012 Dec	51,122	ARIMA_d0D1	63,415.05	-12,293.05
2013 Jan	50,313	ARIMA_d0D1	52,499.67	-2,186.67
2013 Feb	58,615	ARIMA_d0D1	62,995.09	-4,380.09
2013 Mar	92,426	ARIMA_d0D1	79,217.63	13,208.37
2013 Apr	100,996	ARIMA_d0D1	101,325.23	-329.23
2013 May	123,431	ARIMA_d0D1	107,050.99	16,380.01
2013 Jun	143,946	ARIMA_d0D1	122,708.43	21,237.57
2013 Jul	171,016	ARIMA_d0D1	149,118.97	21,897.03
2013 Aug	252,423	ARIMA_d0D1	220,249.36	32,173.64
2013 Sep	158,839	ARIMA_d0D1	152,227.69	6,611.31
2013 Oct	109,956	ARIMA_d0D1	117,429.15	-7,473.15
2013 Nov	82,040	ARIMA_d0D1	69,793.84	12,246.16
2013 Dec	72,692	ARIMA_d0D1	61,494.73	11,197.27
2014 Jan	56,872	ARIMA_d0D1	50,996.91	5,875.09
2014 Feb	64,346	ARIMA_d0D1	57,190.65	7,155.35
2014 Mar	102,852	ARIMA_d0D1	80,400.91	22,451.09
2014 Apr	151,151	ARIMA_d0D1	103,766.05	47,384.95
2014 May	148,593	ARIMA_d0D1	139,838.64	8,754.36
2014 Jun	154,231	ARIMA_d0D1	162,288.44	-8,057.44
2014 Jul	194,227	ARIMA_d0D1	176,896.82	17,330.18
2014 Aug	303,902	ARIMA_d0D1	254,175.59	49,726.41
2014 Sep	186,247	ARIMA_d0D1	192,009.53	-5,762.53
2014 Oct	133,884	ARIMA_d0D1	140,583.99	-6,699.99
2014 Nov	86,161	ARIMA_d0D1	106,875.37	-20,714.37
2014 Dec	81,830	ARIMA_d0D1	84,662.79	-2,832.79
2015 Jan	68,436	ARIMA_d0D1	70,762.75	-2,326.75
2015 Feb	84,417	ARIMA_d0D1	76,154.43	8,262.57
2015 Mar	116,291	ARIMA_d0D1	116,603.59	-312.59
2015 Apr	145,183	ARIMA_d0D1	147,661.48	-2,478.48
2015 May	172,016	ARIMA_d0D1	153,973.87	18,042.13
2015 Jun	182,765	ARIMA_d0D1	172,393.72	10,371.28
2015 Jul	238,708	ARIMA_d0D1	211,690.00	27,018.00
2015 Aug	358,044	ARIMA_d0D1	322,287.63	35,756.37
2015 Sep	216,474	ARIMA_d0D1	225,553.99	-9,079.99
2015 Oct	148,376	ARIMA_d0D1	163,472.69	-15,096.69
2015 Nov	99,794	ARIMA_d0D1	113,914.10	-14,120.10
2015 Dec	93,804	ARIMA_d0D1	97,510.81	-3,706.81
2016 Jan	74,572	ARIMA_d0D1	79,681.70	-5,109.70
2016 Feb	97,522	ARIMA_d0D1	90,189.27	7,332.73
2016 Mar	144,216	ARIMA_d0D1	129,718.86	14,497.14
2016 Apr	153,386	ARIMA_d0D1	177,475.68	-24,089.68
2016 May	168,235	ARIMA_d0D1	180,853.87	-12,618.87
2016 Jun	215,800	ARIMA_d0D1	182,057.01	33,742.99
2016 Jul	271,212	ARIMA_d0D1	250,889.32	20,322.68
2016 Aug	380,776	ARIMA_d0D1	381,994.20	-1,218.20
2016 Sep	249,098	ARIMA_d0D1	237,296.92	11,801.08
2016 Oct	175,862	ARIMA_d0D1	174,669.14	1,192.86
2016 Nov	102,775	ARIMA_d0D1	121,993.91	-19,218.91
2016 Dec	100,859	ARIMA_d0D1	107,125.80	-6,266.80
2017 Jan	83,249	ARIMA_d0D1	84,913.82	-1,664.82
2017 Feb	105,210	ARIMA_d0D1	106,833.63	-1,623.63
2017 Mar	121,167	ARIMA_d0D1	148,756.79	-27,589.79
2017 Apr	217,906	ARIMA_d0D1	150,483.15	67,422.85
2017 May	196,622	ARIMA_d0D1	203,378.28	-6,756.28
2017 Jun	248,582	ARIMA_d0D1	231,939.05	16,642.95
2017 Jul	323,496	ARIMA_d0D1	301,773.29	21,722.71
2017 Aug	431,571	ARIMA_d0D1	423,950.29	7,620.71
2017 Sep	287,242	ARIMA_d0D1	281,610.21	5,631.79
2017 Oct	212,357	ARIMA_d0D1	206,411.87	5,945.13
2017 Nov	127,745	ARIMA_d0D1	133,568.70	-5,823.70
2017 Dec	132,238	ARIMA_d0D1	128,512.79	3,725.21
2018 Jan	95,453	ARIMA_d0D1	106,270.85	-10,817.85
2018 Feb	120,303	ARIMA_d0D1	126,827.81	-6,524.81
2018 Mar	162,886	ARIMA_d0D1	148,882.26	14,003.74
2018 Apr	187,186	ARIMA_d0D1	216,367.56	-29,181.56
2018 May	239,851	ARIMA_d0D1	194,669.31	45,181.69
2018 Jun	264,588	ARIMA_d0D1	269,784.13	-5,196.13
2018 Jul	339,564	ARIMA_d0D1	347,703.00	-8,139.00
2018 Aug	446,375	ARIMA_d0D1	470,388.32	-24,013.32
2018 Sep	304,516	ARIMA_d0D1	303,411.18	1,104.82
2018 Oct	230,827	ARIMA_d0D1	220,440.70	10,386.30
2018 Nov	149,080	ARIMA_d0D1	135,698.12	13,381.88
2018 Dec	135,316	ARIMA_d0D1	142,277.47	-6,961.47
2019 Jan	114,710	ARIMA_d0D1	106,364.36	8,345.64
2019 Feb	122,635	ARIMA_d0D1	137,273.95	-14,638.95
2019 Mar	172,412	ARIMA_d0D1	167,212.45	5,199.55
2019 Apr	241,790	ARIMA_d0D1	223,229.17	18,560.83
2019 May	259,714	ARIMA_d0D1	252,044.53	7,669.47
2019 Jun	306,048	ARIMA_d0D1	298,513.06	7,534.94
2019 Jul	360,566	ARIMA_d0D1	385,264.24	-24,698.24
2019 Aug	484,403	ARIMA_d0D1	471,137.56	13,265.44
2019 Sep	327,937	ARIMA_d0D1	335,187.09	-7,250.09
2019 Oct	238,677	ARIMA_d0D1	252,207.80	-13,530.80
2019 Nov	171,296	ARIMA_d0D1	153,662.99	17,633.01
2019 Dec	138,642	ARIMA_d0D1	157,896.31	-19,254.31
2020 Jan	126,349	ARIMA_d0D1	119,406.97	6,942.03
2020 Feb	167,411	ARIMA_d0D1	138,494.85	28,916.15
2020 Mar	70,530	ARIMA_d0D1	190,740.23	-120,210.23
2020 Apr	13,892	ARIMA_d0D1	226,881.11	-212,989.11
2020 May	38,343	ARIMA_d0D1	80,786.03	-42,443.03
2020 Jun	159,738	ARIMA_d0D1	98,736.43	61,001.57
2020 Jul	272,786	ARIMA_d0D1	267,696.72	5,089.28
2020 Aug	407,020	ARIMA_d0D1	406,597.17	422.83
2020 Sep	258,651	ARIMA_d0D1	275,809.85	-17,158.85
2020 Oct	167,448	ARIMA_d0D1	191,917.18	-24,469.18
2020 Nov	73,734	ARIMA_d0D1	96,778.30	-23,044.30
2020 Dec	73,353	ARIMA_d0D1	71,329.73	2,023.27
2021 Jan	48,435	ARIMA_d0D1	63,639.00	-15,204.00
2021 Feb	40,443	ARIMA_d0D1	80,217.22	-39,774.22
2021 Mar	60,251	ARIMA_d0D1	60,441.40	-190.40
2021 Apr	85,179	ARIMA_d0D1	105,130.36	-19,951.36
2021 May	169,690	ARIMA_d0D1	126,144.86	43,545.14
2021 Jun	254,243	ARIMA_d0D1	245,070.34	9,172.66
2021 Jul	329,058	ARIMA_d0D1	334,528.70	-5,470.70
2021 Aug	461,844	ARIMA_d0D1	452,917.53	8,926.47
2021 Sep	308,273	ARIMA_d0D1	311,791.10	-3,518.10
2021 Oct	250,949	ARIMA_d0D1	221,064.53	29,884.47
2021 Nov	156,624	ARIMA_d0D1	170,644.85	-14,020.85
2021 Dec	115,100	ARIMA_d0D1	131,119.68	-16,019.68
2022 Jan	96,107	ARIMA_d0D1	97,181.03	-1,074.03
2022 Feb	141,508	ARIMA_d0D1	117,333.15	24,174.85
2022 Mar	167,854	ARIMA_d0D1	103,904.27	63,949.73
2022 Apr	248,959	ARIMA_d0D1	159,875.97	89,083.03
2022 May	258,413	ARIMA_d0D1	279,875.95	-21,462.95
2022 Jun	300,520	ARIMA_d0D1	320,482.87	-19,962.87
2010 Jan	53,653	ARIMA_d0D1_log	52,479.36	1,173.64
2010 Feb	62,257	ARIMA_d0D1_log	66,196.39	-3,939.39
2010 Mar	77,588	ARIMA_d0D1_log	81,017.06	-3,429.06
2010 Apr	99,982	ARIMA_d0D1_log	99,548.29	433.71
2010 May	101,387	ARIMA_d0D1_log	101,699.94	-312.94
2010 Jun	108,611	ARIMA_d0D1_log	102,888.79	5,722.21
2010 Jul	126,498	ARIMA_d0D1_log	120,468.70	6,029.30
2010 Aug	178,380	ARIMA_d0D1_log	177,001.32	1,378.68
2010 Sep	127,822	ARIMA_d0D1_log	123,273.47	4,548.53
2010 Oct	104,174	ARIMA_d0D1_log	96,986.25	7,187.75
2010 Nov	69,271	ARIMA_d0D1_log	77,454.89	-8,183.89
2010 Dec	62,935	ARIMA_d0D1_log	65,473.63	-2,538.63
2011 Jan	60,457	ARIMA_d0D1_log	54,838.89	5,618.11
2011 Feb	67,260	ARIMA_d0D1_log	64,545.07	2,714.93
2011 Mar	83,464	ARIMA_d0D1_log	84,109.26	-645.26
2011 Apr	102,958	ARIMA_d0D1_log	107,066.53	-4,108.53
2011 May	101,223	ARIMA_d0D1_log	108,810.21	-7,587.21
2011 Jun	120,148	ARIMA_d0D1_log	111,524.47	8,623.53
2011 Jul	136,999	ARIMA_d0D1_log	131,678.96	5,320.04
2011 Aug	212,668	ARIMA_d0D1_log	185,837.28	26,830.72
2011 Sep	129,606	ARIMA_d0D1_log	129,236.11	369.89
2011 Oct	101,185	ARIMA_d0D1_log	102,280.17	-1,095.17
2011 Nov	62,121	ARIMA_d0D1_log	76,374.07	-14,253.07
2011 Dec	65,563	ARIMA_d0D1_log	64,882.59	680.41
2012 Jan	49,716	ARIMA_d0D1_log	58,560.52	-8,844.52
2012 Feb	58,638	ARIMA_d0D1_log	66,969.51	-8,331.51
2012 Mar	72,210	ARIMA_d0D1_log	82,464.38	-10,254.38
2012 Apr	87,406	ARIMA_d0D1_log	104,200.45	-16,794.45
2012 May	96,946	ARIMA_d0D1_log	102,427.97	-5,481.97
2012 Jun	115,885	ARIMA_d0D1_log	110,315.14	5,569.86
2012 Jul	139,695	ARIMA_d0D1_log	133,899.66	5,795.34
2012 Aug	194,368	ARIMA_d0D1_log	201,366.50	-6,998.50
2012 Sep	127,610	ARIMA_d0D1_log	132,688.81	-5,078.81
2012 Oct	89,649	ARIMA_d0D1_log	104,453.60	-14,804.60
2012 Nov	58,900	ARIMA_d0D1_log	69,842.39	-10,942.39
2012 Dec	51,122	ARIMA_d0D1_log	63,382.09	-12,260.09
2013 Jan	50,313	ARIMA_d0D1_log	50,527.50	-214.50
2013 Feb	58,615	ARIMA_d0D1_log	60,986.15	-2,371.15
2013 Mar	92,426	ARIMA_d0D1_log	77,114.56	15,311.44
2013 Apr	100,996	ARIMA_d0D1_log	102,346.70	-1,350.70
2013 May	123,431	ARIMA_d0D1_log	108,104.63	15,326.37
2013 Jun	143,946	ARIMA_d0D1_log	135,385.13	8,560.87
2013 Jul	171,016	ARIMA_d0D1_log	159,385.09	11,630.91
2013 Aug	252,423	ARIMA_d0D1_log	224,660.03	27,762.97
2013 Sep	158,839	ARIMA_d0D1_log	149,393.98	9,445.02
2013 Oct	109,956	ARIMA_d0D1_log	112,843.17	-2,887.17
2013 Nov	82,040	ARIMA_d0D1_log	72,562.12	9,477.88
2013 Dec	72,692	ARIMA_d0D1_log	68,233.14	4,458.86
2014 Jan	56,872	ARIMA_d0D1_log	61,464.23	-4,592.23
2014 Feb	64,346	ARIMA_d0D1_log	68,396.63	-4,050.63
2014 Mar	102,852	ARIMA_d0D1_log	88,875.26	13,976.74
2014 Apr	151,151	ARIMA_d0D1_log	109,626.70	41,524.30
2014 May	148,593	ARIMA_d0D1_log	137,123.43	11,469.57
2014 Jun	154,231	ARIMA_d0D1_log	157,556.68	-3,325.68
2014 Jul	194,227	ARIMA_d0D1_log	174,141.27	20,085.73
2014 Aug	303,902	ARIMA_d0D1_log	263,475.04	40,426.96
2014 Sep	186,247	ARIMA_d0D1_log	176,393.76	9,853.24
2014 Oct	133,884	ARIMA_d0D1_log	128,130.81	5,753.19
2014 Nov	86,161	ARIMA_d0D1_log	89,376.69	-3,215.69
2014 Dec	81,830	ARIMA_d0D1_log	78,003.64	3,826.36
2015 Jan	68,436	ARIMA_d0D1_log	66,096.68	2,339.32
2015 Feb	84,417	ARIMA_d0D1_log	76,060.49	8,356.51
2015 Mar	116,291	ARIMA_d0D1_log	114,480.84	1,810.16
2015 Apr	145,183	ARIMA_d0D1_log	146,571.43	-1,388.43
2015 May	172,016	ARIMA_d0D1_log	152,363.95	19,652.05
2015 Jun	182,765	ARIMA_d0D1_log	174,253.99	8,511.01
2015 Jul	238,708	ARIMA_d0D1_log	212,820.92	25,887.08
2015 Aug	358,044	ARIMA_d0D1_log	331,813.58	26,230.42
2015 Sep	216,474	ARIMA_d0D1_log	211,773.93	4,700.07
2015 Oct	148,376	ARIMA_d0D1_log	151,882.81	-3,506.81
2015 Nov	99,794	ARIMA_d0D1_log	99,952.76	-158.76
2015 Dec	93,804	ARIMA_d0D1_log	91,383.30	2,420.70
2016 Jan	74,572	ARIMA_d0D1_log	76,679.21	-2,107.21
2016 Feb	97,522	ARIMA_d0D1_log	89,351.29	8,170.71
2016 Mar	144,216	ARIMA_d0D1_log	131,263.92	12,952.08
2016 Apr	153,386	ARIMA_d0D1_log	179,518.36	-26,132.36
2016 May	168,235	ARIMA_d0D1_log	182,354.54	-14,119.54
2016 Jun	215,800	ARIMA_d0D1_log	189,623.83	26,176.17
2016 Jul	271,212	ARIMA_d0D1_log	249,610.66	21,601.34
2016 Aug	380,776	ARIMA_d0D1_log	384,711.92	-3,935.92
2016 Sep	249,098	ARIMA_d0D1_log	234,309.14	14,788.86
2016 Oct	175,862	ARIMA_d0D1_log	167,115.77	8,746.23
2016 Nov	102,775	ARIMA_d0D1_log	113,602.38	-10,827.38
2016 Dec	100,859	ARIMA_d0D1_log	101,498.79	-639.79
2017 Jan	83,249	ARIMA_d0D1_log	82,271.34	977.66
2017 Feb	105,210	ARIMA_d0D1_log	102,528.93	2,681.07
2017 Mar	121,167	ARIMA_d0D1_log	149,931.21	-28,764.21
2017 Apr	217,906	ARIMA_d0D1_log	161,576.83	56,329.17
2017 May	196,622	ARIMA_d0D1_log	198,776.27	-2,154.27
2017 Jun	248,582	ARIMA_d0D1_log	225,878.13	22,703.87
2017 Jul	323,496	ARIMA_d0D1_log	296,946.82	26,549.18
2017 Aug	431,571	ARIMA_d0D1_log	446,682.91	-15,111.91
2017 Sep	287,242	ARIMA_d0D1_log	276,900.88	10,341.12
2017 Oct	212,357	ARIMA_d0D1_log	196,537.91	15,819.09
2017 Nov	127,745	ARIMA_d0D1_log	122,895.84	4,849.16
2017 Dec	132,238	ARIMA_d0D1_log	119,438.16	12,799.84
2018 Jan	95,453	ARIMA_d0D1_log	101,985.43	-6,532.43
2018 Feb	120,303	ARIMA_d0D1_log	126,572.09	-6,269.09
2018 Mar	162,886	ARIMA_d0D1_log	158,264.57	4,621.43
2018 Apr	187,186	ARIMA_d0D1_log	221,264.88	-34,078.88
2018 May	239,851	ARIMA_d0D1_log	215,987.43	23,863.57
2018 Jun	264,588	ARIMA_d0D1_log	273,225.00	-8,637.00
2018 Jul	339,564	ARIMA_d0D1_log	347,594.32	-8,030.32
2018 Aug	446,375	ARIMA_d0D1_log	478,036.95	-31,661.95
2018 Sep	304,516	ARIMA_d0D1_log	301,257.32	3,258.68
2018 Oct	230,827	ARIMA_d0D1_log	215,107.05	15,719.95
2018 Nov	149,080	ARIMA_d0D1_log	135,766.73	13,313.27
2018 Dec	135,316	ARIMA_d0D1_log	138,653.97	-3,337.97
2019 Jan	114,710	ARIMA_d0D1_log	104,607.55	10,102.45
2019 Feb	122,635	ARIMA_d0D1_log	137,137.03	-14,502.03
2019 Mar	172,412	ARIMA_d0D1_log	175,089.84	-2,677.84
2019 Apr	241,790	ARIMA_d0D1_log	223,499.30	18,290.70
2019 May	259,714	ARIMA_d0D1_log	250,105.41	9,608.59
2019 Jun	306,048	ARIMA_d0D1_log	305,317.64	730.36
2019 Jul	360,566	ARIMA_d0D1_log	389,436.93	-28,870.93
2019 Aug	484,403	ARIMA_d0D1_log	506,226.39	-21,823.39
2019 Sep	327,937	ARIMA_d0D1_log	336,272.55	-8,335.55
2019 Oct	238,677	ARIMA_d0D1_log	247,504.44	-8,827.44
2019 Nov	171,296	ARIMA_d0D1_log	148,729.09	22,566.91
2019 Dec	138,642	ARIMA_d0D1_log	150,442.36	-11,800.36
2020 Jan	126,349	ARIMA_d0D1_log	117,984.35	8,364.65
2020 Feb	167,411	ARIMA_d0D1_log	140,241.21	27,169.79
2020 Mar	70,530	ARIMA_d0D1_log	191,880.70	-121,350.70
2020 Apr	13,892	ARIMA_d0D1_log	204,069.48	-190,177.48
2020 May	38,343	ARIMA_d0D1_log	11,815.60	26,527.40
2020 Jun	159,738	ARIMA_d0D1_log	103,537.93	56,200.07
2020 Jul	272,786	ARIMA_d0D1_log	292,735.43	-19,949.43
2020 Aug	407,020	ARIMA_d0D1_log	416,998.48	-9,978.48
2020 Sep	258,651	ARIMA_d0D1_log	290,084.30	-31,433.30
2020 Oct	167,448	ARIMA_d0D1_log	200,305.68	-32,857.68
2020 Nov	73,734	ARIMA_d0D1_log	120,792.95	-47,058.95
2020 Dec	73,353	ARIMA_d0D1_log	77,379.18	-4,026.18
2021 Jan	48,435	ARIMA_d0D1_log	81,027.30	-32,592.30
2021 Feb	40,443	ARIMA_d0D1_log	71,341.97	-30,898.97
2021 Mar	60,251	ARIMA_d0D1_log	56,939.22	3,311.78
2021 Apr	85,179	ARIMA_d0D1_log	77,656.93	7,522.07
2021 May	169,690	ARIMA_d0D1_log	137,040.34	32,649.66
2021 Jun	254,243	ARIMA_d0D1_log	277,374.18	-23,131.18
2021 Jul	329,058	ARIMA_d0D1_log	322,772.09	6,285.91
2021 Aug	461,844	ARIMA_d0D1_log	472,094.01	-10,250.01
2021 Sep	308,273	ARIMA_d0D1_log	301,682.10	6,590.90
2021 Oct	250,949	ARIMA_d0D1_log	222,683.36	28,265.64
2021 Nov	156,624	ARIMA_d0D1_log	152,439.49	4,184.51
2021 Dec	115,100	ARIMA_d0D1_log	138,136.48	-23,036.48
2022 Jan	96,107	ARIMA_d0D1_log	88,158.47	7,948.53
2022 Feb	141,508	ARIMA_d0D1_log	114,441.75	27,066.25
2022 Mar	167,854	ARIMA_d0D1_log	151,629.39	16,224.61
2022 Apr	248,959	ARIMA_d0D1_log	150,308.62	98,650.38
2022 May	258,413	ARIMA_d0D1_log	318,574.88	-60,161.88
2022 Jun	300,520	ARIMA_d0D1_log	292,140.37	8,379.63
2010 Jan	53,653	ARIMA_d1D1	55,515.22	-1,862.22
2010 Feb	62,257	ARIMA_d1D1	66,397.29	-4,140.29
2010 Mar	77,588	ARIMA_d1D1	79,618.71	-2,030.71
2010 Apr	99,982	ARIMA_d1D1	95,889.29	4,092.71
2010 May	101,387	ARIMA_d1D1	98,230.29	3,156.71
2010 Jun	108,611	ARIMA_d1D1	100,054.85	8,556.15
2010 Jul	126,498	ARIMA_d1D1	115,306.75	11,191.25
2010 Aug	178,380	ARIMA_d1D1	168,413.58	9,966.42
2010 Sep	127,822	ARIMA_d1D1	119,144.72	8,677.28
2010 Oct	104,174	ARIMA_d1D1	102,417.84	1,756.16
2010 Nov	69,271	ARIMA_d1D1	83,892.83	-14,621.83
2010 Dec	62,935	ARIMA_d1D1	72,149.01	-9,214.01
2011 Jan	60,457	ARIMA_d1D1	57,288.57	3,168.43
2011 Feb	67,260	ARIMA_d1D1	70,054.30	-2,794.30
2011 Mar	83,464	ARIMA_d1D1	83,249.96	214.04
2011 Apr	102,958	ARIMA_d1D1	102,230.03	727.97
2011 May	101,223	ARIMA_d1D1	104,121.39	-2,898.39
2011 Jun	120,148	ARIMA_d1D1	106,061.04	14,086.96
2011 Jul	136,999	ARIMA_d1D1	125,383.59	11,615.41
2011 Aug	212,668	ARIMA_d1D1	180,819.63	31,848.37
2011 Sep	129,606	ARIMA_d1D1	137,983.81	-8,377.81
2011 Oct	101,185	ARIMA_d1D1	113,521.28	-12,336.28
2011 Nov	62,121	ARIMA_d1D1	75,903.92	-13,782.92
2011 Dec	65,563	ARIMA_d1D1	65,798.61	-235.61
2012 Jan	49,716	ARIMA_d1D1	62,066.61	-12,350.61
2012 Feb	58,638	ARIMA_d1D1	67,490.16	-8,852.16
2012 Mar	72,210	ARIMA_d1D1	79,984.13	-7,774.13
2012 Apr	87,406	ARIMA_d1D1	99,456.90	-12,050.90
2012 May	96,946	ARIMA_d1D1	94,329.50	2,616.50
2012 Jun	115,885	ARIMA_d1D1	107,645.86	8,239.14
2012 Jul	139,695	ARIMA_d1D1	127,606.23	12,088.77
2012 Aug	194,368	ARIMA_d1D1	197,238.07	-2,870.07
2012 Sep	127,610	ARIMA_d1D1	126,608.86	1,001.14
2012 Oct	89,649	ARIMA_d1D1	101,301.54	-11,652.54
2012 Nov	58,900	ARIMA_d1D1	60,800.33	-1,900.33
2012 Dec	51,122	ARIMA_d1D1	58,904.05	-7,782.05
2013 Jan	50,313	ARIMA_d1D1	47,667.85	2,645.15
2013 Feb	58,615	ARIMA_d1D1	56,097.70	2,517.30
2013 Mar	92,426	ARIMA_d1D1	71,595.22	20,830.78
2013 Apr	100,996	ARIMA_d1D1	95,457.40	5,538.60
2013 May	123,431	ARIMA_d1D1	100,870.45	22,560.55
2013 Jun	143,946	ARIMA_d1D1	127,746.43	16,199.57
2013 Jul	171,016	ARIMA_d1D1	155,920.24	15,095.76
2013 Aug	252,423	ARIMA_d1D1	227,164.62	25,258.38
2013 Sep	158,839	ARIMA_d1D1	165,186.41	-6,347.41
2013 Oct	109,956	ARIMA_d1D1	128,005.18	-18,049.18
2013 Nov	82,040	ARIMA_d1D1	83,236.31	-1,196.31
2013 Dec	72,692	ARIMA_d1D1	81,764.07	-9,072.07
2014 Jan	56,872	ARIMA_d1D1	69,788.15	-12,916.15
2014 Feb	64,346	ARIMA_d1D1	72,217.83	-7,871.83
2014 Mar	102,852	ARIMA_d1D1	93,910.46	8,941.54
2014 Apr	151,151	ARIMA_d1D1	108,120.15	43,030.85
2014 May	148,593	ARIMA_d1D1	143,301.28	5,291.72
2014 Jun	154,231	ARIMA_d1D1	167,311.21	-13,080.21
2014 Jul	194,227	ARIMA_d1D1	178,462.36	15,764.64
2014 Aug	303,902	ARIMA_d1D1	261,636.22	42,265.78
2014 Sep	186,247	ARIMA_d1D1	194,681.11	-8,434.11
2014 Oct	133,884	ARIMA_d1D1	144,038.68	-10,154.68
2014 Nov	86,161	ARIMA_d1D1	111,367.16	-25,206.16
2014 Dec	81,830	ARIMA_d1D1	93,032.04	-11,202.04
2015 Jan	68,436	ARIMA_d1D1	77,770.26	-9,334.26
2015 Feb	84,417	ARIMA_d1D1	81,833.76	2,583.24
2015 Mar	116,291	ARIMA_d1D1	122,004.11	-5,713.11
2015 Apr	145,183	ARIMA_d1D1	152,841.31	-7,658.31
2015 May	172,016	ARIMA_d1D1	158,328.37	13,687.63
2015 Jun	182,765	ARIMA_d1D1	175,456.57	7,308.43
2015 Jul	238,708	ARIMA_d1D1	214,968.41	23,739.59
2015 Aug	358,044	ARIMA_d1D1	325,274.25	32,769.75
2015 Sep	216,474	ARIMA_d1D1	228,704.63	-12,230.63
2015 Oct	148,376	ARIMA_d1D1	168,079.86	-19,703.86
2015 Nov	99,794	ARIMA_d1D1	118,434.59	-18,640.59
2015 Dec	93,804	ARIMA_d1D1	101,888.21	-8,084.21
2016 Jan	74,572	ARIMA_d1D1	86,556.00	-11,984.00
2016 Feb	97,522	ARIMA_d1D1	96,774.87	747.13
2016 Mar	144,216	ARIMA_d1D1	136,083.88	8,132.12
2016 Apr	153,386	ARIMA_d1D1	182,329.03	-28,943.03
2016 May	168,235	ARIMA_d1D1	183,723.39	-15,488.39
2016 Jun	215,800	ARIMA_d1D1	184,821.50	30,978.50
2016 Jul	271,212	ARIMA_d1D1	257,805.18	13,406.82
2016 Aug	380,776	ARIMA_d1D1	383,487.12	-2,711.12
2016 Sep	249,098	ARIMA_d1D1	237,821.78	11,276.22
2016 Oct	175,862	ARIMA_d1D1	177,274.05	-1,412.05
2016 Nov	102,775	ARIMA_d1D1	125,550.25	-22,775.25
2016 Dec	100,859	ARIMA_d1D1	108,104.11	-7,245.11
2017 Jan	83,249	ARIMA_d1D1	89,773.97	-6,524.97
2017 Feb	105,210	ARIMA_d1D1	112,243.18	-7,033.18
2017 Mar	121,167	ARIMA_d1D1	153,088.14	-31,921.14
2017 Apr	217,906	ARIMA_d1D1	154,671.03	63,234.97
2017 May	196,622	ARIMA_d1D1	204,992.11	-8,370.11
2017 Jun	248,582	ARIMA_d1D1	233,162.56	15,419.44
2017 Jul	323,496	ARIMA_d1D1	303,088.81	20,407.19
2017 Aug	431,571	ARIMA_d1D1	438,799.49	-7,228.49
2017 Sep	287,242	ARIMA_d1D1	282,660.57	4,581.43
2017 Oct	212,357	ARIMA_d1D1	202,862.37	9,494.63
2017 Nov	127,745	ARIMA_d1D1	136,135.88	-8,390.88
2017 Dec	132,238	ARIMA_d1D1	130,150.54	2,087.46
2018 Jan	95,453	ARIMA_d1D1	109,150.74	-13,697.74
2018 Feb	120,303	ARIMA_d1D1	131,436.11	-11,133.11
2018 Mar	162,886	ARIMA_d1D1	158,840.71	4,045.29
2018 Apr	187,186	ARIMA_d1D1	231,674.48	-44,488.48
2018 May	239,851	ARIMA_d1D1	201,604.21	38,246.79
2018 Jun	264,588	ARIMA_d1D1	274,527.58	-9,939.58
2018 Jul	339,564	ARIMA_d1D1	341,002.20	-1,438.20
2018 Aug	446,375	ARIMA_d1D1	451,645.94	-5,270.94
2018 Sep	304,516	ARIMA_d1D1	303,501.36	1,014.64
2018 Oct	230,827	ARIMA_d1D1	227,839.98	2,987.02
2018 Nov	149,080	ARIMA_d1D1	144,480.51	4,599.49
2018 Dec	135,316	ARIMA_d1D1	149,493.01	-14,177.01
2019 Jan	114,710	ARIMA_d1D1	114,633.85	76.15
2019 Feb	122,635	ARIMA_d1D1	139,294.66	-16,659.66
2019 Mar	172,412	ARIMA_d1D1	162,971.75	9,440.25
2019 Apr	241,790	ARIMA_d1D1	228,210.59	13,579.41
2019 May	259,714	ARIMA_d1D1	250,936.52	8,777.48
2019 Jun	306,048	ARIMA_d1D1	299,218.37	6,829.63
2019 Jul	360,566	ARIMA_d1D1	377,759.90	-17,193.90
2019 Aug	484,403	ARIMA_d1D1	472,819.90	11,583.10
2019 Sep	327,937	ARIMA_d1D1	333,770.67	-5,833.67
2019 Oct	238,677	ARIMA_d1D1	257,861.02	-19,184.02
2019 Nov	171,296	ARIMA_d1D1	161,587.47	9,708.53
2019 Dec	138,642	ARIMA_d1D1	160,341.60	-21,699.60
2020 Jan	126,349	ARIMA_d1D1	125,563.76	785.24
2020 Feb	167,411	ARIMA_d1D1	141,851.82	25,559.18
2020 Mar	70,530	ARIMA_d1D1	196,919.09	-126,389.09
2020 Apr	13,892	ARIMA_d1D1	227,814.12	-213,922.12
2020 May	38,343	ARIMA_d1D1	40,416.69	-2,073.69
2020 Jun	159,738	ARIMA_d1D1	78,829.43	80,908.57
2020 Jul	272,786	ARIMA_d1D1	265,431.49	7,354.51
2020 Aug	407,020	ARIMA_d1D1	383,136.14	23,883.86
2020 Sep	258,651	ARIMA_d1D1	259,413.12	-762.12
2020 Oct	167,448	ARIMA_d1D1	178,713.94	-11,265.94
2020 Nov	73,734	ARIMA_d1D1	84,898.61	-11,164.61
2020 Dec	73,353	ARIMA_d1D1	58,840.02	14,512.98
2021 Jan	48,435	ARIMA_d1D1	55,631.55	-7,196.55
2021 Feb	40,443	ARIMA_d1D1	71,120.00	-30,677.00
2021 Mar	60,251	ARIMA_d1D1	52,639.39	7,611.61
2021 Apr	85,179	ARIMA_d1D1	100,080.44	-14,901.44
2021 May	169,690	ARIMA_d1D1	117,391.81	52,298.19
2021 Jun	254,243	ARIMA_d1D1	231,397.57	22,845.43
2021 Jul	329,058	ARIMA_d1D1	321,588.48	7,469.52
2021 Aug	461,844	ARIMA_d1D1	440,934.00	20,910.00
2021 Sep	308,273	ARIMA_d1D1	303,013.27	5,259.73
2021 Oct	250,949	ARIMA_d1D1	212,718.77	38,230.23
2021 Nov	156,624	ARIMA_d1D1	165,101.29	-8,477.29
2021 Dec	115,100	ARIMA_d1D1	124,323.93	-9,223.93
2022 Jan	96,107	ARIMA_d1D1	91,275.48	4,831.52
2022 Feb	141,508	ARIMA_d1D1	113,082.96	28,425.04
2022 Mar	167,854	ARIMA_d1D1	100,848.69	67,005.31
2022 Apr	248,959	ARIMA_d1D1	158,479.19	90,479.81
2022 May	258,413	ARIMA_d1D1	278,863.38	-20,450.38
2022 Jun	300,520	ARIMA_d1D1	315,842.90	-15,322.90
2010 Jan	53,653	ARIMA_d1D1_log	51,747.40	1,905.60
2010 Feb	62,257	ARIMA_d1D1_log	64,407.48	-2,150.48
2010 Mar	77,588	ARIMA_d1D1_log	77,890.84	-302.84
2010 Apr	99,982	ARIMA_d1D1_log	96,368.38	3,613.62
2010 May	101,387	ARIMA_d1D1_log	99,519.90	1,867.10
2010 Jun	108,611	ARIMA_d1D1_log	101,200.65	7,410.35
2010 Jul	126,498	ARIMA_d1D1_log	117,277.82	9,220.18
2010 Aug	178,380	ARIMA_d1D1_log	176,183.27	2,196.73
2010 Sep	127,822	ARIMA_d1D1_log	118,720.68	9,101.32
2010 Oct	104,174	ARIMA_d1D1_log	98,819.21	5,354.79
2010 Nov	69,271	ARIMA_d1D1_log	78,235.68	-8,964.68
2010 Dec	62,935	ARIMA_d1D1_log	67,587.63	-4,652.63
2011 Jan	60,457	ARIMA_d1D1_log	55,690.87	4,766.13
2011 Feb	67,260	ARIMA_d1D1_log	68,422.96	-1,162.96
2011 Mar	83,464	ARIMA_d1D1_log	83,671.94	-207.94
2011 Apr	102,958	ARIMA_d1D1_log	105,067.98	-2,109.98
2011 May	101,223	ARIMA_d1D1_log	106,944.11	-5,721.11
2011 Jun	120,148	ARIMA_d1D1_log	109,294.37	10,853.63
2011 Jul	136,999	ARIMA_d1D1_log	128,149.40	8,849.60
2011 Aug	212,668	ARIMA_d1D1_log	189,076.00	23,592.00
2011 Sep	129,606	ARIMA_d1D1_log	133,536.30	-3,930.30
2011 Oct	101,185	ARIMA_d1D1_log	108,557.77	-7,372.77
2011 Nov	62,121	ARIMA_d1D1_log	78,771.68	-16,650.68
2011 Dec	65,563	ARIMA_d1D1_log	66,950.69	-1,387.69
2012 Jan	49,716	ARIMA_d1D1_log	59,120.67	-9,404.67
2012 Feb	58,638	ARIMA_d1D1_log	66,359.19	-7,721.19
2012 Mar	72,210	ARIMA_d1D1_log	78,817.35	-6,607.35
2012 Apr	87,406	ARIMA_d1D1_log	95,960.56	-8,554.56
2012 May	96,946	ARIMA_d1D1_log	93,946.28	2,999.72
2012 Jun	115,885	ARIMA_d1D1_log	103,981.60	11,903.40
2012 Jul	139,695	ARIMA_d1D1_log	122,922.38	16,772.62
2012 Aug	194,368	ARIMA_d1D1_log	190,264.73	4,103.27
2012 Sep	127,610	ARIMA_d1D1_log	125,159.18	2,450.82
2012 Oct	89,649	ARIMA_d1D1_log	101,034.29	-11,385.29
2012 Nov	58,900	ARIMA_d1D1_log	66,022.63	-7,122.63
2012 Dec	51,122	ARIMA_d1D1_log	61,697.77	-10,575.77
2013 Jan	50,313	ARIMA_d1D1_log	48,607.68	1,705.32
2013 Feb	58,615	ARIMA_d1D1_log	57,434.39	1,180.61
2013 Mar	92,426	ARIMA_d1D1_log	71,108.59	21,317.41
2013 Apr	100,996	ARIMA_d1D1_log	103,170.54	-2,174.54
2013 May	123,431	ARIMA_d1D1_log	102,903.43	20,527.57
2013 Jun	143,946	ARIMA_d1D1_log	124,629.62	19,316.38
2013 Jul	171,016	ARIMA_d1D1_log	153,657.89	17,358.11
2013 Aug	252,423	ARIMA_d1D1_log	232,749.33	19,673.67
2013 Sep	158,839	ARIMA_d1D1_log	157,476.09	1,362.91
2013 Oct	109,956	ARIMA_d1D1_log	119,030.80	-9,074.80
2013 Nov	82,040	ARIMA_d1D1_log	76,320.51	5,719.49
2013 Dec	72,692	ARIMA_d1D1_log	72,290.60	401.40
2014 Jan	56,872	ARIMA_d1D1_log	65,279.51	-8,407.51
2014 Feb	64,346	ARIMA_d1D1_log	72,590.32	-8,244.32
2014 Mar	102,852	ARIMA_d1D1_log	96,297.72	6,554.28
2014 Apr	151,151	ARIMA_d1D1_log	115,055.79	36,095.21
2014 May	148,593	ARIMA_d1D1_log	143,901.61	4,691.39
2014 Jun	154,231	ARIMA_d1D1_log	169,383.57	-15,152.57
2014 Jul	194,227	ARIMA_d1D1_log	193,420.28	806.72
2014 Aug	303,902	ARIMA_d1D1_log	283,392.78	20,509.22
2014 Sep	186,247	ARIMA_d1D1_log	186,437.90	-190.90
2014 Oct	133,884	ARIMA_d1D1_log	134,524.43	-640.43
2014 Nov	86,161	ARIMA_d1D1_log	94,371.28	-8,210.28
2014 Dec	81,830	ARIMA_d1D1_log	82,643.48	-813.48
2015 Jan	68,436	ARIMA_d1D1_log	69,305.69	-869.69
2015 Feb	84,417	ARIMA_d1D1_log	79,388.55	5,028.45
2015 Mar	116,291	ARIMA_d1D1_log	121,070.03	-4,779.03
2015 Apr	145,183	ARIMA_d1D1_log	155,877.55	-10,694.55
2015 May	172,016	ARIMA_d1D1_log	160,762.42	11,253.58
2015 Jun	182,765	ARIMA_d1D1_log	181,112.06	1,652.94
2015 Jul	238,708	ARIMA_d1D1_log	228,837.18	9,870.82
2015 Aug	358,044	ARIMA_d1D1_log	343,940.29	14,103.71
2015 Sep	216,474	ARIMA_d1D1_log	221,069.82	-4,595.82
2015 Oct	148,376	ARIMA_d1D1_log	153,510.30	-5,134.30
2015 Nov	99,794	ARIMA_d1D1_log	104,442.05	-4,648.05
2015 Dec	93,804	ARIMA_d1D1_log	91,248.16	2,555.84
2016 Jan	74,572	ARIMA_d1D1_log	80,867.02	-6,295.02
2016 Feb	97,522	ARIMA_d1D1_log	93,145.69	4,376.31
2016 Mar	144,216	ARIMA_d1D1_log	145,135.51	-919.51
2016 Apr	153,386	ARIMA_d1D1_log	184,250.89	-30,864.89
2016 May	168,235	ARIMA_d1D1_log	193,411.49	-25,176.49
2016 Jun	215,800	ARIMA_d1D1_log	196,272.05	19,527.95
2016 Jul	271,212	ARIMA_d1D1_log	264,973.31	6,238.69
2016 Aug	380,776	ARIMA_d1D1_log	404,746.71	-23,970.71
2016 Sep	249,098	ARIMA_d1D1_log	240,346.01	8,751.99
2016 Oct	175,862	ARIMA_d1D1_log	171,330.69	4,531.31
2016 Nov	102,775	ARIMA_d1D1_log	118,809.35	-16,034.35
2016 Dec	100,859	ARIMA_d1D1_log	103,451.11	-2,592.11
2017 Jan	83,249	ARIMA_d1D1_log	83,548.77	-299.77
2017 Feb	105,210	ARIMA_d1D1_log	103,339.08	1,870.92
2017 Mar	121,167	ARIMA_d1D1_log	154,750.10	-33,583.10
2017 Apr	217,906	ARIMA_d1D1_log	171,794.93	46,111.07
2017 May	196,622	ARIMA_d1D1_log	207,279.31	-10,657.31
2017 Jun	248,582	ARIMA_d1D1_log	228,858.15	19,723.85
2017 Jul	323,496	ARIMA_d1D1_log	300,593.20	22,902.80
2017 Aug	431,571	ARIMA_d1D1_log	453,108.63	-21,537.63
2017 Sep	287,242	ARIMA_d1D1_log	281,500.84	5,741.16
2017 Oct	212,357	ARIMA_d1D1_log	199,939.94	12,417.06
2017 Nov	127,745	ARIMA_d1D1_log	125,161.32	2,583.68
2017 Dec	132,238	ARIMA_d1D1_log	121,738.48	10,499.52
2018 Jan	95,453	ARIMA_d1D1_log	103,815.49	-8,362.49
2018 Feb	120,303	ARIMA_d1D1_log	129,170.87	-8,867.87
2018 Mar	162,886	ARIMA_d1D1_log	161,788.00	1,098.00
2018 Apr	187,186	ARIMA_d1D1_log	226,639.62	-39,453.62
2018 May	239,851	ARIMA_d1D1_log	221,202.42	18,648.58
2018 Jun	264,588	ARIMA_d1D1_log	277,783.20	-13,195.20
2018 Jul	339,564	ARIMA_d1D1_log	353,418.79	-13,854.79
2018 Aug	446,375	ARIMA_d1D1_log	485,943.07	-39,568.07
2018 Sep	304,516	ARIMA_d1D1_log	305,813.88	-1,297.88
2018 Oct	230,827	ARIMA_d1D1_log	217,808.77	13,018.23
2018 Nov	149,080	ARIMA_d1D1_log	137,186.18	11,893.82
2018 Dec	135,316	ARIMA_d1D1_log	139,977.04	-4,661.04
2019 Jan	114,710	ARIMA_d1D1_log	105,999.58	8,710.42
2019 Feb	122,635	ARIMA_d1D1_log	138,899.51	-16,264.51
2019 Mar	172,412	ARIMA_d1D1_log	177,792.53	-5,380.53
2019 Apr	241,790	ARIMA_d1D1_log	226,320.83	15,469.17
2019 May	259,714	ARIMA_d1D1_log	253,270.16	6,443.84
2019 Jun	306,048	ARIMA_d1D1_log	309,120.62	-3,072.62
2019 Jul	360,566	ARIMA_d1D1_log	394,526.96	-33,960.96
2019 Aug	484,403	ARIMA_d1D1_log	513,616.63	-29,213.63
2019 Sep	327,937	ARIMA_d1D1_log	340,603.60	-12,666.60
2019 Oct	238,677	ARIMA_d1D1_log	250,135.94	-11,458.94
2019 Nov	171,296	ARIMA_d1D1_log	150,240.87	21,055.13
2019 Dec	138,642	ARIMA_d1D1_log	151,532.00	-12,890.00
2020 Jan	126,349	ARIMA_d1D1_log	118,975.91	7,373.09
2020 Feb	167,411	ARIMA_d1D1_log	141,424.14	25,986.86
2020 Mar	70,530	ARIMA_d1D1_log	193,445.08	-122,915.08
2020 Apr	13,892	ARIMA_d1D1_log	206,643.05	-192,751.05
2020 May	38,343	ARIMA_d1D1_log	10,380.61	27,962.39
2020 Jun	159,738	ARIMA_d1D1_log	127,414.31	32,323.69
2020 Jul	272,786	ARIMA_d1D1_log	335,312.14	-62,526.14
2020 Aug	407,020	ARIMA_d1D1_log	291,973.30	115,046.70
2020 Sep	258,651	ARIMA_d1D1_log	223,373.82	35,277.18
2020 Oct	167,448	ARIMA_d1D1_log	165,349.98	2,098.02
2020 Nov	73,734	ARIMA_d1D1_log	115,228.83	-41,494.83
2020 Dec	73,353	ARIMA_d1D1_log	65,908.61	7,444.39
2021 Jan	48,435	ARIMA_d1D1_log	73,626.08	-25,191.08
2021 Feb	40,443	ARIMA_d1D1_log	64,431.60	-23,988.60
2021 Mar	60,251	ARIMA_d1D1_log	53,888.23	6,362.77
2021 Apr	85,179	ARIMA_d1D1_log	86,400.45	-1,221.45
2021 May	169,690	ARIMA_d1D1_log	114,121.65	55,568.35
2021 Jun	254,243	ARIMA_d1D1_log	229,343.80	24,899.20
2021 Jul	329,058	ARIMA_d1D1_log	280,334.48	48,723.52
2021 Aug	461,844	ARIMA_d1D1_log	391,848.75	69,995.25
2021 Sep	308,273	ARIMA_d1D1_log	277,109.05	31,163.95
2021 Oct	250,949	ARIMA_d1D1_log	197,419.25	53,529.75
2021 Nov	156,624	ARIMA_d1D1_log	141,965.27	14,658.73
2021 Dec	115,100	ARIMA_d1D1_log	125,569.19	-10,469.19
2022 Jan	96,107	ARIMA_d1D1_log	83,548.39	12,558.61
2022 Feb	141,508	ARIMA_d1D1_log	113,365.97	28,142.03
2022 Mar	167,854	ARIMA_d1D1_log	136,949.21	30,904.79
2022 Apr	248,959	ARIMA_d1D1_log	123,089.12	125,869.88
2022 May	258,413	ARIMA_d1D1_log	310,961.18	-52,548.18
2022 Jun	300,520	ARIMA_d1D1_log	284,316.24	16,203.76
2010 Jan	53,653	Drift_STL	48,728.64	4,924.36
2010 Feb	62,257	Drift_STL	64,880.81	-2,623.81
2010 Mar	77,588	Drift_STL	76,834.74	753.26
2010 Apr	99,982	Drift_STL	94,283.63	5,698.37
2010 May	101,387	Drift_STL	101,162.45	224.55
2010 Jun	108,611	Drift_STL	100,470.48	8,140.52
2010 Jul	126,498	Drift_STL	121,218.95	5,279.05
2010 Aug	178,380	Drift_STL	174,712.78	3,667.22
2010 Sep	127,822	Drift_STL	126,427.97	1,394.03
2010 Oct	104,174	Drift_STL	107,601.63	-3,427.63
2010 Nov	69,271	Drift_STL	86,538.91	-17,267.91
2010 Dec	62,935	Drift_STL	65,103.25	-2,168.25
2011 Jan	60,457	Drift_STL	53,586.08	6,870.92
2011 Feb	67,260	Drift_STL	71,679.61	-4,419.61
2011 Mar	83,464	Drift_STL	82,545.15	918.85
2011 Apr	102,958	Drift_STL	101,613.57	1,344.43
2011 May	101,223	Drift_STL	104,746.19	-3,523.19
2011 Jun	120,148	Drift_STL	102,349.33	17,798.67
2011 Jul	136,999	Drift_STL	132,395.52	4,603.48
2011 Aug	212,668	Drift_STL	185,193.02	27,474.98
2011 Sep	129,606	Drift_STL	156,928.22	-27,322.22
2011 Oct	101,185	Drift_STL	109,702.29	-8,517.29
2011 Nov	62,121	Drift_STL	81,872.09	-19,751.09
2011 Dec	65,563	Drift_STL	59,576.52	5,986.48
2012 Jan	49,716	Drift_STL	57,404.12	-7,688.12
2012 Feb	58,638	Drift_STL	61,873.63	-3,235.63
2012 Mar	72,210	Drift_STL	74,872.05	-2,662.05
2012 Apr	87,406	Drift_STL	91,535.32	-4,129.32
2012 May	96,946	Drift_STL	89,727.91	7,218.09
2012 Jun	115,885	Drift_STL	100,445.69	15,439.31
2012 Jul	139,695	Drift_STL	127,445.54	12,249.46
2012 Aug	194,368	Drift_STL	190,727.38	3,640.62
2012 Sep	127,610	Drift_STL	134,198.29	-6,588.29
2012 Oct	89,649	Drift_STL	104,915.23	-15,266.23
2012 Nov	58,900	Drift_STL	66,656.90	-7,756.90
2012 Dec	51,122	Drift_STL	56,960.13	-5,838.13
2013 Jan	50,313	Drift_STL	42,837.01	7,475.99
2013 Feb	58,615	Drift_STL	60,985.37	-2,370.37
2013 Mar	92,426	Drift_STL	74,087.66	18,338.34
2013 Apr	100,996	Drift_STL	108,791.38	-7,795.38
2013 May	123,431	Drift_STL	103,669.05	19,761.95
2013 Jun	143,946	Drift_STL	128,247.22	15,698.78
2013 Jul	171,016	Drift_STL	155,767.78	15,248.22
2013 Aug	252,423	Drift_STL	221,886.77	30,536.23
2013 Sep	158,839	Drift_STL	186,085.23	-27,246.23
2013 Oct	109,956	Drift_STL	134,147.79	-24,191.79
2013 Nov	82,040	Drift_STL	87,139.70	-5,099.70
2013 Dec	72,692	Drift_STL	81,529.90	-8,837.90
2014 Jan	56,872	Drift_STL	68,148.63	-11,276.63
2014 Feb	64,346	Drift_STL	70,574.89	-6,228.89
2014 Mar	102,852	Drift_STL	85,563.02	17,288.98
2014 Apr	151,151	Drift_STL	119,095.77	32,055.23
2014 May	148,593	Drift_STL	153,428.77	-4,835.77
2014 Jun	154,231	Drift_STL	156,514.19	-2,283.19
2014 Jul	194,227	Drift_STL	169,556.43	24,670.57
2014 Aug	303,902	Drift_STL	249,441.73	54,460.27
2014 Sep	186,247	Drift_STL	226,518.26	-40,271.26
2014 Oct	133,884	Drift_STL	156,251.38	-22,367.38
2014 Nov	86,161	Drift_STL	109,373.11	-23,212.11
2014 Dec	81,830	Drift_STL	86,985.57	-5,155.57
2015 Jan	68,436	Drift_STL	77,697.28	-9,261.28
2015 Feb	84,417	Drift_STL	82,243.23	2,173.77
2015 Mar	116,291	Drift_STL	108,896.87	7,394.13
2015 Apr	145,183	Drift_STL	137,851.00	7,332.00
2015 May	172,016	Drift_STL	149,230.00	22,786.00
2015 Jun	182,765	Drift_STL	178,693.50	4,071.50
2015 Jul	238,708	Drift_STL	200,208.86	38,499.14
2015 Aug	358,044	Drift_STL	299,710.38	58,333.62
2015 Sep	216,474	Drift_STL	266,411.24	-49,937.24
2015 Oct	148,376	Drift_STL	181,017.46	-32,641.46
2015 Nov	99,794	Drift_STL	120,992.85	-21,198.85
2015 Dec	93,804	Drift_STL	101,786.33	-7,982.33
2016 Jan	74,572	Drift_STL	90,494.60	-15,922.60
2016 Feb	97,522	Drift_STL	91,038.04	6,483.96
2016 Mar	144,216	Drift_STL	125,164.18	19,051.82
2016 Apr	153,386	Drift_STL	166,308.01	-12,922.01
2016 May	168,235	Drift_STL	162,723.92	5,511.08
2016 Jun	215,800	Drift_STL	178,298.20	37,501.80
2016 Jul	271,212	Drift_STL	237,290.41	33,921.59
2016 Aug	380,776	Drift_STL	340,538.97	40,237.03
2016 Sep	249,098	Drift_STL	275,122.38	-26,024.38
2016 Oct	175,862	Drift_STL	203,976.56	-28,114.56
2016 Nov	102,775	Drift_STL	142,980.41	-40,205.41
2016 Dec	100,859	Drift_STL	106,041.40	-5,182.40
2017 Jan	83,249	Drift_STL	96,707.69	-13,458.69
2017 Feb	105,210	Drift_STL	102,318.07	2,891.93
2017 Mar	121,167	Drift_STL	138,237.07	-17,070.07
2017 Apr	217,906	Drift_STL	146,035.84	71,870.16
2017 May	196,622	Drift_STL	221,804.47	-25,182.47
2017 Jun	248,582	Drift_STL	212,100.86	36,481.14
2017 Jul	323,496	Drift_STL	275,432.52	48,063.48
2017 Aug	431,571	Drift_STL	398,069.24	33,501.76
2017 Sep	287,242	Drift_STL	313,617.27	-26,375.27
2017 Oct	212,357	Drift_STL	234,201.14	-21,844.14
2017 Nov	127,745	Drift_STL	171,692.41	-43,947.41
2017 Dec	132,238	Drift_STL	132,409.44	-171.44
2018 Jan	95,453	Drift_STL	126,809.83	-31,356.83
2018 Feb	120,303	Drift_STL	119,138.68	1,164.32
2018 Mar	162,886	Drift_STL	154,744.66	8,141.34
2018 Apr	187,186	Drift_STL	198,748.46	-11,562.46
2018 May	239,851	Drift_STL	194,376.23	45,474.77
2018 Jun	264,588	Drift_STL	258,586.42	6,001.58
2018 Jul	339,564	Drift_STL	300,979.52	38,584.48
2018 Aug	446,375	Drift_STL	421,521.30	24,853.70
2018 Sep	304,516	Drift_STL	317,595.01	-13,079.01
2018 Oct	230,827	Drift_STL	242,898.49	-12,071.49
2018 Nov	149,080	Drift_STL	179,325.32	-30,245.32
2018 Dec	135,316	Drift_STL	152,482.71	-17,166.71
2019 Jan	114,710	Drift_STL	125,293.57	-10,583.57
2019 Feb	122,635	Drift_STL	138,765.07	-16,130.07
2019 Mar	172,412	Drift_STL	161,129.61	11,282.39
2019 Apr	241,790	Drift_STL	209,026.20	32,763.80
2019 May	259,714	Drift_STL	251,462.96	8,251.04
2019 Jun	306,048	Drift_STL	280,973.12	25,074.88
2019 Jul	360,566	Drift_STL	349,159.59	11,406.41
2019 Aug	484,403	Drift_STL	450,112.13	34,290.87
2019 Sep	327,937	Drift_STL	346,963.13	-19,026.13
2019 Oct	238,677	Drift_STL	261,460.93	-22,783.93
2019 Nov	171,296	Drift_STL	181,341.74	-10,045.74
2019 Dec	138,642	Drift_STL	172,049.24	-33,407.24
2020 Jan	126,349	Drift_STL	128,077.96	-1,728.96
2020 Feb	167,411	Drift_STL	149,618.72	17,792.28
2020 Mar	70,530	Drift_STL	205,582.87	-135,052.87
2020 Apr	13,892	Drift_STL	129,256.52	-115,364.52
2020 May	38,343	Drift_STL	51,257.94	-12,914.94
2020 Jun	159,738	Drift_STL	81,935.37	77,802.63
2020 Jul	272,786	Drift_STL	208,902.73	63,883.27
2020 Aug	407,020	Drift_STL	363,156.34	43,863.66
2020 Sep	258,651	Drift_STL	252,763.20	5,887.80
2020 Oct	167,448	Drift_STL	175,420.86	-7,972.86
2020 Nov	73,734	Drift_STL	96,992.01	-23,258.01
2020 Dec	73,353	Drift_STL	65,060.89	8,292.11
2021 Jan	48,435	Drift_STL	54,760.51	-6,325.51
2021 Feb	40,443	Drift_STL	70,924.75	-30,481.75
2021 Mar	60,251	Drift_STL	60,905.43	-654.43
2021 Apr	85,179	Drift_STL	95,315.68	-10,136.68
2021 May	169,690	Drift_STL	109,611.31	60,078.69
2021 Jun	254,243	Drift_STL	214,438.37	39,804.63
2021 Jul	329,058	Drift_STL	312,083.23	16,974.77
2021 Aug	461,844	Drift_STL	431,640.99	30,203.01
2021 Sep	308,273	Drift_STL	309,625.24	-1,352.24
2021 Oct	250,949	Drift_STL	226,785.01	24,163.99
2021 Nov	156,624	Drift_STL	174,532.92	-17,908.92
2021 Dec	115,100	Drift_STL	150,316.90	-35,216.90
2022 Jan	96,107	Drift_STL	101,847.61	-5,740.61
2022 Feb	141,508	Drift_STL	120,007.25	21,500.75
2022 Mar	167,854	Drift_STL	157,856.43	9,997.57
2022 Apr	248,959	Drift_STL	199,688.11	49,270.89
2022 May	258,413	Drift_STL	277,593.01	-19,180.01
2022 Jun	300,520	Drift_STL	316,599.71	-16,079.71
2010 Jan	53,653	Drift_STL_log	48,562.60	5,090.40
2010 Feb	62,257	Drift_STL_log	65,633.72	-3,376.72
2010 Mar	77,588	Drift_STL_log	77,425.90	162.10
2010 Apr	99,982	Drift_STL_log	96,077.33	3,904.67
2010 May	101,387	Drift_STL_log	102,183.08	-796.08
2010 Jun	108,611	Drift_STL_log	100,921.01	7,689.99
2010 Jul	126,498	Drift_STL_log	124,816.94	1,681.06
2010 Aug	178,380	Drift_STL_log	185,433.36	-7,053.36
2010 Sep	127,822	Drift_STL_log	120,769.56	7,052.44
2010 Oct	104,174	Drift_STL_log	103,807.56	366.44
2010 Nov	69,271	Drift_STL_log	82,718.92	-13,447.92
2010 Dec	62,935	Drift_STL_log	63,928.14	-993.14
2011 Jan	60,457	Drift_STL_log	52,385.85	8,071.15
2011 Feb	67,260	Drift_STL_log	72,993.35	-5,733.35
2011 Mar	83,464	Drift_STL_log	83,862.56	-398.56
2011 Apr	102,958	Drift_STL_log	104,712.27	-1,754.27
2011 May	101,223	Drift_STL_log	106,061.72	-4,838.72
2011 Jun	120,148	Drift_STL_log	103,049.09	17,098.91
2011 Jul	136,999	Drift_STL_log	137,350.50	-351.50
2011 Aug	212,668	Drift_STL_log	199,375.84	13,292.16
2011 Sep	129,606	Drift_STL_log	143,545.06	-13,939.06
2011 Oct	101,185	Drift_STL_log	106,088.00	-4,903.00
2011 Nov	62,121	Drift_STL_log	78,587.50	-16,466.50
2011 Dec	65,563	Drift_STL_log	58,280.64	7,282.36
2012 Jan	49,716	Drift_STL_log	55,511.55	-5,795.55
2012 Feb	58,638	Drift_STL_log	60,482.51	-1,844.51
2012 Mar	72,210	Drift_STL_log	73,411.77	-1,201.77
2012 Apr	87,406	Drift_STL_log	90,829.29	-3,423.29
2012 May	96,946	Drift_STL_log	89,868.90	7,077.10
2012 Jun	115,885	Drift_STL_log	100,181.29	15,703.71
2012 Jul	139,695	Drift_STL_log	129,835.01	9,859.99
2012 Aug	194,368	Drift_STL_log	201,121.50	-6,753.50
2012 Sep	127,610	Drift_STL_log	128,897.92	-1,287.92
2012 Oct	89,649	Drift_STL_log	102,954.21	-13,305.21
2012 Nov	58,900	Drift_STL_log	67,105.33	-8,205.33
2012 Dec	51,122	Drift_STL_log	56,642.40	-5,520.40
2013 Jan	50,313	Drift_STL_log	43,750.34	6,562.66
2013 Feb	58,615	Drift_STL_log	60,142.20	-1,527.20
2013 Mar	92,426	Drift_STL_log	72,758.69	19,667.31
2013 Apr	100,996	Drift_STL_log	111,991.36	-10,995.36
2013 May	123,431	Drift_STL_log	104,151.68	19,279.32
2013 Jun	143,946	Drift_STL_log	129,395.81	14,550.19
2013 Jul	171,016	Drift_STL_log	161,120.58	9,895.42
2013 Aug	252,423	Drift_STL_log	243,444.63	8,978.37
2013 Sep	158,839	Drift_STL_log	165,810.01	-6,971.01
2013 Oct	109,956	Drift_STL_log	125,852.61	-15,896.61
2013 Nov	82,040	Drift_STL_log	80,499.51	1,540.49
2013 Dec	72,692	Drift_STL_log	77,829.80	-5,137.80
2014 Jan	56,872	Drift_STL_log	64,115.81	-7,243.81
2014 Feb	64,346	Drift_STL_log	69,527.71	-5,181.71
2014 Mar	102,852	Drift_STL_log	85,243.09	17,608.91
2014 Apr	151,151	Drift_STL_log	124,292.22	26,858.78
2014 May	148,593	Drift_STL_log	156,951.52	-8,358.52
2014 Jun	154,231	Drift_STL_log	160,787.59	-6,556.59
2014 Jul	194,227	Drift_STL_log	176,382.24	17,844.76
2014 Aug	303,902	Drift_STL_log	277,786.98	26,115.02
2014 Sep	186,247	Drift_STL_log	195,668.02	-9,421.02
2014 Oct	133,884	Drift_STL_log	143,016.67	-9,132.67
2014 Nov	86,161	Drift_STL_log	96,218.11	-10,057.11
2014 Dec	81,830	Drift_STL_log	81,687.75	142.25
2015 Jan	68,436	Drift_STL_log	71,459.00	-3,023.00
2015 Feb	84,417	Drift_STL_log	81,956.20	2,460.80
2015 Mar	116,291	Drift_STL_log	114,398.87	1,892.13
2015 Apr	145,183	Drift_STL_log	145,068.08	114.92
2015 May	172,016	Drift_STL_log	153,079.75	18,936.25
2015 Jun	182,765	Drift_STL_log	185,627.17	-2,862.17
2015 Jul	238,708	Drift_STL_log	210,770.68	27,937.32
2015 Aug	358,044	Drift_STL_log	341,815.55	16,228.45
2015 Sep	216,474	Drift_STL_log	225,813.03	-9,339.03
2015 Oct	148,376	Drift_STL_log	162,611.59	-14,235.59
2015 Nov	99,794	Drift_STL_log	103,909.05	-4,115.05
2015 Dec	93,804	Drift_STL_log	94,306.55	-502.55
2016 Jan	74,572	Drift_STL_log	81,730.14	-7,158.14
2016 Feb	97,522	Drift_STL_log	90,045.65	7,476.35
2016 Mar	144,216	Drift_STL_log	133,704.24	10,511.76
2016 Apr	153,386	Drift_STL_log	178,296.25	-24,910.25
2016 May	168,235	Drift_STL_log	167,141.04	1,093.96
2016 Jun	215,800	Drift_STL_log	185,388.47	30,411.53
2016 Jul	271,212	Drift_STL_log	252,443.14	18,768.86
2016 Aug	380,776	Drift_STL_log	389,621.67	-8,845.67
2016 Sep	249,098	Drift_STL_log	237,299.66	11,798.34
2016 Oct	175,862	Drift_STL_log	180,969.48	-5,107.48
2016 Nov	102,775	Drift_STL_log	119,873.77	-17,098.77
2016 Dec	100,859	Drift_STL_log	97,690.01	3,168.99
2017 Jan	83,249	Drift_STL_log	86,662.04	-3,413.04
2017 Feb	105,210	Drift_STL_log	101,404.86	3,805.14
2017 Mar	121,167	Drift_STL_log	147,698.30	-26,531.30
2017 Apr	217,906	Drift_STL_log	150,695.50	67,210.50
2017 May	196,622	Drift_STL_log	229,912.52	-33,290.52
2017 Jun	248,582	Drift_STL_log	221,718.87	26,863.13
2017 Jul	323,496	Drift_STL_log	295,416.39	28,079.61
2017 Aug	431,571	Drift_STL_log	460,776.14	-29,205.14
2017 Sep	287,242	Drift_STL_log	269,868.93	17,373.07
2017 Oct	212,357	Drift_STL_log	205,142.12	7,214.88
2017 Nov	127,745	Drift_STL_log	139,243.80	-11,498.80
2017 Dec	132,238	Drift_STL_log	121,198.46	11,039.54
2018 Jan	95,453	Drift_STL_log	111,159.76	-15,706.76
2018 Feb	120,303	Drift_STL_log	118,274.39	2,028.61
2018 Mar	162,886	Drift_STL_log	166,873.32	-3,987.32
2018 Apr	187,186	Drift_STL_log	212,785.80	-25,599.80
2018 May	239,851	Drift_STL_log	201,464.30	38,386.70
2018 Jun	264,588	Drift_STL_log	274,361.79	-9,773.79
2018 Jul	339,564	Drift_STL_log	324,222.67	15,341.33
2018 Aug	446,375	Drift_STL_log	481,863.18	-35,488.18
2018 Sep	304,516	Drift_STL_log	282,511.96	22,004.04
2018 Oct	230,827	Drift_STL_log	215,858.65	14,968.35
2018 Nov	149,080	Drift_STL_log	146,920.70	2,159.30
2018 Dec	135,316	Drift_STL_log	141,158.87	-5,842.87
2019 Jan	114,710	Drift_STL_log	110,243.69	4,466.31
2019 Feb	122,635	Drift_STL_log	140,523.67	-17,888.67
2019 Mar	172,412	Drift_STL_log	171,044.61	1,367.39
2019 Apr	241,790	Drift_STL_log	222,645.59	19,144.41
2019 May	259,714	Drift_STL_log	262,028.44	-2,314.44
2019 Jun	306,048	Drift_STL_log	297,888.93	8,159.07
2019 Jul	360,566	Drift_STL_log	380,046.04	-19,480.04
2019 Aug	484,403	Drift_STL_log	509,481.01	-25,078.01
2019 Sep	327,937	Drift_STL_log	312,578.39	15,358.61
2019 Oct	238,677	Drift_STL_log	234,663.15	4,013.85
2019 Nov	171,296	Drift_STL_log	151,967.72	19,328.28
2019 Dec	138,642	Drift_STL_log	159,800.85	-21,158.85
2020 Jan	126,349	Drift_STL_log	113,170.49	13,178.51
2020 Feb	167,411	Drift_STL_log	151,077.32	16,333.68
2020 Mar	70,530	Drift_STL_log	226,936.22	-156,406.22
2020 Apr	13,892	Drift_STL_log	105,169.61	-91,277.61
2020 May	38,343	Drift_STL_log	20,998.19	17,344.81
2020 Jun	159,738	Drift_STL_log	50,255.61	109,482.39
2020 Jul	272,786	Drift_STL_log	184,065.86	88,720.14
2020 Aug	407,020	Drift_STL_log	342,539.50	64,480.50
2020 Sep	258,651	Drift_STL_log	239,261.86	19,389.14
2020 Oct	167,448	Drift_STL_log	171,338.83	-3,890.83
2020 Nov	73,734	Drift_STL_log	103,183.03	-29,449.03
2020 Dec	73,353	Drift_STL_log	69,057.28	4,295.72
2021 Jan	48,435	Drift_STL_log	60,667.45	-12,232.45
2021 Feb	40,443	Drift_STL_log	61,000.99	-20,557.99
2021 Mar	60,251	Drift_STL_log	49,397.62	10,853.38
2021 Apr	85,179	Drift_STL_log	62,074.21	23,104.79
2021 May	169,690	Drift_STL_log	113,520.41	56,169.59
2021 Jun	254,243	Drift_STL_log	237,818.69	16,424.31
2021 Jul	329,058	Drift_STL_log	321,815.24	7,242.76
2021 Aug	461,844	Drift_STL_log	449,735.90	12,108.10
2021 Sep	308,273	Drift_STL_log	296,638.10	11,634.90
2021 Oct	250,949	Drift_STL_log	216,456.49	34,492.51
2021 Nov	156,624	Drift_STL_log	149,283.40	7,340.60
2021 Dec	115,100	Drift_STL_log	145,943.61	-30,843.61
2022 Jan	96,107	Drift_STL_log	94,766.16	1,340.84
2022 Feb	141,508	Drift_STL_log	114,647.55	26,860.45
2022 Mar	167,854	Drift_STL_log	164,699.56	3,154.44
2022 Apr	248,959	Drift_STL_log	173,783.49	75,175.51
2022 May	258,413	Drift_STL_log	359,855.07	-101,442.07
2022 Jun	300,520	Drift_STL_log	404,950.00	-104,430.00
2010 Jan	53,653	ETS_auto	55,527.88	-1,874.88
2010 Feb	62,257	ETS_auto	66,732.56	-4,475.56
2010 Mar	77,588	ETS_auto	82,133.55	-4,545.55
2010 Apr	99,982	ETS_auto	96,967.08	3,014.92
2010 May	101,387	ETS_auto	96,952.95	4,434.05
2010 Jun	108,611	ETS_auto	98,200.44	10,410.56
2010 Jul	126,498	ETS_auto	114,051.20	12,446.80
2010 Aug	178,380	ETS_auto	158,784.79	19,595.21
2010 Sep	127,822	ETS_auto	109,343.55	18,478.45
2010 Oct	104,174	ETS_auto	91,437.78	12,736.22
2010 Nov	69,271	ETS_auto	75,251.62	-5,980.62
2010 Dec	62,935	ETS_auto	66,907.50	-3,972.50
2011 Jan	60,457	ETS_auto	53,832.02	6,624.98
2011 Feb	67,260	ETS_auto	69,105.66	-1,845.66
2011 Mar	83,464	ETS_auto	88,351.42	-4,887.42
2011 Apr	102,958	ETS_auto	104,593.35	-1,635.35
2011 May	101,223	ETS_auto	103,547.29	-2,324.29
2011 Jun	120,148	ETS_auto	106,881.14	13,266.86
2011 Jul	136,999	ETS_auto	125,230.67	11,768.33
2011 Aug	212,668	ETS_auto	178,857.83	33,810.17
2011 Sep	129,606	ETS_auto	124,253.42	5,352.58
2011 Oct	101,185	ETS_auto	102,182.45	-997.45
2011 Nov	62,121	ETS_auto	79,414.61	-17,293.61
2011 Dec	65,563	ETS_auto	67,294.78	-1,731.78
2012 Jan	49,716	ETS_auto	55,984.27	-6,268.27
2012 Feb	58,638	ETS_auto	68,431.32	-9,793.32
2012 Mar	72,210	ETS_auto	87,956.24	-15,746.24
2012 Apr	87,406	ETS_auto	94,769.11	-7,363.11
2012 May	96,946	ETS_auto	91,938.62	5,007.38
2012 Jun	115,885	ETS_auto	97,170.12	18,714.88
2012 Jul	139,695	ETS_auto	121,602.27	18,092.73
2012 Aug	194,368	ETS_auto	183,683.38	10,684.62
2012 Sep	127,610	ETS_auto	122,159.51	5,450.49
2012 Oct	89,649	ETS_auto	96,851.30	-7,202.30
2012 Nov	58,900	ETS_auto	73,921.33	-15,021.33
2012 Dec	51,122	ETS_auto	65,631.74	-14,509.74
2013 Jan	50,313	ETS_auto	47,273.48	3,039.52
2013 Feb	58,615	ETS_auto	60,073.78	-1,458.78
2013 Mar	92,426	ETS_auto	76,089.17	16,336.83
2013 Apr	100,996	ETS_auto	102,319.58	-1,323.58
2013 May	123,431	ETS_auto	99,262.22	24,168.78
2013 Jun	143,946	ETS_auto	108,529.40	35,416.60
2013 Jul	171,016	ETS_auto	149,391.55	21,624.45
2013 Aug	252,423	ETS_auto	231,200.42	21,222.58
2013 Sep	158,839	ETS_auto	161,764.45	-2,925.45
2013 Oct	109,956	ETS_auto	124,725.25	-14,769.25
2013 Nov	82,040	ETS_auto	88,945.38	-6,905.38
2013 Dec	72,692	ETS_auto	76,130.02	-3,438.02
2014 Jan	56,872	ETS_auto	62,590.29	-5,718.29
2014 Feb	64,346	ETS_auto	72,026.42	-7,680.42
2014 Mar	102,852	ETS_auto	89,202.35	13,649.65
2014 Apr	151,151	ETS_auto	117,732.56	33,418.44
2014 May	148,593	ETS_auto	137,899.77	10,693.23
2014 Jun	154,231	ETS_auto	152,682.48	1,548.52
2014 Jul	194,227	ETS_auto	179,316.97	14,910.03
2014 Aug	303,902	ETS_auto	267,752.16	36,149.84
2014 Sep	186,247	ETS_auto	190,122.22	-3,875.22
2014 Oct	133,884	ETS_auto	144,193.31	-10,309.31
2014 Nov	86,161	ETS_auto	104,830.30	-18,669.30
2014 Dec	81,830	ETS_auto	82,873.35	-1,043.35
2015 Jan	68,436	ETS_auto	69,183.95	-747.95
2015 Feb	84,417	ETS_auto	82,498.56	1,918.44
2015 Mar	116,291	ETS_auto	111,798.22	4,492.78
2015 Apr	145,183	ETS_auto	141,845.93	3,337.07
2015 May	172,016	ETS_auto	143,377.55	28,638.45
2015 Jun	182,765	ETS_auto	170,794.18	11,970.82
2015 Jul	238,708	ETS_auto	208,890.90	29,817.10
2015 Aug	358,044	ETS_auto	328,016.56	30,027.44
2015 Sep	216,474	ETS_auto	227,222.05	-10,748.05
2015 Oct	148,376	ETS_auto	169,421.48	-21,045.48
2015 Nov	99,794	ETS_auto	116,888.08	-17,094.08
2015 Dec	93,804	ETS_auto	93,854.15	-50.15
2016 Jan	74,572	ETS_auto	79,194.80	-4,622.80
2016 Feb	97,522	ETS_auto	91,243.32	6,278.68
2016 Mar	144,216	ETS_auto	127,772.62	16,443.38
2016 Apr	153,386	ETS_auto	171,463.13	-18,077.13
2016 May	168,235	ETS_auto	160,328.79	7,906.21
2016 Jun	215,800	ETS_auto	173,411.37	42,388.63
2016 Jul	271,212	ETS_auto	238,723.41	32,488.59
2016 Aug	380,776	ETS_auto	377,123.29	3,652.71
2016 Sep	249,098	ETS_auto	244,705.66	4,392.34
2016 Oct	175,862	ETS_auto	188,918.83	-13,056.83
2016 Nov	102,775	ETS_auto	135,138.60	-32,363.60
2016 Dec	100,859	ETS_auto	99,556.37	1,302.63
2017 Jan	83,249	ETS_auto	85,147.53	-1,898.53
2017 Feb	105,210	ETS_auto	100,980.97	4,229.03
2017 Mar	121,167	ETS_auto	139,761.27	-18,594.27
2017 Apr	217,906	ETS_auto	154,703.30	63,202.70
2017 May	196,622	ETS_auto	197,935.53	-1,313.53
2017 Jun	248,582	ETS_auto	230,052.89	18,529.11
2017 Jul	323,496	ETS_auto	288,714.17	34,781.83
2017 Aug	431,571	ETS_auto	422,017.51	9,553.49
2017 Sep	287,242	ETS_auto	263,973.22	23,268.78
2017 Oct	212,357	ETS_auto	186,025.80	26,331.20
2017 Nov	127,745	ETS_auto	159,914.96	-32,169.96
2017 Dec	132,238	ETS_auto	116,105.17	16,132.83
2018 Jan	95,453	ETS_auto	98,421.88	-2,968.88
2018 Feb	120,303	ETS_auto	122,584.98	-2,281.98
2018 Mar	162,886	ETS_auto	159,529.19	3,356.81
2018 Apr	187,186	ETS_auto	233,354.60	-46,168.60
2018 May	239,851	ETS_auto	191,628.77	48,222.23
2018 Jun	264,588	ETS_auto	268,509.21	-3,921.21
2018 Jul	339,564	ETS_auto	335,981.15	3,582.85
2018 Aug	446,375	ETS_auto	459,033.86	-12,658.86
2018 Sep	304,516	ETS_auto	292,278.83	12,237.17
2018 Oct	230,827	ETS_auto	230,410.03	416.97
2018 Nov	149,080	ETS_auto	169,586.72	-20,506.72
2018 Dec	135,316	ETS_auto	131,443.72	3,872.28
2019 Jan	114,710	ETS_auto	113,603.87	1,106.13
2019 Feb	122,635	ETS_auto	137,636.56	-15,001.56
2019 Mar	172,412	ETS_auto	171,244.11	1,167.89
2019 Apr	241,790	ETS_auto	216,324.60	25,465.40
2019 May	259,714	ETS_auto	238,037.36	21,676.64
2019 Jun	306,048	ETS_auto	270,309.02	35,738.98
2019 Jul	360,566	ETS_auto	377,382.70	-16,816.70
2019 Aug	484,403	ETS_auto	500,931.85	-16,528.85
2019 Sep	327,937	ETS_auto	328,121.52	-184.52
2019 Oct	238,677	ETS_auto	248,435.34	-9,758.34
2019 Nov	171,296	ETS_auto	176,404.58	-5,108.58
2019 Dec	138,642	ETS_auto	156,408.67	-17,766.67
2020 Jan	126,349	ETS_auto	119,491.82	6,857.18
2020 Feb	167,411	ETS_auto	150,521.15	16,889.85
2020 Mar	70,530	ETS_auto	217,956.28	-147,426.28
2020 Apr	13,892	ETS_auto	145,381.47	-131,489.47
2020 May	38,343	ETS_auto	42,967.01	-4,624.01
2020 Jun	159,738	ETS_auto	41,334.03	118,403.97
2020 Jul	272,786	ETS_auto	210,110.24	62,675.76
2020 Aug	407,020	ETS_auto	318,388.79	88,631.21
2020 Sep	258,651	ETS_auto	234,925.01	23,725.99
2020 Oct	167,448	ETS_auto	174,903.01	-7,455.01
2020 Nov	73,734	ETS_auto	114,933.31	-41,199.31
2020 Dec	73,353	ETS_auto	90,783.84	-17,430.84
2021 Jan	48,435	ETS_auto	74,254.29	-25,819.29
2021 Feb	40,443	ETS_auto	82,775.14	-42,332.14
2021 Mar	60,251	ETS_auto	56,715.04	3,535.96
2021 Apr	85,179	ETS_auto	60,588.42	24,590.58
2021 May	169,690	ETS_auto	91,442.54	78,247.46
2021 Jun	254,243	ETS_auto	162,853.15	91,389.85
2021 Jul	329,058	ETS_auto	253,278.62	75,779.38
2021 Aug	461,844	ETS_auto	382,199.80	79,644.20
2021 Sep	308,273	ETS_auto	256,893.06	51,379.94
2021 Oct	250,949	ETS_auto	183,648.12	67,300.88
2021 Nov	156,624	ETS_auto	114,823.85	41,800.15
2021 Dec	115,100	ETS_auto	117,711.55	-2,611.55
2022 Jan	96,107	ETS_auto	93,080.36	3,026.64
2022 Feb	141,508	ETS_auto	106,144.88	35,363.12
2022 Mar	167,854	ETS_auto	133,905.87	33,948.13
2022 Apr	248,959	ETS_auto	183,305.42	65,653.58
2022 May	258,413	ETS_auto	295,836.61	-37,423.61
2022 Jun	300,520	ETS_auto	395,071.49	-94,551.49
2010 Jan	53,653	ETS_auto_log	52,753.15	899.85
2010 Feb	62,257	ETS_auto_log	64,785.92	-2,528.92
2010 Mar	77,588	ETS_auto_log	85,637.03	-8,049.03
2010 Apr	99,982	ETS_auto_log	103,395.72	-3,413.72
2010 May	101,387	ETS_auto_log	100,731.62	655.38
2010 Jun	108,611	ETS_auto_log	102,203.18	6,407.82
2010 Jul	126,498	ETS_auto_log	120,886.07	5,611.93
2010 Aug	178,380	ETS_auto_log	175,361.37	3,018.63
2010 Sep	127,822	ETS_auto_log	115,303.20	12,518.80
2010 Oct	104,174	ETS_auto_log	91,971.38	12,202.62
2010 Nov	69,271	ETS_auto_log	73,069.68	-3,798.68
2010 Dec	62,935	ETS_auto_log	65,257.15	-2,322.15
2011 Jan	60,457	ETS_auto_log	54,674.66	5,782.34
2011 Feb	67,260	ETS_auto_log	68,721.53	-1,461.53
2011 Mar	83,464	ETS_auto_log	87,941.87	-4,477.87
2011 Apr	102,958	ETS_auto_log	108,160.39	-5,202.39
2011 May	101,223	ETS_auto_log	105,549.39	-4,326.39
2011 Jun	120,148	ETS_auto_log	105,862.46	14,285.54
2011 Jul	136,999	ETS_auto_log	126,788.41	10,210.59
2011 Aug	212,668	ETS_auto_log	182,467.94	30,200.06
2011 Sep	129,606	ETS_auto_log	123,345.05	6,260.95
2011 Oct	101,185	ETS_auto_log	101,107.75	77.25
2011 Nov	62,121	ETS_auto_log	77,393.15	-15,272.15
2011 Dec	65,563	ETS_auto_log	67,873.58	-2,310.58
2012 Jan	49,716	ETS_auto_log	57,739.90	-8,023.90
2012 Feb	58,638	ETS_auto_log	70,402.72	-11,764.72
2012 Mar	72,210	ETS_auto_log	90,162.60	-17,952.60
2012 Apr	87,406	ETS_auto_log	96,265.40	-8,859.40
2012 May	96,946	ETS_auto_log	90,381.44	6,564.56
2012 Jun	115,885	ETS_auto_log	95,700.89	20,184.11
2012 Jul	139,695	ETS_auto_log	120,079.80	19,615.20
2012 Aug	194,368	ETS_auto_log	179,258.07	15,109.93
2012 Sep	127,610	ETS_auto_log	123,325.57	4,284.43
2012 Oct	89,649	ETS_auto_log	99,536.40	-9,887.40
2012 Nov	58,900	ETS_auto_log	76,045.82	-17,145.82
2012 Dec	51,122	ETS_auto_log	67,803.59	-16,681.59
2013 Jan	50,313	ETS_auto_log	50,241.26	71.74
2013 Feb	58,615	ETS_auto_log	59,032.56	-417.56
2013 Mar	92,426	ETS_auto_log	76,477.94	15,948.06
2013 Apr	100,996	ETS_auto_log	100,672.53	323.47
2013 May	123,431	ETS_auto_log	100,225.68	23,205.32
2013 Jun	143,946	ETS_auto_log	112,520.23	31,425.77
2013 Jul	171,016	ETS_auto_log	146,943.94	24,072.06
2013 Aug	252,423	ETS_auto_log	223,769.61	28,653.39
2013 Sep	158,839	ETS_auto_log	161,927.01	-3,088.01
2013 Oct	109,956	ETS_auto_log	124,416.34	-14,460.34
2013 Nov	82,040	ETS_auto_log	88,238.53	-6,198.53
2013 Dec	72,692	ETS_auto_log	75,713.26	-3,021.26
2014 Jan	56,872	ETS_auto_log	63,124.37	-6,252.37
2014 Feb	64,346	ETS_auto_log	72,713.02	-8,367.02
2014 Mar	102,852	ETS_auto_log	89,507.87	13,344.13
2014 Apr	151,151	ETS_auto_log	118,379.63	32,771.37
2014 May	148,593	ETS_auto_log	133,550.96	15,042.04
2014 Jun	154,231	ETS_auto_log	149,411.99	4,819.01
2014 Jul	194,227	ETS_auto_log	180,228.32	13,998.68
2014 Aug	303,902	ETS_auto_log	270,476.30	33,425.70
2014 Sep	186,247	ETS_auto_log	192,985.59	-6,738.59
2014 Oct	133,884	ETS_auto_log	145,751.59	-11,867.59
2014 Nov	86,161	ETS_auto_log	104,998.24	-18,837.24
2014 Dec	81,830	ETS_auto_log	82,469.48	-639.48
2015 Jan	68,436	ETS_auto_log	69,880.27	-1,444.27
2015 Feb	84,417	ETS_auto_log	83,984.53	432.47
2015 Mar	116,291	ETS_auto_log	111,702.28	4,588.72
2015 Apr	145,183	ETS_auto_log	141,416.50	3,766.50
2015 May	172,016	ETS_auto_log	144,494.45	27,521.55
2015 Jun	182,765	ETS_auto_log	167,667.83	15,097.17
2015 Jul	238,708	ETS_auto_log	211,349.31	27,358.69
2015 Aug	358,044	ETS_auto_log	332,785.75	25,258.25
2015 Sep	216,474	ETS_auto_log	223,351.93	-6,877.93
2015 Oct	148,376	ETS_auto_log	166,318.00	-17,942.00
2015 Nov	99,794	ETS_auto_log	115,710.73	-15,916.73
2015 Dec	93,804	ETS_auto_log	95,171.01	-1,367.01
2016 Jan	74,572	ETS_auto_log	77,830.18	-3,258.18
2016 Feb	97,522	ETS_auto_log	92,710.97	4,811.03
2016 Mar	144,216	ETS_auto_log	134,810.60	9,405.40
2016 Apr	153,386	ETS_auto_log	174,489.67	-21,103.67
2016 May	168,235	ETS_auto_log	188,854.73	-20,619.73
2016 Jun	215,800	ETS_auto_log	197,546.79	18,253.21
2016 Jul	271,212	ETS_auto_log	251,069.51	20,142.49
2016 Aug	380,776	ETS_auto_log	377,425.47	3,350.53
2016 Sep	249,098	ETS_auto_log	229,127.06	19,970.94
2016 Oct	175,862	ETS_auto_log	161,926.46	13,935.54
2016 Nov	102,775	ETS_auto_log	110,318.25	-7,543.25
2016 Dec	100,859	ETS_auto_log	101,694.03	-835.03
2017 Jan	83,249	ETS_auto_log	83,033.07	215.93
2017 Feb	105,210	ETS_auto_log	104,460.63	749.37
2017 Mar	121,167	ETS_auto_log	151,638.08	-30,471.08
2017 Apr	217,906	ETS_auto_log	168,925.61	48,980.39
2017 May	196,622	ETS_auto_log	197,584.36	-962.36
2017 Jun	248,582	ETS_auto_log	231,831.83	16,750.17
2017 Jul	323,496	ETS_auto_log	292,636.99	30,859.01
2017 Aug	431,571	ETS_auto_log	427,140.03	4,430.97
2017 Sep	287,242	ETS_auto_log	268,608.56	18,633.44
2017 Oct	212,357	ETS_auto_log	189,750.91	22,606.09
2017 Nov	127,745	ETS_auto_log	122,309.19	5,435.81
2017 Dec	132,238	ETS_auto_log	119,311.91	12,926.09
2018 Jan	95,453	ETS_auto_log	100,460.51	-5,007.51
2018 Feb	120,303	ETS_auto_log	125,595.82	-5,292.82
2018 Mar	162,886	ETS_auto_log	161,839.92	1,046.08
2018 Apr	187,186	ETS_auto_log	238,149.87	-50,963.87
2018 May	239,851	ETS_auto_log	222,476.26	17,374.74
2018 Jun	264,588	ETS_auto_log	273,849.88	-9,261.88
2018 Jul	339,564	ETS_auto_log	343,915.54	-4,351.54
2018 Aug	446,375	ETS_auto_log	479,871.87	-33,496.87
2018 Sep	304,516	ETS_auto_log	301,170.00	3,346.00
2018 Oct	230,827	ETS_auto_log	219,486.30	11,340.70
2018 Nov	149,080	ETS_auto_log	132,687.13	16,392.87
2018 Dec	135,316	ETS_auto_log	134,101.93	1,214.07
2019 Jan	114,710	ETS_auto_log	104,335.55	10,374.45
2019 Feb	122,635	ETS_auto_log	134,504.51	-11,869.51
2019 Mar	172,412	ETS_auto_log	176,234.20	-3,822.20
2019 Apr	241,790	ETS_auto_log	227,942.24	13,847.76
2019 May	259,714	ETS_auto_log	262,749.32	-3,035.32
2019 Jun	306,048	ETS_auto_log	303,826.42	2,221.58
2019 Jul	360,566	ETS_auto_log	390,160.25	-29,594.25
2019 Aug	484,403	ETS_auto_log	519,572.72	-35,169.72
2019 Sep	327,937	ETS_auto_log	341,627.00	-13,690.00
2019 Oct	238,677	ETS_auto_log	249,038.73	-10,361.73
2019 Nov	171,296	ETS_auto_log	155,567.76	15,728.24
2019 Dec	138,642	ETS_auto_log	148,550.43	-9,908.43
2020 Jan	126,349	ETS_auto_log	116,635.56	9,713.44
2020 Feb	167,411	ETS_auto_log	138,828.74	28,582.26
2020 Mar	70,530	ETS_auto_log	197,572.58	-127,042.58
2020 Apr	13,892	ETS_auto_log	226,197.77	-212,305.77
2020 May	38,343	ETS_auto_log	10,366.71	27,976.29
2020 Jun	159,738	ETS_auto_log	39,556.52	120,181.48
2020 Jul	272,786	ETS_auto_log	196,788.38	75,997.62
2020 Aug	407,020	ETS_auto_log	399,859.85	7,160.15
2020 Sep	258,651	ETS_auto_log	269,135.85	-10,484.85
2020 Oct	167,448	ETS_auto_log	201,782.01	-34,334.01
2020 Nov	73,734	ETS_auto_log	124,113.44	-50,379.44
2020 Dec	73,353	ETS_auto_log	69,367.38	3,985.62
2021 Jan	48,435	ETS_auto_log	63,509.77	-15,074.77
2021 Feb	40,443	ETS_auto_log	61,524.79	-21,081.79
2021 Mar	60,251	ETS_auto_log	51,317.61	8,933.39
2021 Apr	85,179	ETS_auto_log	70,327.74	14,851.26
2021 May	169,690	ETS_auto_log	92,494.18	77,195.82
2021 Jun	254,243	ETS_auto_log	200,340.66	53,902.34
2021 Jul	329,058	ETS_auto_log	315,585.98	13,472.02
2021 Aug	461,844	ETS_auto_log	483,607.79	-21,763.79
2021 Sep	308,273	ETS_auto_log	307,126.29	1,146.71
2021 Oct	250,949	ETS_auto_log	239,379.05	11,569.95
2021 Nov	156,624	ETS_auto_log	185,428.58	-28,804.58
2021 Dec	115,100	ETS_auto_log	146,159.22	-31,059.22
2022 Jan	96,107	ETS_auto_log	97,144.63	-1,037.63
2022 Feb	141,508	ETS_auto_log	117,828.84	23,679.16
2022 Mar	167,854	ETS_auto_log	183,647.77	-15,793.77
2022 Apr	248,959	ETS_auto_log	198,527.77	50,431.23
2022 May	258,413	ETS_auto_log	286,860.98	-28,447.98
2022 Jun	300,520	ETS_auto_log	324,227.06	-23,707.06
2010 Jan	53,653	HWA	57,017.89	-3,364.89
2010 Feb	62,257	HWA	68,465.63	-6,208.63
2010 Mar	77,588	HWA	82,725.54	-5,137.54
2010 Apr	99,982	HWA	97,490.06	2,491.94
2010 May	101,387	HWA	97,136.04	4,250.96
2010 Jun	108,611	HWA	99,061.83	9,549.17
2010 Jul	126,498	HWA	114,081.70	12,416.30
2010 Aug	178,380	HWA	162,596.66	15,783.34
2010 Sep	127,822	HWA	117,374.23	10,447.77
2010 Oct	104,174	HWA	102,074.25	2,099.75
2010 Nov	69,271	HWA	87,111.80	-17,840.80
2010 Dec	62,935	HWA	74,317.89	-11,382.89
2011 Jan	60,457	HWA	62,515.75	-2,058.75
2011 Feb	67,260	HWA	73,250.36	-5,990.36
2011 Mar	83,464	HWA	87,287.15	-3,823.15
2011 Apr	102,958	HWA	102,830.93	127.07
2011 May	101,223	HWA	101,939.26	-716.26
2011 Jun	120,148	HWA	103,596.40	16,551.60
2011 Jul	136,999	HWA	122,416.37	14,582.63
2011 Aug	212,668	HWA	172,053.18	40,614.82
2011 Sep	129,606	HWA	145,045.70	-15,439.70
2011 Oct	101,185	HWA	115,671.73	-14,486.73
2011 Nov	62,121	HWA	89,559.08	-27,438.08
2011 Dec	65,563	HWA	71,034.53	-5,471.53
2012 Jan	49,716	HWA	63,964.64	-14,248.64
2012 Feb	58,638	HWA	71,355.49	-12,717.49
2012 Mar	72,210	HWA	85,065.03	-12,855.03
2012 Apr	87,406	HWA	91,856.17	-4,450.17
2012 May	96,946	HWA	88,509.68	8,436.32
2012 Jun	115,885	HWA	96,251.17	19,633.83
2012 Jul	139,695	HWA	122,671.40	17,023.60
2012 Aug	194,368	HWA	180,658.87	13,709.13
2012 Sep	127,610	HWA	123,834.23	3,775.77
2012 Oct	89,649	HWA	98,938.30	-9,289.30
2012 Nov	58,900	HWA	63,863.27	-4,963.27
2012 Dec	51,122	HWA	62,446.85	-11,324.85
2013 Jan	50,313	HWA	50,368.78	-55.78
2013 Feb	58,615	HWA	59,554.50	-939.50
2013 Mar	92,426	HWA	74,625.75	17,800.25
2013 Apr	100,996	HWA	102,569.92	-1,573.92
2013 May	123,431	HWA	101,578.70	21,852.30
2013 Jun	143,946	HWA	120,963.16	22,982.84
2013 Jul	171,016	HWA	145,347.71	25,668.29
2013 Aug	252,423	HWA	209,795.29	42,627.71
2013 Sep	158,839	HWA	151,184.81	7,654.19
2013 Oct	109,956	HWA	119,953.91	-9,997.91
2013 Nov	82,040	HWA	85,348.66	-3,308.66
2013 Dec	72,692	HWA	80,783.91	-8,091.91
2014 Jan	56,872	HWA	75,274.45	-18,402.45
2014 Feb	64,346	HWA	79,969.15	-15,623.15
2014 Mar	102,852	HWA	103,510.07	-658.07
2014 Apr	151,151	HWA	113,525.53	37,625.47
2014 May	148,593	HWA	137,302.49	11,290.51
2014 Jun	154,231	HWA	156,854.99	-2,623.99
2014 Jul	194,227	HWA	178,240.09	15,986.91
2014 Aug	303,902	HWA	251,405.81	52,496.19
2014 Sep	186,247	HWA	172,404.40	13,842.60
2014 Oct	133,884	HWA	129,452.21	4,431.79
2014 Nov	86,161	HWA	102,828.43	-16,667.43
2014 Dec	81,830	HWA	91,002.59	-9,172.59
2015 Jan	68,436	HWA	77,197.63	-8,761.63
2015 Feb	84,417	HWA	84,936.34	-519.34
2015 Mar	116,291	HWA	122,750.00	-6,459.00
2015 Apr	145,183	HWA	159,939.20	-14,756.20
2015 May	172,016	HWA	155,226.67	16,789.33
2015 Jun	182,765	HWA	165,782.26	16,982.74
2015 Jul	238,708	HWA	205,085.64	33,622.36
2015 Aug	358,044	HWA	311,506.42	46,537.58
2015 Sep	216,474	HWA	204,218.78	12,255.22
2015 Oct	148,376	HWA	153,389.32	-5,013.32
2015 Nov	99,794	HWA	107,640.94	-7,846.94
2015 Dec	93,804	HWA	103,197.90	-9,393.90
2016 Jan	74,572	HWA	89,453.80	-14,881.80
2016 Feb	97,522	HWA	103,005.39	-5,483.39
2016 Mar	144,216	HWA	135,126.50	9,089.50
2016 Apr	153,386	HWA	168,787.77	-15,401.77
2016 May	168,235	HWA	191,593.13	-23,358.13
2016 Jun	215,800	HWA	196,130.88	19,669.12
2016 Jul	271,212	HWA	252,000.97	19,211.03
2016 Aug	380,776	HWA	369,687.13	11,088.87
2016 Sep	249,098	HWA	228,348.64	20,749.36
2016 Oct	175,862	HWA	163,631.71	12,230.29
2016 Nov	102,775	HWA	117,360.10	-14,585.10
2016 Dec	100,859	HWA	110,576.33	-9,717.33
2017 Jan	83,249	HWA	91,760.83	-8,511.83
2017 Feb	105,210	HWA	114,323.72	-9,113.72
2017 Mar	121,167	HWA	158,890.65	-37,723.65
2017 Apr	217,906	HWA	164,511.77	53,394.23
2017 May	196,622	HWA	188,934.10	7,687.90
2017 Jun	248,582	HWA	235,316.59	13,265.41
2017 Jul	323,496	HWA	290,781.15	32,714.85
2017 Aug	431,571	HWA	403,779.24	27,791.76
2017 Sep	287,242	HWA	273,829.24	13,412.76
2017 Oct	212,357	HWA	201,373.27	10,983.73
2017 Nov	127,745	HWA	131,951.25	-4,206.25
2017 Dec	132,238	HWA	131,206.81	1,031.19
2018 Jan	95,453	HWA	115,406.24	-19,953.24
2018 Feb	120,303	HWA	136,260.99	-15,957.99
2018 Mar	162,886	HWA	154,780.56	8,105.44
2018 Apr	187,186	HWA	247,501.33	-60,315.33
2018 May	239,851	HWA	218,098.07	21,752.93
2018 Jun	264,588	HWA	271,506.93	-6,918.93
2018 Jul	339,564	HWA	341,400.45	-1,836.45
2018 Aug	446,375	HWA	446,351.68	23.32
2018 Sep	304,516	HWA	300,841.13	3,674.87
2018 Oct	230,827	HWA	225,019.23	5,807.77
2018 Nov	149,080	HWA	141,911.22	7,168.78
2018 Dec	135,316	HWA	146,509.94	-11,193.94
2019 Jan	114,710	HWA	110,905.90	3,804.10
2019 Feb	122,635	HWA	137,308.79	-14,673.79
2019 Mar	172,412	HWA	176,318.52	-3,906.52
2019 Apr	241,790	HWA	208,270.49	33,519.51
2019 May	259,714	HWA	258,423.75	1,290.25
2019 Jun	306,048	HWA	285,975.83	20,072.17
2019 Jul	360,566	HWA	363,012.22	-2,446.22
2019 Aug	484,403	HWA	469,598.06	14,804.94
2019 Sep	327,937	HWA	329,009.32	-1,072.32
2019 Oct	238,677	HWA	254,700.56	-16,023.56
2019 Nov	171,296	HWA	170,663.02	632.98
2019 Dec	138,642	HWA	159,495.37	-20,853.37
2020 Jan	126,349	HWA	135,444.09	-9,095.09
2020 Feb	167,411	HWA	145,177.77	22,233.23
2020 Mar	70,530	HWA	197,064.30	-126,534.30
2020 Apr	13,892	HWA	247,561.16	-233,669.16
2020 May	38,343	HWA	205,108.49	-166,765.49
2020 Jun	159,738	HWA	169,137.80	-9,399.80
2020 Jul	272,786	HWA	220,635.11	52,150.89
2020 Aug	407,020	HWA	358,619.34	48,400.66
2020 Sep	258,651	HWA	217,049.62	41,601.38
2020 Oct	167,448	HWA	142,526.44	24,921.56
2020 Nov	73,734	HWA	78,607.17	-4,873.17
2020 Dec	73,353	HWA	48,004.76	25,348.24
2021 Jan	48,435	HWA	42,783.94	5,651.06
2021 Feb	40,443	HWA	77,416.03	-36,973.03
2021 Mar	60,251	HWA	60,364.38	-113.38
2021 Apr	85,179	HWA	83,561.45	1,617.55
2021 May	169,690	HWA	93,303.62	76,386.38
2021 Jun	254,243	HWA	189,269.81	64,973.19
2021 Jul	329,058	HWA	287,838.06	41,219.94
2021 Aug	461,844	HWA	402,127.78	59,716.22
2021 Sep	308,273	HWA	377,932.45	-69,659.45
2021 Oct	250,949	HWA	267,714.94	-16,765.94
2021 Nov	156,624	HWA	213,711.40	-57,087.40
2021 Dec	115,100	HWA	149,691.92	-34,591.92
2022 Jan	96,107	HWA	101,380.63	-5,273.63
2022 Feb	141,508	HWA	110,321.84	31,186.16
2022 Mar	167,854	HWA	159,954.32	7,899.68
2022 Apr	248,959	HWA	189,807.21	59,151.79
2022 May	258,413	HWA	257,735.56	677.44
2022 Jun	300,520	HWA	280,856.67	19,663.33
2010 Jan	53,653	HWA_log	52,753.15	899.85
2010 Feb	62,257	HWA_log	65,656.67	-3,399.67
2010 Mar	77,588	HWA_log	85,637.03	-8,049.03
2010 Apr	99,982	HWA_log	103,395.72	-3,413.72
2010 May	101,387	HWA_log	100,731.62	655.38
2010 Jun	108,611	HWA_log	102,203.18	6,407.82
2010 Jul	126,498	HWA_log	120,886.07	5,611.93
2010 Aug	178,380	HWA_log	175,361.37	3,018.63
2010 Sep	127,822	HWA_log	116,630.76	11,191.24
2010 Oct	104,174	HWA_log	91,971.38	12,202.62
2010 Nov	69,271	HWA_log	73,948.83	-4,677.83
2010 Dec	62,935	HWA_log	65,257.15	-2,322.15
2011 Jan	60,457	HWA_log	54,674.66	5,782.34
2011 Feb	67,260	HWA_log	68,721.53	-1,461.53
2011 Mar	83,464	HWA_log	87,941.87	-4,477.87
2011 Apr	102,958	HWA_log	108,160.39	-5,202.39
2011 May	101,223	HWA_log	105,549.39	-4,326.39
2011 Jun	120,148	HWA_log	105,862.46	14,285.54
2011 Jul	136,999	HWA_log	126,788.41	10,210.59
2011 Aug	212,668	HWA_log	182,467.94	30,200.06
2011 Sep	129,606	HWA_log	123,641.93	5,964.07
2011 Oct	101,185	HWA_log	97,070.72	4,114.28
2011 Nov	62,121	HWA_log	77,393.15	-15,272.15
2011 Dec	65,563	HWA_log	67,873.58	-2,310.58
2012 Jan	49,716	HWA_log	57,739.90	-8,023.90
2012 Feb	58,638	HWA_log	70,402.72	-11,764.72
2012 Mar	72,210	HWA_log	90,162.60	-17,952.60
2012 Apr	87,406	HWA_log	109,711.20	-22,305.20
2012 May	96,946	HWA_log	106,829.91	-9,883.91
2012 Jun	115,885	HWA_log	109,254.32	6,630.68
2012 Jul	139,695	HWA_log	130,601.92	9,093.08
2012 Aug	194,368	HWA_log	186,732.07	7,635.93
2012 Sep	127,610	HWA_log	125,267.24	2,342.76
2012 Oct	89,649	HWA_log	99,514.19	-9,865.19
2012 Nov	58,900	HWA_log	76,045.82	-17,145.82
2012 Dec	51,122	HWA_log	67,803.59	-16,681.59
2013 Jan	50,313	HWA_log	56,262.06	-5,949.06
2013 Feb	58,615	HWA_log	68,489.90	-9,874.90
2013 Mar	92,426	HWA_log	75,504.22	16,921.78
2013 Apr	100,996	HWA_log	105,160.07	-4,164.07
2013 May	123,431	HWA_log	103,770.98	19,660.02
2013 Jun	143,946	HWA_log	112,520.23	31,425.77
2013 Jul	171,016	HWA_log	133,326.54	37,689.46
2013 Aug	252,423	HWA_log	193,058.62	59,364.38
2013 Sep	158,839	HWA_log	128,076.74	30,762.26
2013 Oct	109,956	HWA_log	101,750.91	8,205.09
2013 Nov	82,040	HWA_log	77,031.07	5,008.93
2013 Dec	72,692	HWA_log	69,026.64	3,665.36
2014 Jan	56,872	HWA_log	57,246.99	-374.99
2014 Feb	64,346	HWA_log	71,995.12	-7,649.12
2014 Mar	102,852	HWA_log	92,880.20	9,971.80
2014 Apr	151,151	HWA_log	113,785.85	37,365.15
2014 May	148,593	HWA_log	115,079.13	33,513.87
2014 Jun	154,231	HWA_log	160,771.25	-6,540.25
2014 Jul	194,227	HWA_log	180,205.28	14,021.72
2014 Aug	303,902	HWA_log	267,002.85	36,899.15
2014 Sep	186,247	HWA_log	171,377.08	14,869.92
2014 Oct	133,884	HWA_log	125,221.91	8,662.09
2014 Nov	86,161	HWA_log	91,065.95	-4,904.95
2014 Dec	81,830	HWA_log	81,654.58	175.42
2015 Jan	68,436	HWA_log	69,474.47	-1,038.47
2015 Feb	84,417	HWA_log	80,693.70	3,723.30
2015 Mar	116,291	HWA_log	122,337.43	-6,046.43
2015 Apr	145,183	HWA_log	153,539.97	-8,356.97
2015 May	172,016	HWA_log	159,475.52	12,540.48
2015 Jun	182,765	HWA_log	175,982.15	6,782.85
2015 Jul	238,708	HWA_log	214,419.81	24,288.19
2015 Aug	358,044	HWA_log	324,451.96	33,592.04
2015 Sep	216,474	HWA_log	203,604.07	12,869.93
2015 Oct	148,376	HWA_log	146,955.90	1,420.10
2015 Nov	99,794	HWA_log	98,868.78	925.22
2015 Dec	93,804	HWA_log	91,780.15	2,023.85
2016 Jan	74,572	HWA_log	77,565.02	-2,993.02
2016 Feb	97,522	HWA_log	93,218.88	4,303.12
2016 Mar	144,216	HWA_log	134,511.00	9,705.00
2016 Apr	153,386	HWA_log	173,835.10	-20,449.10
2016 May	168,235	HWA_log	189,018.97	-20,783.97
2016 Jun	215,800	HWA_log	197,572.16	18,227.84
2016 Jul	271,212	HWA_log	252,286.33	18,925.67
2016 Aug	380,776	HWA_log	377,425.47	3,350.53
2016 Sep	249,098	HWA_log	229,127.06	19,970.94
2016 Oct	175,862	HWA_log	161,926.46	13,935.54
2016 Nov	102,775	HWA_log	110,318.25	-7,543.25
2016 Dec	100,859	HWA_log	101,694.03	-835.03
2017 Jan	83,249	HWA_log	83,033.07	215.93
2017 Feb	105,210	HWA_log	104,460.63	749.37
2017 Mar	121,167	HWA_log	151,638.08	-30,471.08
2017 Apr	217,906	HWA_log	168,925.61	48,980.39
2017 May	196,622	HWA_log	198,190.56	-1,568.56
2017 Jun	248,582	HWA_log	232,094.33	16,487.67
2017 Jul	323,496	HWA_log	292,636.99	30,859.01
2017 Aug	431,571	HWA_log	427,140.03	4,430.97
2017 Sep	287,242	HWA_log	271,708.71	15,533.29
2017 Oct	212,357	HWA_log	192,234.89	20,122.11
2017 Nov	127,745	HWA_log	120,442.89	7,302.11
2017 Dec	132,238	HWA_log	119,311.91	12,926.09
2018 Jan	95,453	HWA_log	100,460.51	-5,007.51
2018 Feb	120,303	HWA_log	125,595.82	-5,292.82
2018 Mar	162,886	HWA_log	161,839.92	1,046.08
2018 Apr	187,186	HWA_log	238,149.87	-50,963.87
2018 May	239,851	HWA_log	227,810.06	12,040.94
2018 Jun	264,588	HWA_log	277,696.10	-13,108.10
2018 Jul	339,564	HWA_log	350,100.04	-10,536.04
2018 Aug	446,375	HWA_log	479,871.87	-33,496.87
2018 Sep	304,516	HWA_log	307,199.48	-2,683.48
2018 Oct	230,827	HWA_log	219,486.30	11,340.70
2018 Nov	149,080	HWA_log	132,687.13	16,392.87
2018 Dec	135,316	HWA_log	135,743.75	-427.75
2019 Jan	114,710	HWA_log	104,335.55	10,374.45
2019 Feb	122,635	HWA_log	134,504.51	-11,869.51
2019 Mar	172,412	HWA_log	176,234.20	-3,822.20
2019 Apr	241,790	HWA_log	227,942.24	13,847.76
2019 May	259,714	HWA_log	262,749.32	-3,035.32
2019 Jun	306,048	HWA_log	303,826.42	2,221.58
2019 Jul	360,566	HWA_log	390,160.25	-29,594.25
2019 Aug	484,403	HWA_log	519,572.72	-35,169.72
2019 Sep	327,937	HWA_log	341,627.00	-13,690.00
2019 Oct	238,677	HWA_log	249,038.73	-10,361.73
2019 Nov	171,296	HWA_log	155,567.76	15,728.24
2019 Dec	138,642	HWA_log	148,550.43	-9,908.43
2020 Jan	126,349	HWA_log	116,635.56	9,713.44
2020 Feb	167,411	HWA_log	138,828.74	28,582.26
2020 Mar	70,530	HWA_log	197,572.58	-127,042.58
2020 Apr	13,892	HWA_log	222,092.11	-208,200.11
2020 May	38,343	HWA_log	11,847.53	26,495.47
2020 Jun	159,738	HWA_log	39,498.38	120,239.62
2020 Jul	272,786	HWA_log	118,239.91	154,546.09
2020 Aug	407,020	HWA_log	223,174.55	183,845.45
2020 Sep	258,651	HWA_log	204,737.39	53,913.61
2020 Oct	167,448	HWA_log	168,634.03	-1,186.03
2020 Nov	73,734	HWA_log	111,629.18	-37,895.18
2020 Dec	73,353	HWA_log	76,022.26	-2,669.26
2021 Jan	48,435	HWA_log	66,367.05	-17,932.05
2021 Feb	40,443	HWA_log	68,246.31	-27,803.31
2021 Mar	60,251	HWA_log	37,186.80	23,064.20
2021 Apr	85,179	HWA_log	56,631.76	28,547.24
2021 May	169,690	HWA_log	109,140.93	60,549.07
2021 Jun	254,243	HWA_log	204,714.46	49,528.54
2021 Jul	329,058	HWA_log	278,703.13	50,354.87
2021 Aug	461,844	HWA_log	415,111.09	46,732.91
2021 Sep	308,273	HWA_log	305,208.84	3,064.16
2021 Oct	250,949	HWA_log	226,053.82	24,895.18
2021 Nov	156,624	HWA_log	164,561.24	-7,937.24
2021 Dec	115,100	HWA_log	145,839.24	-30,739.24
2022 Jan	96,107	HWA_log	100,871.28	-4,764.28
2022 Feb	141,508	HWA_log	119,110.38	22,397.62
2022 Mar	167,854	HWA_log	189,534.79	-21,680.79
2022 Apr	248,959	HWA_log	211,531.49	37,427.51
2022 May	258,413	HWA_log	347,966.17	-89,553.17
2022 Jun	300,520	HWA_log	303,339.82	-2,819.82
2010 Jan	53,653	Naive	59,473.00	-5,820.00
2010 Feb	62,257	Naive	53,653.00	8,604.00
2010 Mar	77,588	Naive	62,257.00	15,331.00
2010 Apr	99,982	Naive	77,588.00	22,394.00
2010 May	101,387	Naive	99,982.00	1,405.00
2010 Jun	108,611	Naive	101,387.00	7,224.00
2010 Jul	126,498	Naive	108,611.00	17,887.00
2010 Aug	178,380	Naive	126,498.00	51,882.00
2010 Sep	127,822	Naive	178,380.00	-50,558.00
2010 Oct	104,174	Naive	127,822.00	-23,648.00
2010 Nov	69,271	Naive	104,174.00	-34,903.00
2010 Dec	62,935	Naive	69,271.00	-6,336.00
2011 Jan	60,457	Naive	62,935.00	-2,478.00
2011 Feb	67,260	Naive	60,457.00	6,803.00
2011 Mar	83,464	Naive	67,260.00	16,204.00
2011 Apr	102,958	Naive	83,464.00	19,494.00
2011 May	101,223	Naive	102,958.00	-1,735.00
2011 Jun	120,148	Naive	101,223.00	18,925.00
2011 Jul	136,999	Naive	120,148.00	16,851.00
2011 Aug	212,668	Naive	136,999.00	75,669.00
2011 Sep	129,606	Naive	212,668.00	-83,062.00
2011 Oct	101,185	Naive	129,606.00	-28,421.00
2011 Nov	62,121	Naive	101,185.00	-39,064.00
2011 Dec	65,563	Naive	62,121.00	3,442.00
2012 Jan	49,716	Naive	65,563.00	-15,847.00
2012 Feb	58,638	Naive	49,716.00	8,922.00
2012 Mar	72,210	Naive	58,638.00	13,572.00
2012 Apr	87,406	Naive	72,210.00	15,196.00
2012 May	96,946	Naive	87,406.00	9,540.00
2012 Jun	115,885	Naive	96,946.00	18,939.00
2012 Jul	139,695	Naive	115,885.00	23,810.00
2012 Aug	194,368	Naive	139,695.00	54,673.00
2012 Sep	127,610	Naive	194,368.00	-66,758.00
2012 Oct	89,649	Naive	127,610.00	-37,961.00
2012 Nov	58,900	Naive	89,649.00	-30,749.00
2012 Dec	51,122	Naive	58,900.00	-7,778.00
2013 Jan	50,313	Naive	51,122.00	-809.00
2013 Feb	58,615	Naive	50,313.00	8,302.00
2013 Mar	92,426	Naive	58,615.00	33,811.00
2013 Apr	100,996	Naive	92,426.00	8,570.00
2013 May	123,431	Naive	100,996.00	22,435.00
2013 Jun	143,946	Naive	123,431.00	20,515.00
2013 Jul	171,016	Naive	143,946.00	27,070.00
2013 Aug	252,423	Naive	171,016.00	81,407.00
2013 Sep	158,839	Naive	252,423.00	-93,584.00
2013 Oct	109,956	Naive	158,839.00	-48,883.00
2013 Nov	82,040	Naive	109,956.00	-27,916.00
2013 Dec	72,692	Naive	82,040.00	-9,348.00
2014 Jan	56,872	Naive	72,692.00	-15,820.00
2014 Feb	64,346	Naive	56,872.00	7,474.00
2014 Mar	102,852	Naive	64,346.00	38,506.00
2014 Apr	151,151	Naive	102,852.00	48,299.00
2014 May	148,593	Naive	151,151.00	-2,558.00
2014 Jun	154,231	Naive	148,593.00	5,638.00
2014 Jul	194,227	Naive	154,231.00	39,996.00
2014 Aug	303,902	Naive	194,227.00	109,675.00
2014 Sep	186,247	Naive	303,902.00	-117,655.00
2014 Oct	133,884	Naive	186,247.00	-52,363.00
2014 Nov	86,161	Naive	133,884.00	-47,723.00
2014 Dec	81,830	Naive	86,161.00	-4,331.00
2015 Jan	68,436	Naive	81,830.00	-13,394.00
2015 Feb	84,417	Naive	68,436.00	15,981.00
2015 Mar	116,291	Naive	84,417.00	31,874.00
2015 Apr	145,183	Naive	116,291.00	28,892.00
2015 May	172,016	Naive	145,183.00	26,833.00
2015 Jun	182,765	Naive	172,016.00	10,749.00
2015 Jul	238,708	Naive	182,765.00	55,943.00
2015 Aug	358,044	Naive	238,708.00	119,336.00
2015 Sep	216,474	Naive	358,044.00	-141,570.00
2015 Oct	148,376	Naive	216,474.00	-68,098.00
2015 Nov	99,794	Naive	148,376.00	-48,582.00
2015 Dec	93,804	Naive	99,794.00	-5,990.00
2016 Jan	74,572	Naive	93,804.00	-19,232.00
2016 Feb	97,522	Naive	74,572.00	22,950.00
2016 Mar	144,216	Naive	97,522.00	46,694.00
2016 Apr	153,386	Naive	144,216.00	9,170.00
2016 May	168,235	Naive	153,386.00	14,849.00
2016 Jun	215,800	Naive	168,235.00	47,565.00
2016 Jul	271,212	Naive	215,800.00	55,412.00
2016 Aug	380,776	Naive	271,212.00	109,564.00
2016 Sep	249,098	Naive	380,776.00	-131,678.00
2016 Oct	175,862	Naive	249,098.00	-73,236.00
2016 Nov	102,775	Naive	175,862.00	-73,087.00
2016 Dec	100,859	Naive	102,775.00	-1,916.00
2017 Jan	83,249	Naive	100,859.00	-17,610.00
2017 Feb	105,210	Naive	83,249.00	21,961.00
2017 Mar	121,167	Naive	105,210.00	15,957.00
2017 Apr	217,906	Naive	121,167.00	96,739.00
2017 May	196,622	Naive	217,906.00	-21,284.00
2017 Jun	248,582	Naive	196,622.00	51,960.00
2017 Jul	323,496	Naive	248,582.00	74,914.00
2017 Aug	431,571	Naive	323,496.00	108,075.00
2017 Sep	287,242	Naive	431,571.00	-144,329.00
2017 Oct	212,357	Naive	287,242.00	-74,885.00
2017 Nov	127,745	Naive	212,357.00	-84,612.00
2017 Dec	132,238	Naive	127,745.00	4,493.00
2018 Jan	95,453	Naive	132,238.00	-36,785.00
2018 Feb	120,303	Naive	95,453.00	24,850.00
2018 Mar	162,886	Naive	120,303.00	42,583.00
2018 Apr	187,186	Naive	162,886.00	24,300.00
2018 May	239,851	Naive	187,186.00	52,665.00
2018 Jun	264,588	Naive	239,851.00	24,737.00
2018 Jul	339,564	Naive	264,588.00	74,976.00
2018 Aug	446,375	Naive	339,564.00	106,811.00
2018 Sep	304,516	Naive	446,375.00	-141,859.00
2018 Oct	230,827	Naive	304,516.00	-73,689.00
2018 Nov	149,080	Naive	230,827.00	-81,747.00
2018 Dec	135,316	Naive	149,080.00	-13,764.00
2019 Jan	114,710	Naive	135,316.00	-20,606.00
2019 Feb	122,635	Naive	114,710.00	7,925.00
2019 Mar	172,412	Naive	122,635.00	49,777.00
2019 Apr	241,790	Naive	172,412.00	69,378.00
2019 May	259,714	Naive	241,790.00	17,924.00
2019 Jun	306,048	Naive	259,714.00	46,334.00
2019 Jul	360,566	Naive	306,048.00	54,518.00
2019 Aug	484,403	Naive	360,566.00	123,837.00
2019 Sep	327,937	Naive	484,403.00	-156,466.00
2019 Oct	238,677	Naive	327,937.00	-89,260.00
2019 Nov	171,296	Naive	238,677.00	-67,381.00
2019 Dec	138,642	Naive	171,296.00	-32,654.00
2020 Jan	126,349	Naive	138,642.00	-12,293.00
2020 Feb	167,411	Naive	126,349.00	41,062.00
2020 Mar	70,530	Naive	167,411.00	-96,881.00
2020 Apr	13,892	Naive	70,530.00	-56,638.00
2020 May	38,343	Naive	13,892.00	24,451.00
2020 Jun	159,738	Naive	38,343.00	121,395.00
2020 Jul	272,786	Naive	159,738.00	113,048.00
2020 Aug	407,020	Naive	272,786.00	134,234.00
2020 Sep	258,651	Naive	407,020.00	-148,369.00
2020 Oct	167,448	Naive	258,651.00	-91,203.00
2020 Nov	73,734	Naive	167,448.00	-93,714.00
2020 Dec	73,353	Naive	73,734.00	-381.00
2021 Jan	48,435	Naive	73,353.00	-24,918.00
2021 Feb	40,443	Naive	48,435.00	-7,992.00
2021 Mar	60,251	Naive	40,443.00	19,808.00
2021 Apr	85,179	Naive	60,251.00	24,928.00
2021 May	169,690	Naive	85,179.00	84,511.00
2021 Jun	254,243	Naive	169,690.00	84,553.00
2021 Jul	329,058	Naive	254,243.00	74,815.00
2021 Aug	461,844	Naive	329,058.00	132,786.00
2021 Sep	308,273	Naive	461,844.00	-153,571.00
2021 Oct	250,949	Naive	308,273.00	-57,324.00
2021 Nov	156,624	Naive	250,949.00	-94,325.00
2021 Dec	115,100	Naive	156,624.00	-41,524.00
2022 Jan	96,107	Naive	115,100.00	-18,993.00
2022 Feb	141,508	Naive	96,107.00	45,401.00
2022 Mar	167,854	Naive	141,508.00	26,346.00
2022 Apr	248,959	Naive	167,854.00	81,105.00
2022 May	258,413	Naive	248,959.00	9,454.00
2022 Jun	300,520	Naive	258,413.00	42,107.00
2010 Jan	53,653	Naive_log	61,333.28	-7,680.28
2010 Feb	62,257	Naive_log	55,319.62	6,937.38
2010 Mar	77,588	Naive_log	64,180.59	13,407.41
2010 Apr	99,982	Naive_log	79,981.04	20,000.96
2010 May	101,387	Naive_log	103,066.80	-1,679.80
2010 Jun	108,611	Naive_log	104,490.00	4,121.00
2010 Jul	126,498	Naive_log	111,910.56	14,587.44
2010 Aug	178,380	Naive_log	130,322.13	48,057.87
2010 Sep	127,822	Naive_log	183,813.06	-55,991.06
2010 Oct	104,174	Naive_log	131,740.22	-27,566.22
2010 Nov	69,271	Naive_log	107,359.46	-38,088.46
2010 Dec	62,935	Naive_log	71,417.25	-8,482.25
2011 Jan	60,457	Naive_log	64,872.27	-4,415.27
2011 Feb	67,260	Naive_log	62,304.26	4,955.74
2011 Mar	83,464	Naive_log	69,302.55	14,161.45
2011 Apr	102,958	Naive_log	85,994.23	16,963.77
2011 May	101,223	Naive_log	106,072.87	-4,849.87
2011 Jun	120,148	Naive_log	104,262.97	15,885.03
2011 Jul	136,999	Naive_log	123,742.88	13,256.12
2011 Aug	212,668	Naive_log	141,076.91	71,591.09
2011 Sep	129,606	Naive_log	219,100.68	-89,494.68
2011 Oct	101,185	Naive_log	133,611.78	-32,426.78
2011 Nov	62,121	Naive_log	104,312.17	-42,191.17
2011 Dec	65,563	Naive_log	64,079.42	1,483.58
2012 Jan	49,716	Naive_log	67,616.15	-17,900.15
2012 Feb	58,638	Naive_log	51,275.29	7,362.71
2012 Mar	72,210	Naive_log	60,469.95	11,740.05
2012 Apr	87,406	Naive_log	74,461.22	12,944.78
2012 May	96,946	Naive_log	90,123.28	6,822.72
2012 Jun	115,885	Naive_log	99,943.01	15,941.99
2012 Jul	139,695	Naive_log	119,455.84	20,239.16
2012 Aug	194,368	Naive_log	143,987.07	50,380.93
2012 Sep	127,610	Naive_log	200,370.54	-72,760.54
2012 Oct	89,649	Naive_log	131,599.29	-41,950.29
2012 Nov	58,900	Naive_log	92,469.77	-33,569.77
2012 Dec	51,122	Naive_log	60,774.98	-9,652.98
2013 Jan	50,313	Naive_log	52,742.19	-2,429.19
2013 Feb	58,615	Naive_log	51,897.37	6,717.63
2013 Mar	92,426	Naive_log	60,453.40	31,972.60
2013 Apr	100,996	Naive_log	95,367.16	5,628.84
2013 May	123,431	Naive_log	104,192.16	19,238.84
2013 Jun	143,946	Naive_log	127,328.25	16,617.75
2013 Jul	171,016	Naive_log	148,473.34	22,542.66
2013 Aug	252,423	Naive_log	176,377.20	76,045.80
2013 Sep	158,839	Naive_log	260,405.07	-101,566.07
2013 Oct	109,956	Naive_log	163,935.06	-53,979.06
2013 Nov	82,040	Naive_log	113,507.43	-31,467.43
2013 Dec	72,692	Naive_log	84,695.02	-12,003.02
2014 Jan	56,872	Naive_log	75,033.59	-18,161.59
2014 Feb	64,346	Naive_log	58,703.28	5,642.72
2014 Mar	102,852	Naive_log	66,408.58	36,443.42
2014 Apr	151,151	Naive_log	106,196.03	44,954.97
2014 May	148,593	Naive_log	156,102.14	-7,509.14
2014 Jun	154,231	Naive_log	153,432.18	798.82
2014 Jul	194,227	Naive_log	159,225.38	35,001.62
2014 Aug	303,902	Naive_log	200,510.07	103,391.93
2014 Sep	186,247	Naive_log	313,850.80	-127,603.80
2014 Oct	133,884	Naive_log	192,436.35	-58,552.35
2014 Nov	86,161	Naive_log	138,349.30	-52,188.30
2014 Dec	81,830	Naive_log	89,065.52	-7,235.52
2015 Jan	68,436	Naive_log	84,573.71	-16,137.71
2015 Feb	84,417	Naive_log	70,723.95	13,693.05
2015 Mar	116,291	Naive_log	87,233.90	29,057.10
2015 Apr	145,183	Naive_log	120,182.96	25,000.04
2015 May	172,016	Naive_log	150,034.88	21,981.12
2015 Jun	182,765	Naive_log	177,746.82	5,018.18
2015 Jul	238,708	Naive_log	188,822.83	49,885.17
2015 Aug	358,044	Naive_log	246,623.30	111,420.70
2015 Sep	216,474	Naive_log	370,010.22	-153,536.22
2015 Oct	148,376	Naive_log	223,816.08	-75,440.08
2015 Nov	99,794	Naive_log	153,437.80	-53,643.80
2015 Dec	93,804	Naive_log	103,221.84	-9,417.84
2016 Jan	74,572	Naive_log	97,010.16	-22,438.16
2016 Feb	97,522	Naive_log	77,117.77	20,404.23
2016 Mar	144,216	Naive_log	100,852.19	43,363.81
2016 Apr	153,386	Naive_log	149,172.20	4,213.80
2016 May	168,235	Naive_log	158,631.81	9,603.19
2016 Jun	215,800	Naive_log	173,962.95	41,837.05
2016 Jul	271,212	Naive_log	223,144.07	48,067.93
2016 Aug	380,776	Naive_log	280,431.00	100,345.00
2016 Sep	249,098	Naive_log	393,764.39	-144,666.39
2016 Oct	175,862	Naive_log	257,664.48	-81,802.48
2016 Nov	102,775	Naive_log	181,932.83	-79,157.83
2016 Dec	100,859	Naive_log	106,378.67	-5,519.67
2017 Jan	83,249	Naive_log	104,378.16	-21,129.16
2017 Feb	105,210	Naive_log	86,146.99	19,063.01
2017 Mar	121,167	Naive_log	108,868.67	12,298.33
2017 Apr	217,906	Naive_log	125,365.99	92,540.01
2017 May	196,622	Naive_log	225,602.25	-28,980.25
2017 Jun	248,582	Naive_log	203,538.12	45,043.88
2017 Jul	323,496	Naive_log	257,316.66	66,179.34
2017 Aug	431,571	Naive_log	334,862.30	96,708.70
2017 Sep	287,242	Naive_log	446,747.71	-159,505.71
2017 Oct	212,357	Naive_log	297,407.84	-85,050.84
2017 Nov	127,745	Naive_log	219,882.77	-92,137.77
2017 Dec	132,238	Naive_log	132,328.12	-90.12
2018 Jan	95,453	Naive_log	136,960.62	-41,507.62
2018 Feb	120,303	Naive_log	98,869.61	21,433.39
2018 Mar	162,886	Naive_log	124,604.08	38,281.92
2018 Apr	187,186	Naive_log	168,717.11	18,468.89
2018 May	239,851	Naive_log	193,864.68	45,986.32
2018 Jun	264,588	Naive_log	248,403.34	16,184.66
2018 Jul	339,564	Naive_log	273,985.46	65,578.54
2018 Aug	446,375	Naive_log	351,617.68	94,757.32
2018 Sep	304,516	Naive_log	462,224.02	-157,708.02
2018 Oct	230,827	Naive_log	315,379.31	-84,552.31
2018 Nov	149,080	Naive_log	239,064.30	-89,984.30
2018 Dec	135,316	Naive_log	154,439.58	-19,123.58
2019 Jan	114,710	Naive_log	140,162.11	-25,452.11
2019 Feb	122,635	Naive_log	118,806.99	3,828.01
2019 Mar	172,412	Naive_log	126,997.11	45,414.89
2019 Apr	241,790	Naive_log	178,561.51	63,228.49
2019 May	259,714	Naive_log	250,436.57	9,277.43
2019 Jun	306,048	Naive_log	268,964.37	37,083.63
2019 Jul	360,566	Naive_log	316,919.59	43,646.41
2019 Aug	484,403	Naive_log	373,340.17	111,062.83
2019 Sep	327,937	Naive_log	501,581.30	-173,644.30
2019 Oct	238,677	Naive_log	339,623.02	-100,946.02
2019 Nov	171,296	Naive_log	247,197.18	-75,901.18
2019 Dec	138,642	Naive_log	177,424.75	-38,782.75
2020 Jan	126,349	Naive_log	143,594.65	-17,245.65
2020 Feb	167,411	Naive_log	130,845.98	36,565.02
2020 Mar	70,530	Naive_log	173,372.23	-102,842.23
2020 Apr	13,892	Naive_log	73,139.96	-59,247.96
2020 May	38,343	Naive_log	14,479.41	23,863.59
2020 Jun	159,738	Naive_log	40,038.65	119,699.35
2020 Jul	272,786	Naive_log	167,437.09	105,348.91
2020 Aug	407,020	Naive_log	286,039.14	120,980.86
2020 Sep	258,651	Naive_log	426,846.70	-168,195.70
2020 Oct	167,448	Naive_log	271,306.76	-103,858.76
2020 Nov	73,734	Naive_log	175,671.87	-101,937.87
2020 Dec	73,353	Naive_log	77,440.02	-4,087.02
2021 Jan	48,435	Naive_log	77,025.19	-28,590.19
2021 Feb	40,443	Naive_log	50,866.68	-10,423.68
2021 Mar	60,251	Naive_log	42,468.01	17,782.99
2021 Apr	85,179	Naive_log	63,274.79	21,904.21
2021 May	169,690	Naive_log	89,457.09	80,232.91
2021 Jun	254,243	Naive_log	178,336.78	75,906.22
2021 Jul	329,058	Naive_log	267,228.74	61,829.26
2021 Aug	461,844	Naive_log	345,842.28	116,001.72
2021 Sep	308,273	Naive_log	485,412.81	-177,139.81
2021 Oct	250,949	Naive_log	324,041.15	-73,092.15
2021 Nov	156,624	Naive_log	263,756.20	-107,132.20
2021 Dec	115,100	Naive_log	164,653.23	-49,553.23
2022 Jan	96,107	Naive_log	120,998.86	-24,891.86
2022 Feb	141,508	Naive_log	101,019.73	40,488.27
2022 Mar	167,854	Naive_log	148,754.18	19,099.82
2022 Apr	248,959	Naive_log	176,426.16	72,532.84
2022 May	258,413	Naive_log	261,697.95	-3,284.95
2022 Jun	300,520	Naive_log	271,587.03	28,932.97
2010 Jan	53,653	Prophet	59,604.17	-5,951.17
2010 Feb	62,257	Prophet	69,644.71	-7,387.71
2010 Mar	77,588	Prophet	84,455.44	-6,867.44
2010 Apr	99,982	Prophet	100,657.83	-675.83
2010 May	101,387	Prophet	98,390.38	2,996.62
2010 Jun	108,611	Prophet	100,945.57	7,665.43
2010 Jul	126,498	Prophet	117,755.55	8,742.45
2010 Aug	178,380	Prophet	161,455.76	16,924.24
2010 Sep	127,822	Prophet	111,981.69	15,840.31
2010 Oct	104,174	Prophet	92,843.44	11,330.56
2010 Nov	69,271	Prophet	79,794.43	-10,523.43
2010 Dec	62,935	Prophet	71,678.41	-8,743.41
2011 Jan	60,457	Prophet	62,444.87	-1,987.87
2011 Feb	67,260	Prophet	73,322.62	-6,062.62
2011 Mar	83,464	Prophet	87,958.11	-4,494.11
2011 Apr	102,958	Prophet	105,362.04	-2,404.04
2011 May	101,223	Prophet	103,030.48	-1,807.48
2011 Jun	120,148	Prophet	106,372.16	13,775.84
2011 Jul	136,999	Prophet	122,739.13	14,259.87
2011 Aug	212,668	Prophet	166,170.47	46,497.53
2011 Sep	129,606	Prophet	116,967.47	12,638.53
2011 Oct	101,185	Prophet	98,252.41	2,932.59
2011 Nov	62,121	Prophet	86,119.75	-23,998.75
2011 Dec	65,563	Prophet	77,838.98	-12,275.98
2012 Jan	49,716	Prophet	67,780.80	-18,064.80
2012 Feb	58,638	Prophet	78,722.64	-20,084.64
2012 Mar	72,210	Prophet	93,014.42	-20,804.42
2012 Apr	87,406	Prophet	108,242.03	-20,836.03
2012 May	96,946	Prophet	107,074.30	-10,128.30
2012 Jun	115,885	Prophet	108,817.94	7,067.06
2012 Jul	139,695	Prophet	124,278.44	15,416.56
2012 Aug	194,368	Prophet	169,567.29	24,800.71
2012 Sep	127,610	Prophet	121,575.62	6,034.38
2012 Oct	89,649	Prophet	100,975.04	-11,326.04
2012 Nov	58,900	Prophet	80,895.20	-21,995.20
2012 Dec	51,122	Prophet	74,264.80	-23,142.80
2013 Jan	50,313	Prophet	65,240.76	-14,927.76
2013 Feb	58,615	Prophet	76,364.10	-17,749.10
2013 Mar	92,426	Prophet	90,239.15	2,186.85
2013 Apr	100,996	Prophet	106,397.42	-5,401.42
2013 May	123,431	Prophet	105,456.69	17,974.31
2013 Jun	143,946	Prophet	110,665.70	33,280.30
2013 Jul	171,016	Prophet	128,489.55	42,526.45
2013 Aug	252,423	Prophet	177,801.65	74,621.35
2013 Sep	158,839	Prophet	127,526.64	31,312.36
2013 Oct	109,956	Prophet	106,710.59	3,245.41
2013 Nov	82,040	Prophet	86,979.84	-4,939.84
2013 Dec	72,692	Prophet	80,706.97	-8,014.97
2014 Jan	56,872	Prophet	72,178.58	-15,306.58
2014 Feb	64,346	Prophet	81,265.05	-16,919.05
2014 Mar	102,852	Prophet	97,190.52	5,661.48
2014 Apr	151,151	Prophet	114,365.39	36,785.61
2014 May	148,593	Prophet	116,567.10	32,025.90
2014 Jun	154,231	Prophet	124,561.95	29,669.05
2014 Jul	194,227	Prophet	144,011.47	50,215.53
2014 Aug	303,902	Prophet	199,136.88	104,765.12
2014 Sep	186,247	Prophet	148,794.11	37,452.89
2014 Oct	133,884	Prophet	128,955.27	4,928.73
2014 Nov	86,161	Prophet	109,537.19	-23,376.19
2014 Dec	81,830	Prophet	102,347.03	-20,517.03
2015 Jan	68,436	Prophet	93,686.33	-25,250.33
2015 Feb	84,417	Prophet	101,122.80	-16,705.80
2015 Mar	116,291	Prophet	117,025.46	-734.46
2015 Apr	145,183	Prophet	138,069.43	7,113.57
2015 May	172,016	Prophet	138,050.93	33,965.07
2015 Jun	182,765	Prophet	147,317.09	35,447.91
2015 Jul	238,708	Prophet	168,732.98	69,975.02
2015 Aug	358,044	Prophet	231,079.15	126,964.85
2015 Sep	216,474	Prophet	173,432.19	43,041.81
2015 Oct	148,376	Prophet	152,985.89	-4,609.89
2015 Nov	99,794	Prophet	136,104.03	-36,310.03
2015 Dec	93,804	Prophet	132,030.57	-38,226.57
2016 Jan	74,572	Prophet	121,419.84	-46,847.84
2016 Feb	97,522	Prophet	130,038.28	-32,516.28
2016 Mar	144,216	Prophet	144,804.09	-588.09
2016 Apr	153,386	Prophet	163,436.31	-10,050.31
2016 May	168,235	Prophet	168,115.48	119.52
2016 Jun	215,800	Prophet	176,306.84	39,493.16
2016 Jul	271,212	Prophet	197,207.35	74,004.65
2016 Aug	380,776	Prophet	250,270.41	130,505.59
2016 Sep	249,098	Prophet	202,292.61	46,805.39
2016 Oct	175,862	Prophet	178,158.54	-2,296.54
2016 Nov	102,775	Prophet	156,009.61	-53,234.61
2016 Dec	100,859	Prophet	147,045.24	-46,186.24
2017 Jan	83,249	Prophet	139,159.07	-55,910.07
2017 Feb	105,210	Prophet	144,924.25	-39,714.25
2017 Mar	121,167	Prophet	163,815.65	-42,648.65
2017 Apr	217,906	Prophet	178,964.97	38,941.03
2017 May	196,622	Prophet	185,776.36	10,845.64
2017 Jun	248,582	Prophet	196,218.74	52,363.26
2017 Jul	323,496	Prophet	222,905.79	100,590.21
2017 Aug	431,571	Prophet	289,402.32	142,168.68
2017 Sep	287,242	Prophet	231,316.06	55,925.94
2017 Oct	212,357	Prophet	204,387.40	7,969.60
2017 Nov	127,745	Prophet	177,015.01	-49,270.01
2017 Dec	132,238	Prophet	169,545.59	-37,307.59
2018 Jan	95,453	Prophet	157,506.62	-62,053.62
2018 Feb	120,303	Prophet	168,881.04	-48,578.04
2018 Mar	162,886	Prophet	185,490.68	-22,604.68
2018 Apr	187,186	Prophet	209,021.33	-21,835.33
2018 May	239,851	Prophet	211,456.00	28,395.00
2018 Jun	264,588	Prophet	224,419.81	40,168.19
2018 Jul	339,564	Prophet	252,970.83	86,593.17
2018 Aug	446,375	Prophet	323,458.11	122,916.89
2018 Sep	304,516	Prophet	254,413.01	50,102.99
2018 Oct	230,827	Prophet	225,430.33	5,396.67
2018 Nov	149,080	Prophet	197,591.50	-48,511.50
2018 Dec	135,316	Prophet	189,818.71	-54,502.71
2019 Jan	114,710	Prophet	177,949.89	-63,239.89
2019 Feb	122,635	Prophet	187,924.00	-65,289.00
2019 Mar	172,412	Prophet	205,589.51	-33,177.51
2019 Apr	241,790	Prophet	228,775.79	13,014.21
2019 May	259,714	Prophet	235,371.97	24,342.03
2019 Jun	306,048	Prophet	247,359.65	58,688.35
2019 Jul	360,566	Prophet	280,537.37	80,028.63
2019 Aug	484,403	Prophet	352,862.18	131,540.82
2019 Sep	327,937	Prophet	273,752.45	54,184.55
2019 Oct	238,677	Prophet	244,731.03	-6,054.03
2019 Nov	171,296	Prophet	216,384.09	-45,088.09
2019 Dec	138,642	Prophet	211,347.98	-72,705.98
2020 Jan	126,349	Prophet	200,102.07	-73,753.07
2020 Feb	167,411	Prophet	210,465.04	-43,054.04
2020 Mar	70,530	Prophet	231,173.79	-160,643.79
2020 Apr	13,892	Prophet	249,247.65	-235,355.65
2020 May	38,343	Prophet	247,486.99	-209,143.99
2020 Jun	159,738	Prophet	253,543.63	-93,805.63
2020 Jul	272,786	Prophet	278,534.29	-5,748.29
2020 Aug	407,020	Prophet	342,947.40	64,072.60
2020 Sep	258,651	Prophet	267,073.30	-8,422.30
2020 Oct	167,448	Prophet	229,937.18	-62,489.18
2020 Nov	73,734	Prophet	192,770.32	-119,036.32
2020 Dec	73,353	Prophet	183,711.53	-110,358.53
2021 Jan	48,435	Prophet	169,323.54	-120,888.54
2021 Feb	40,443	Prophet	179,490.12	-139,047.12
2021 Mar	60,251	Prophet	193,013.12	-132,762.12
2021 Apr	85,179	Prophet	210,389.54	-125,210.54
2021 May	169,690	Prophet	212,668.01	-42,978.01
2021 Jun	254,243	Prophet	230,853.10	23,389.90
2021 Jul	329,058	Prophet	265,951.44	63,106.56
2021 Aug	461,844	Prophet	338,961.65	122,882.35
2021 Sep	308,273	Prophet	258,886.79	49,386.21
2021 Oct	250,949	Prophet	217,305.09	33,643.91
2021 Nov	156,624	Prophet	182,740.86	-26,116.86
2021 Dec	115,100	Prophet	175,127.88	-60,027.88
2022 Jan	96,107	Prophet	161,474.49	-65,367.49
2022 Feb	141,508	Prophet	174,369.42	-32,861.42
2022 Mar	167,854	Prophet	189,509.22	-21,655.22
2022 Apr	248,959	Prophet	212,649.01	36,309.99
2022 May	258,413	Prophet	224,287.89	34,125.11
2022 Jun	300,520	Prophet	246,248.20	54,271.80
2010 Jan	53,653	Prophet_log	51,745.78	1,907.22
2010 Feb	62,257	Prophet_log	64,075.91	-1,818.91
2010 Mar	77,588	Prophet_log	81,382.84	-3,794.84
2010 Apr	99,982	Prophet_log	100,227.11	-245.11
2010 May	101,387	Prophet_log	96,975.70	4,411.30
2010 Jun	108,611	Prophet_log	99,741.69	8,869.31
2010 Jul	126,498	Prophet_log	119,044.65	7,453.35
2010 Aug	178,380	Prophet_log	169,337.70	9,042.30
2010 Sep	127,822	Prophet_log	112,383.85	15,438.15
2010 Oct	104,174	Prophet_log	89,716.11	14,457.89
2010 Nov	69,271	Prophet_log	75,231.17	-5,960.17
2010 Dec	62,935	Prophet_log	65,464.09	-2,529.09
2011 Jan	60,457	Prophet_log	54,043.31	6,413.69
2011 Feb	67,260	Prophet_log	67,557.96	-297.96
2011 Mar	83,464	Prophet_log	84,425.89	-961.89
2011 Apr	102,958	Prophet_log	107,665.63	-4,707.63
2011 May	101,223	Prophet_log	105,041.13	-3,818.13
2011 Jun	120,148	Prophet_log	109,314.50	10,833.50
2011 Jul	136,999	Prophet_log	129,629.82	7,369.18
2011 Aug	212,668	Prophet_log	180,606.38	32,061.62
2011 Sep	129,606	Prophet_log	122,662.05	6,943.95
2011 Oct	101,185	Prophet_log	98,019.37	3,165.63
2011 Nov	62,121	Prophet_log	82,669.51	-20,548.51
2011 Dec	65,563	Prophet_log	71,191.66	-5,628.66
2012 Jan	49,716	Prophet_log	58,143.26	-8,427.26
2012 Feb	58,638	Prophet_log	71,012.18	-12,374.18
2012 Mar	72,210	Prophet_log	90,023.03	-17,813.03
2012 Apr	87,406	Prophet_log	107,199.00	-19,793.00
2012 May	96,946	Prophet_log	105,047.94	-8,101.94
2012 Jun	115,885	Prophet_log	104,680.35	11,204.65
2012 Jul	139,695	Prophet_log	125,058.82	14,636.18
2012 Aug	194,368	Prophet_log	183,470.22	10,897.78
2012 Sep	127,610	Prophet_log	122,296.35	5,313.65
2012 Oct	89,649	Prophet_log	96,964.60	-7,315.60
2012 Nov	58,900	Prophet_log	73,071.32	-14,171.32
2012 Dec	51,122	Prophet_log	63,732.34	-12,610.34
2013 Jan	50,313	Prophet_log	55,094.19	-4,781.19
2013 Feb	58,615	Prophet_log	66,010.17	-7,395.17
2013 Mar	92,426	Prophet_log	81,687.59	10,738.41
2013 Apr	100,996	Prophet_log	99,883.89	1,112.11
2013 May	123,431	Prophet_log	98,482.89	24,948.11
2013 Jun	143,946	Prophet_log	104,558.88	39,387.12
2013 Jul	171,016	Prophet_log	127,799.45	43,216.55
2013 Aug	252,423	Prophet_log	189,043.23	63,379.77
2013 Sep	158,839	Prophet_log	127,055.90	31,783.10
2013 Oct	109,956	Prophet_log	100,993.37	8,962.63
2013 Nov	82,040	Prophet_log	76,957.97	5,082.03
2013 Dec	72,692	Prophet_log	69,218.50	3,473.50
2014 Jan	56,872	Prophet_log	60,569.08	-3,697.08
2014 Feb	64,346	Prophet_log	73,214.08	-8,868.08
2014 Mar	102,852	Prophet_log	93,167.34	9,684.66
2014 Apr	151,151	Prophet_log	115,754.95	35,396.05
2014 May	148,593	Prophet_log	118,227.41	30,365.59
2014 Jun	154,231	Prophet_log	128,612.54	25,618.46
2014 Jul	194,227	Prophet_log	155,071.84	39,155.16
2014 Aug	303,902	Prophet_log	229,582.98	74,319.02
2014 Sep	186,247	Prophet_log	154,368.24	31,878.76
2014 Oct	133,884	Prophet_log	124,466.99	9,417.01
2014 Nov	86,161	Prophet_log	97,425.98	-11,264.98
2014 Dec	81,830	Prophet_log	89,207.69	-7,377.69
2015 Jan	68,436	Prophet_log	73,766.38	-5,330.38
2015 Feb	84,417	Prophet_log	90,150.16	-5,733.16
2015 Mar	116,291	Prophet_log	116,110.72	180.28
2015 Apr	145,183	Prophet_log	152,193.66	-7,010.66
2015 May	172,016	Prophet_log	151,424.30	20,591.70
2015 Jun	182,765	Prophet_log	163,348.02	19,416.98
2015 Jul	238,708	Prophet_log	195,893.79	42,814.21
2015 Aug	358,044	Prophet_log	290,949.04	67,094.96
2015 Sep	216,474	Prophet_log	193,249.52	23,224.48
2015 Oct	148,376	Prophet_log	155,110.30	-6,734.30
2015 Nov	99,794	Prophet_log	121,140.55	-21,346.55
2015 Dec	93,804	Prophet_log	111,657.04	-17,853.04
2016 Jan	74,572	Prophet_log	90,070.73	-15,498.73
2016 Feb	97,522	Prophet_log	109,978.37	-12,456.37
2016 Mar	144,216	Prophet_log	147,595.98	-3,379.98
2016 Apr	153,386	Prophet_log	178,408.21	-25,022.21
2016 May	168,235	Prophet_log	182,047.72	-13,812.72
2016 Jun	215,800	Prophet_log	192,478.85	23,321.15
2016 Jul	271,212	Prophet_log	232,888.85	38,323.15
2016 Aug	380,776	Prophet_log	341,240.84	39,535.16
2016 Sep	249,098	Prophet_log	229,290.74	19,807.26
2016 Oct	175,862	Prophet_log	178,706.18	-2,844.18
2016 Nov	102,775	Prophet_log	132,250.09	-29,475.09
2016 Dec	100,859	Prophet_log	116,542.70	-15,683.70
2017 Jan	83,249	Prophet_log	104,327.12	-21,078.12
2017 Feb	105,210	Prophet_log	124,381.60	-19,171.60
2017 Mar	121,167	Prophet_log	164,287.61	-43,120.61
2017 Apr	217,906	Prophet_log	194,656.86	23,249.14
2017 May	196,622	Prophet_log	200,223.37	-3,601.37
2017 Jun	248,582	Prophet_log	215,938.30	32,643.70
2017 Jul	323,496	Prophet_log	263,887.41	59,608.59
2017 Aug	431,571	Prophet_log	387,488.55	44,082.45
2017 Sep	287,242	Prophet_log	259,361.77	27,880.23
2017 Oct	212,357	Prophet_log	200,520.83	11,836.17
2017 Nov	127,745	Prophet_log	148,084.48	-20,339.48
2017 Dec	132,238	Prophet_log	133,817.78	-1,579.78
2018 Jan	95,453	Prophet_log	115,543.54	-20,090.54
2018 Feb	120,303	Prophet_log	139,114.44	-18,811.44
2018 Mar	162,886	Prophet_log	180,592.12	-17,706.12
2018 Apr	187,186	Prophet_log	228,154.18	-40,968.18
2018 May	239,851	Prophet_log	228,493.61	11,357.39
2018 Jun	264,588	Prophet_log	246,964.84	17,623.16
2018 Jul	339,564	Prophet_log	300,334.13	39,229.87
2018 Aug	446,375	Prophet_log	440,857.09	5,517.91
2018 Sep	304,516	Prophet_log	289,125.86	15,390.14
2018 Oct	230,827	Prophet_log	222,935.86	7,891.14
2018 Nov	149,080	Prophet_log	165,769.70	-16,689.70
2018 Dec	135,316	Prophet_log	151,648.94	-16,332.94
2019 Jan	114,710	Prophet_log	124,636.40	-9,926.40
2019 Feb	122,635	Prophet_log	152,619.30	-29,984.30
2019 Mar	172,412	Prophet_log	194,530.27	-22,118.27
2019 Apr	241,790	Prophet_log	250,641.98	-8,851.98
2019 May	259,714	Prophet_log	256,710.88	3,003.12
2019 Jun	306,048	Prophet_log	274,783.08	31,264.92
2019 Jul	360,566	Prophet_log	334,164.18	26,401.82
2019 Aug	484,403	Prophet_log	483,320.16	1,082.84
2019 Sep	327,937	Prophet_log	314,906.96	13,030.04
2019 Oct	238,677	Prophet_log	243,377.19	-4,700.19
2019 Nov	171,296	Prophet_log	183,325.12	-12,029.12
2019 Dec	138,642	Prophet_log	169,383.81	-30,741.81
2020 Jan	126,349	Prophet_log	136,033.45	-9,684.45
2020 Feb	167,411	Prophet_log	166,050.46	1,360.54
2020 Mar	70,530	Prophet_log	228,256.35	-157,726.35
2020 Apr	13,892	Prophet_log	263,619.08	-249,727.08
2020 May	38,343	Prophet_log	250,779.05	-212,436.05
2020 Jun	159,738	Prophet_log	246,869.22	-87,131.22
2020 Jul	272,786	Prophet_log	283,239.03	-10,453.03
2020 Aug	407,020	Prophet_log	389,997.03	17,022.97
2020 Sep	258,651	Prophet_log	249,066.37	9,584.63
2020 Oct	167,448	Prophet_log	184,246.35	-16,798.35
2020 Nov	73,734	Prophet_log	128,828.41	-55,094.41
2020 Dec	73,353	Prophet_log	116,419.94	-43,066.94
2021 Jan	48,435	Prophet_log	98,041.78	-49,606.78
2021 Feb	40,443	Prophet_log	119,392.04	-78,949.04
2021 Mar	60,251	Prophet_log	129,645.18	-69,394.18
2021 Apr	85,179	Prophet_log	136,061.17	-50,882.17
2021 May	169,690	Prophet_log	136,798.43	32,891.57
2021 Jun	254,243	Prophet_log	169,174.24	85,068.76
2021 Jul	329,058	Prophet_log	208,454.78	120,603.22
2021 Aug	461,844	Prophet_log	296,205.63	165,638.37
2021 Sep	308,273	Prophet_log	194,803.89	113,469.11
2021 Oct	250,949	Prophet_log	150,747.33	100,201.67
2021 Nov	156,624	Prophet_log	104,818.17	51,805.83
2021 Dec	115,100	Prophet_log	99,019.64	16,080.36
2022 Jan	96,107	Prophet_log	83,104.36	13,002.64
2022 Feb	141,508	Prophet_log	100,559.41	40,948.59
2022 Mar	167,854	Prophet_log	124,362.71	43,491.29
2022 Apr	248,959	Prophet_log	154,177.01	94,781.99
2022 May	258,413	Prophet_log	169,796.55	88,616.45
2022 Jun	300,520	Prophet_log	199,672.52	100,847.48
2010 Jan	53,653	SNaive	50,256.00	3,397.00
2010 Feb	62,257	SNaive	63,694.00	-1,437.00
2010 Mar	77,588	SNaive	67,975.00	9,613.00
2010 Apr	99,982	SNaive	96,647.00	3,335.00
2010 May	101,387	SNaive	97,936.00	3,451.00
2010 Jun	108,611	SNaive	107,295.00	1,316.00
2010 Jul	126,498	SNaive	114,085.00	12,413.00
2010 Aug	178,380	SNaive	176,426.00	1,954.00
2010 Sep	127,822	SNaive	109,573.00	18,249.00
2010 Oct	104,174	SNaive	92,353.00	11,821.00
2010 Nov	69,271	SNaive	68,602.00	669.00
2010 Dec	62,935	SNaive	59,473.00	3,462.00
2011 Jan	60,457	SNaive	53,653.00	6,804.00
2011 Feb	67,260	SNaive	62,257.00	5,003.00
2011 Mar	83,464	SNaive	77,588.00	5,876.00
2011 Apr	102,958	SNaive	99,982.00	2,976.00
2011 May	101,223	SNaive	101,387.00	-164.00
2011 Jun	120,148	SNaive	108,611.00	11,537.00
2011 Jul	136,999	SNaive	126,498.00	10,501.00
2011 Aug	212,668	SNaive	178,380.00	34,288.00
2011 Sep	129,606	SNaive	127,822.00	1,784.00
2011 Oct	101,185	SNaive	104,174.00	-2,989.00
2011 Nov	62,121	SNaive	69,271.00	-7,150.00
2011 Dec	65,563	SNaive	62,935.00	2,628.00
2012 Jan	49,716	SNaive	60,457.00	-10,741.00
2012 Feb	58,638	SNaive	67,260.00	-8,622.00
2012 Mar	72,210	SNaive	83,464.00	-11,254.00
2012 Apr	87,406	SNaive	102,958.00	-15,552.00
2012 May	96,946	SNaive	101,223.00	-4,277.00
2012 Jun	115,885	SNaive	120,148.00	-4,263.00
2012 Jul	139,695	SNaive	136,999.00	2,696.00
2012 Aug	194,368	SNaive	212,668.00	-18,300.00
2012 Sep	127,610	SNaive	129,606.00	-1,996.00
2012 Oct	89,649	SNaive	101,185.00	-11,536.00
2012 Nov	58,900	SNaive	62,121.00	-3,221.00
2012 Dec	51,122	SNaive	65,563.00	-14,441.00
2013 Jan	50,313	SNaive	49,716.00	597.00
2013 Feb	58,615	SNaive	58,638.00	-23.00
2013 Mar	92,426	SNaive	72,210.00	20,216.00
2013 Apr	100,996	SNaive	87,406.00	13,590.00
2013 May	123,431	SNaive	96,946.00	26,485.00
2013 Jun	143,946	SNaive	115,885.00	28,061.00
2013 Jul	171,016	SNaive	139,695.00	31,321.00
2013 Aug	252,423	SNaive	194,368.00	58,055.00
2013 Sep	158,839	SNaive	127,610.00	31,229.00
2013 Oct	109,956	SNaive	89,649.00	20,307.00
2013 Nov	82,040	SNaive	58,900.00	23,140.00
2013 Dec	72,692	SNaive	51,122.00	21,570.00
2014 Jan	56,872	SNaive	50,313.00	6,559.00
2014 Feb	64,346	SNaive	58,615.00	5,731.00
2014 Mar	102,852	SNaive	92,426.00	10,426.00
2014 Apr	151,151	SNaive	100,996.00	50,155.00
2014 May	148,593	SNaive	123,431.00	25,162.00
2014 Jun	154,231	SNaive	143,946.00	10,285.00
2014 Jul	194,227	SNaive	171,016.00	23,211.00
2014 Aug	303,902	SNaive	252,423.00	51,479.00
2014 Sep	186,247	SNaive	158,839.00	27,408.00
2014 Oct	133,884	SNaive	109,956.00	23,928.00
2014 Nov	86,161	SNaive	82,040.00	4,121.00
2014 Dec	81,830	SNaive	72,692.00	9,138.00
2015 Jan	68,436	SNaive	56,872.00	11,564.00
2015 Feb	84,417	SNaive	64,346.00	20,071.00
2015 Mar	116,291	SNaive	102,852.00	13,439.00
2015 Apr	145,183	SNaive	151,151.00	-5,968.00
2015 May	172,016	SNaive	148,593.00	23,423.00
2015 Jun	182,765	SNaive	154,231.00	28,534.00
2015 Jul	238,708	SNaive	194,227.00	44,481.00
2015 Aug	358,044	SNaive	303,902.00	54,142.00
2015 Sep	216,474	SNaive	186,247.00	30,227.00
2015 Oct	148,376	SNaive	133,884.00	14,492.00
2015 Nov	99,794	SNaive	86,161.00	13,633.00
2015 Dec	93,804	SNaive	81,830.00	11,974.00
2016 Jan	74,572	SNaive	68,436.00	6,136.00
2016 Feb	97,522	SNaive	84,417.00	13,105.00
2016 Mar	144,216	SNaive	116,291.00	27,925.00
2016 Apr	153,386	SNaive	145,183.00	8,203.00
2016 May	168,235	SNaive	172,016.00	-3,781.00
2016 Jun	215,800	SNaive	182,765.00	33,035.00
2016 Jul	271,212	SNaive	238,708.00	32,504.00
2016 Aug	380,776	SNaive	358,044.00	22,732.00
2016 Sep	249,098	SNaive	216,474.00	32,624.00
2016 Oct	175,862	SNaive	148,376.00	27,486.00
2016 Nov	102,775	SNaive	99,794.00	2,981.00
2016 Dec	100,859	SNaive	93,804.00	7,055.00
2017 Jan	83,249	SNaive	74,572.00	8,677.00
2017 Feb	105,210	SNaive	97,522.00	7,688.00
2017 Mar	121,167	SNaive	144,216.00	-23,049.00
2017 Apr	217,906	SNaive	153,386.00	64,520.00
2017 May	196,622	SNaive	168,235.00	28,387.00
2017 Jun	248,582	SNaive	215,800.00	32,782.00
2017 Jul	323,496	SNaive	271,212.00	52,284.00
2017 Aug	431,571	SNaive	380,776.00	50,795.00
2017 Sep	287,242	SNaive	249,098.00	38,144.00
2017 Oct	212,357	SNaive	175,862.00	36,495.00
2017 Nov	127,745	SNaive	102,775.00	24,970.00
2017 Dec	132,238	SNaive	100,859.00	31,379.00
2018 Jan	95,453	SNaive	83,249.00	12,204.00
2018 Feb	120,303	SNaive	105,210.00	15,093.00
2018 Mar	162,886	SNaive	121,167.00	41,719.00
2018 Apr	187,186	SNaive	217,906.00	-30,720.00
2018 May	239,851	SNaive	196,622.00	43,229.00
2018 Jun	264,588	SNaive	248,582.00	16,006.00
2018 Jul	339,564	SNaive	323,496.00	16,068.00
2018 Aug	446,375	SNaive	431,571.00	14,804.00
2018 Sep	304,516	SNaive	287,242.00	17,274.00
2018 Oct	230,827	SNaive	212,357.00	18,470.00
2018 Nov	149,080	SNaive	127,745.00	21,335.00
2018 Dec	135,316	SNaive	132,238.00	3,078.00
2019 Jan	114,710	SNaive	95,453.00	19,257.00
2019 Feb	122,635	SNaive	120,303.00	2,332.00
2019 Mar	172,412	SNaive	162,886.00	9,526.00
2019 Apr	241,790	SNaive	187,186.00	54,604.00
2019 May	259,714	SNaive	239,851.00	19,863.00
2019 Jun	306,048	SNaive	264,588.00	41,460.00
2019 Jul	360,566	SNaive	339,564.00	21,002.00
2019 Aug	484,403	SNaive	446,375.00	38,028.00
2019 Sep	327,937	SNaive	304,516.00	23,421.00
2019 Oct	238,677	SNaive	230,827.00	7,850.00
2019 Nov	171,296	SNaive	149,080.00	22,216.00
2019 Dec	138,642	SNaive	135,316.00	3,326.00
2020 Jan	126,349	SNaive	114,710.00	11,639.00
2020 Feb	167,411	SNaive	122,635.00	44,776.00
2020 Mar	70,530	SNaive	172,412.00	-101,882.00
2020 Apr	13,892	SNaive	241,790.00	-227,898.00
2020 May	38,343	SNaive	259,714.00	-221,371.00
2020 Jun	159,738	SNaive	306,048.00	-146,310.00
2020 Jul	272,786	SNaive	360,566.00	-87,780.00
2020 Aug	407,020	SNaive	484,403.00	-77,383.00
2020 Sep	258,651	SNaive	327,937.00	-69,286.00
2020 Oct	167,448	SNaive	238,677.00	-71,229.00
2020 Nov	73,734	SNaive	171,296.00	-97,562.00
2020 Dec	73,353	SNaive	138,642.00	-65,289.00
2021 Jan	48,435	SNaive	126,349.00	-77,914.00
2021 Feb	40,443	SNaive	167,411.00	-126,968.00
2021 Mar	60,251	SNaive	70,530.00	-10,279.00
2021 Apr	85,179	SNaive	13,892.00	71,287.00
2021 May	169,690	SNaive	38,343.00	131,347.00
2021 Jun	254,243	SNaive	159,738.00	94,505.00
2021 Jul	329,058	SNaive	272,786.00	56,272.00
2021 Aug	461,844	SNaive	407,020.00	54,824.00
2021 Sep	308,273	SNaive	258,651.00	49,622.00
2021 Oct	250,949	SNaive	167,448.00	83,501.00
2021 Nov	156,624	SNaive	73,734.00	82,890.00
2021 Dec	115,100	SNaive	73,353.00	41,747.00
2022 Jan	96,107	SNaive	48,435.00	47,672.00
2022 Feb	141,508	SNaive	40,443.00	101,065.00
2022 Mar	167,854	SNaive	60,251.00	107,603.00
2022 Apr	248,959	SNaive	85,179.00	163,780.00
2022 May	258,413	SNaive	169,690.00	88,723.00
2022 Jun	300,520	SNaive	254,243.00	46,277.00
2010 Jan	53,653	SNaive_log	50,590.14	3,062.86
2010 Feb	62,257	SNaive_log	64,114.85	-1,857.85
2010 Mar	77,588	SNaive_log	68,420.21	9,167.79
2010 Apr	99,982	SNaive_log	97,281.92	2,700.08
2010 May	101,387	SNaive_log	98,574.14	2,812.86
2010 Jun	108,611	SNaive_log	107,988.51	622.49
2010 Jul	126,498	SNaive_log	114,816.00	11,682.00
2010 Aug	178,380	SNaive_log	177,554.81	825.19
2010 Sep	127,822	SNaive_log	110,268.08	17,553.92
2010 Oct	104,174	SNaive_log	92,943.20	11,230.80
2010 Nov	69,271	SNaive_log	69,040.92	230.08
2010 Dec	62,935	SNaive_log	59,850.34	3,084.66
2011 Jan	60,457	SNaive_log	53,991.29	6,465.71
2011 Feb	67,260	SNaive_log	62,649.96	4,610.04
2011 Mar	83,464	SNaive_log	78,075.62	5,388.38
2011 Apr	102,958	SNaive_log	100,607.41	2,350.59
2011 May	101,223	SNaive_log	102,016.44	-793.44
2011 Jun	120,148	SNaive_log	109,279.90	10,868.10
2011 Jul	136,999	SNaive_log	127,275.99	9,723.01
2011 Aug	212,668	SNaive_log	179,472.90	33,195.10
2011 Sep	129,606	SNaive_log	128,614.46	991.54
2011 Oct	101,185	SNaive_log	104,814.92	-3,629.92
2011 Nov	62,121	SNaive_log	69,694.13	-7,573.13
2011 Dec	65,563	SNaive_log	63,319.34	2,243.66
2012 Jan	49,716	SNaive_log	60,823.80	-11,107.80
2012 Feb	58,638	SNaive_log	67,674.68	-9,036.68
2012 Mar	72,210	SNaive_log	83,980.60	-11,770.60
2012 Apr	87,406	SNaive_log	103,598.54	-16,192.54
2012 May	96,946	SNaive_log	101,858.09	-4,912.09
2012 Jun	115,885	SNaive_log	120,897.15	-5,012.15
2012 Jul	139,695	SNaive_log	137,847.67	1,847.33
2012 Aug	194,368	SNaive_log	213,976.23	-19,608.23
2012 Sep	127,610	SNaive_log	130,401.33	-2,791.33
2012 Oct	89,649	SNaive_log	101,801.61	-12,152.61
2012 Nov	58,900	SNaive_log	62,500.09	-3,600.09
2012 Dec	51,122	SNaive_log	65,960.95	-14,838.95
2013 Jan	50,313	SNaive_log	50,026.35	286.65
2013 Feb	58,615	SNaive_log	59,001.55	-386.55
2013 Mar	92,426	SNaive_log	72,654.63	19,771.37
2013 Apr	100,996	SNaive_log	87,958.66	13,037.34
2013 May	123,431	SNaive_log	97,561.67	25,869.33
2013 Jun	143,946	SNaive_log	116,638.70	27,307.30
2013 Jul	171,016	SNaive_log	140,619.39	30,396.61
2013 Aug	252,423	SNaive_log	195,671.99	56,751.01
2013 Sep	158,839	SNaive_log	128,489.16	30,349.84
2013 Oct	109,956	SNaive_log	90,276.63	19,679.37
2013 Nov	82,040	SNaive_log	59,317.65	22,722.35
2013 Dec	72,692	SNaive_log	51,500.27	21,191.73
2014 Jan	56,872	SNaive_log	50,702.88	6,169.12
2014 Feb	64,346	SNaive_log	59,069.12	5,276.88
2014 Mar	102,852	SNaive_log	93,140.09	9,711.91
2014 Apr	151,151	SNaive_log	101,775.02	49,375.98
2014 May	148,593	SNaive_log	124,439.83	24,153.17
2014 Jun	154,231	SNaive_log	145,130.58	9,100.42
2014 Jul	194,227	SNaive_log	172,417.18	21,809.82
2014 Aug	303,902	SNaive_log	254,491.02	49,410.98
2014 Sep	186,247	SNaive_log	160,149.06	26,097.94
2014 Oct	133,884	SNaive_log	110,865.83	23,018.17
2014 Nov	86,161	SNaive_log	82,724.33	3,436.67
2014 Dec	81,830	SNaive_log	73,295.25	8,534.75
2015 Jan	68,436	SNaive_log	57,343.53	11,092.47
2015 Feb	84,417	SNaive_log	64,882.86	19,534.14
2015 Mar	116,291	SNaive_log	103,727.38	12,563.62
2015 Apr	145,183	SNaive_log	152,436.60	-7,253.60
2015 May	172,016	SNaive_log	149,850.19	22,165.81
2015 Jun	182,765	SNaive_log	155,537.90	27,227.10
2015 Jul	238,708	SNaive_log	195,879.44	42,828.56
2015 Aug	358,044	SNaive_log	306,509.68	51,534.32
2015 Sep	216,474	SNaive_log	187,850.26	28,623.74
2015 Oct	148,376	SNaive_log	135,038.55	13,337.45
2015 Nov	99,794	SNaive_log	86,902.39	12,891.61
2015 Dec	93,804	SNaive_log	82,535.12	11,268.88
2016 Jan	74,572	SNaive_log	69,025.98	5,546.02
2016 Feb	97,522	SNaive_log	85,142.45	12,379.55
2016 Mar	144,216	SNaive_log	117,291.52	26,924.48
2016 Apr	153,386	SNaive_log	146,443.64	6,942.36
2016 May	168,235	SNaive_log	173,502.93	-5,267.93
2016 Jun	215,800	SNaive_log	184,336.55	31,463.45
2016 Jul	271,212	SNaive_log	240,767.27	30,444.73
2016 Aug	380,776	SNaive_log	361,131.84	19,644.16
2016 Sep	249,098	SNaive_log	218,333.16	30,764.84
2016 Oct	175,862	SNaive_log	149,651.30	26,210.70
2016 Nov	102,775	SNaive_log	100,654.81	2,120.19
2016 Dec	100,859	SNaive_log	94,609.12	6,249.88
2017 Jan	83,249	SNaive_log	75,209.74	8,039.26
2017 Feb	105,210	SNaive_log	98,354.74	6,855.26
2017 Mar	121,167	SNaive_log	145,443.26	-24,276.26
2017 Apr	217,906	SNaive_log	154,696.53	63,209.47
2017 May	196,622	SNaive_log	169,717.97	26,904.03
2017 Jun	248,582	SNaive_log	217,705.91	30,876.09
2017 Jul	323,496	SNaive_log	273,608.90	49,887.10
2017 Aug	431,571	SNaive_log	384,154.01	47,416.99
2017 Sep	287,242	SNaive_log	251,306.56	35,935.44
2017 Oct	212,357	SNaive_log	177,422.36	34,934.64
2017 Nov	127,745	SNaive_log	103,691.42	24,053.58
2017 Dec	132,238	SNaive_log	101,765.65	30,472.35
2018 Jan	95,453	SNaive_log	84,008.65	11,444.35
2018 Feb	120,303	SNaive_log	106,170.17	14,132.83
2018 Mar	162,886	SNaive_log	122,272.71	40,613.29
2018 Apr	187,186	SNaive_log	219,930.98	-32,744.98
2018 May	239,851	SNaive_log	198,451.32	41,399.68
2018 Jun	264,588	SNaive_log	250,907.16	13,680.84
2018 Jul	339,564	SNaive_log	326,510.48	13,053.52
2018 Aug	446,375	SNaive_log	435,575.91	10,799.09
2018 Sep	304,516	SNaive_log	289,895.76	14,620.24
2018 Oct	230,827	SNaive_log	214,311.40	16,515.60
2018 Nov	149,080	SNaive_log	128,917.27	20,162.73
2018 Dec	135,316	SNaive_log	133,453.19	1,862.81
2019 Jan	114,710	SNaive_log	96,326.21	18,383.79
2019 Feb	122,635	SNaive_log	121,407.83	1,227.17
2019 Mar	172,412	SNaive_log	164,375.18	8,036.82
2019 Apr	241,790	SNaive_log	188,890.91	52,899.09
2019 May	259,714	SNaive_log	242,061.37	17,652.63
2019 Jun	306,048	SNaive_log	267,019.10	39,028.90
2019 Jul	360,566	SNaive_log	342,686.15	17,879.85
2019 Aug	484,403	SNaive_log	450,464.43	33,938.57
2019 Sep	327,937	SNaive_log	307,297.89	20,639.11
2019 Oct	238,677	SNaive_log	232,929.15	5,747.85
2019 Nov	171,296	SNaive_log	150,432.04	20,863.96
2019 Dec	138,642	SNaive_log	136,543.55	2,098.45
2020 Jan	126,349	SNaive_log	115,746.21	10,602.79
2020 Feb	167,411	SNaive_log	123,740.46	43,670.54
2020 Mar	70,530	SNaive_log	173,995.71	-103,465.71
2020 Apr	13,892	SNaive_log	244,419.52	-230,527.52
2020 May	38,343	SNaive_log	267,094.25	-228,751.25
2020 Jun	159,738	SNaive_log	317,111.05	-157,373.05
2020 Jul	272,786	SNaive_log	373,869.79	-101,083.79
2020 Aug	407,020	SNaive_log	502,280.16	-95,260.16
2020 Sep	258,651	SNaive_log	340,009.46	-81,358.46
2020 Oct	167,448	SNaive_log	247,454.79	-80,006.79
2020 Nov	73,734	SNaive_log	177,614.47	-103,880.47
2020 Dec	73,353	SNaive_log	143,940.67	-70,587.67
2021 Jan	48,435	SNaive_log	131,264.41	-82,829.41
2021 Feb	40,443	SNaive_log	174,216.16	-133,773.16
2021 Mar	60,251	SNaive_log	73,679.22	-13,428.22
2021 Apr	85,179	SNaive_log	14,510.45	70,668.55
2021 May	169,690	SNaive_log	40,301.35	129,388.65
2021 Jun	254,243	SNaive_log	168,584.47	85,658.53
2021 Jul	329,058	SNaive_log	287,951.54	41,106.46
2021 Aug	461,844	SNaive_log	429,585.65	32,258.35
2021 Sep	308,273	SNaive_log	272,941.41	35,331.59
2021 Oct	250,949	SNaive_log	176,672.67	74,276.33
2021 Nov	156,624	SNaive_log	77,803.88	78,820.12
2021 Dec	115,100	SNaive_log	77,468.65	37,631.35
2022 Jan	96,107	SNaive_log	51,161.29	44,945.71
2022 Feb	141,508	SNaive_log	42,747.97	98,760.03
2022 Mar	167,854	SNaive_log	63,857.42	103,996.58
2022 Apr	248,959	SNaive_log	90,432.86	158,526.14
2022 May	258,413	SNaive_log	180,496.87	77,916.13
2022 Jun	300,520	SNaive_log	270,459.21	30,060.79
2010 Jan	53,653	TSLM	57,922.22	-4,269.22
2010 Feb	62,257	TSLM	68,532.53	-6,275.53
2010 Mar	77,588	TSLM	84,776.29	-7,188.29
2010 Apr	99,982	TSLM	100,177.17	-195.17
2010 May	101,387	TSLM	98,095.99	3,291.01
2010 Jun	108,611	TSLM	99,752.86	8,858.14
2010 Jul	126,498	TSLM	115,890.47	10,607.53
2010 Aug	178,380	TSLM	161,089.06	17,290.94
2010 Sep	127,822	TSLM	111,803.83	16,018.17
2010 Oct	104,174	TSLM	92,103.49	12,070.51
2010 Nov	69,271	TSLM	76,551.79	-7,280.79
2010 Dec	62,935	TSLM	69,493.58	-6,558.58
2011 Jan	60,457	TSLM	60,747.90	-290.90
2011 Feb	67,260	TSLM	71,273.63	-4,013.63
2011 Mar	83,464	TSLM	87,488.97	-4,024.97
2011 Apr	102,958	TSLM	103,599.55	-641.55
2011 May	101,223	TSLM	101,825.15	-602.15
2011 Jun	120,148	TSLM	103,901.77	16,246.23
2011 Jul	136,999	TSLM	120,359.86	16,639.14
2011 Aug	212,668	TSLM	166,295.79	46,372.21
2011 Sep	129,606	TSLM	117,503.70	12,102.30
2011 Oct	101,185	TSLM	97,367.87	3,817.13
2011 Nov	62,121	TSLM	79,894.75	-17,773.75
2011 Dec	65,563	TSLM	72,694.52	-7,131.52
2012 Jan	49,716	TSLM	64,615.14	-14,899.14
2012 Feb	58,638	TSLM	74,506.04	-15,868.04
2012 Mar	72,210	TSLM	90,463.09	-18,253.09
2012 Apr	87,406	TSLM	106,553.06	-19,147.06
2012 May	96,946	TSLM	104,396.41	-7,450.41
2012 Jun	115,885	TSLM	107,737.28	8,147.72
2012 Jul	139,695	TSLM	124,067.31	15,627.69
2012 Aug	194,368	TSLM	172,462.91	21,905.09
2012 Sep	127,610	TSLM	120,350.66	7,259.34
2012 Oct	89,649	TSLM	99,434.96	-9,785.96
2012 Nov	58,900	TSLM	79,911.41	-21,011.41
2012 Dec	51,122	TSLM	73,535.46	-22,413.46
2013 Jan	50,313	TSLM	64,510.43	-14,197.43
2013 Feb	58,615	TSLM	74,342.69	-15,727.69
2013 Mar	92,426	TSLM	90,120.14	2,305.86
2013 Apr	100,996	TSLM	106,545.04	-5,549.04
2013 May	123,431	TSLM	105,549.64	17,881.36
2013 Jun	143,946	TSLM	110,568.10	33,377.90
2013 Jul	171,016	TSLM	127,941.21	43,074.79
2013 Aug	252,423	TSLM	177,320.00	75,103.00
2013 Sep	158,839	TSLM	125,033.43	33,805.57
2013 Oct	109,956	TSLM	103,273.21	6,682.79
2013 Nov	82,040	TSLM	83,168.66	-1,128.66
2013 Dec	72,692	TSLM	77,018.37	-4,326.37
2014 Jan	56,872	TSLM	69,217.20	-12,345.20
2014 Feb	64,346	TSLM	78,976.27	-14,630.27
2014 Mar	102,852	TSLM	96,062.99	6,789.01
2014 Apr	151,151	TSLM	112,008.28	39,142.72
2014 May	148,593	TSLM	113,484.54	35,108.46
2014 Jun	154,231	TSLM	119,912.55	34,318.45
2014 Jul	194,227	TSLM	137,996.04	56,230.96
2014 Aug	303,902	TSLM	189,888.39	114,013.61
2014 Sep	186,247	TSLM	135,306.90	50,940.10
2014 Oct	133,884	TSLM	111,893.70	21,990.30
2014 Nov	86,161	TSLM	91,478.88	-5,317.88
2014 Dec	81,830	TSLM	85,033.54	-3,203.54
2015 Jan	68,436	TSLM	77,097.60	-8,661.60
2015 Feb	84,417	TSLM	86,769.78	-2,352.78
2015 Mar	116,291	TSLM	105,496.75	10,794.25
2015 Apr	145,183	TSLM	123,666.70	21,516.30
2015 May	172,016	TSLM	124,580.24	47,435.76
2015 Jun	182,765	TSLM	131,158.34	51,606.66
2015 Jul	238,708	TSLM	150,982.77	87,725.23
2015 Aug	358,044	TSLM	207,230.24	150,813.76
2015 Sep	216,474	TSLM	149,026.77	67,447.23
2015 Oct	148,376	TSLM	123,941.82	24,434.18
2015 Nov	99,794	TSLM	101,745.63	-1,951.63
2015 Dec	93,804	TSLM	95,490.91	-1,686.91
2016 Jan	74,572	TSLM	87,690.47	-13,118.47
2016 Feb	97,522	TSLM	97,684.35	-162.35
2016 Mar	144,216	TSLM	117,268.42	26,947.58
2016 Apr	153,386	TSLM	136,364.72	17,021.28
2016 May	168,235	TSLM	138,827.99	29,407.01
2016 Jun	215,800	TSLM	145,390.15	70,409.85
2016 Jul	271,212	TSLM	167,758.47	103,453.53
2016 Aug	380,776	TSLM	228,187.61	152,588.39
2016 Sep	249,098	TSLM	164,808.50	84,289.50
2016 Oct	175,862	TSLM	137,284.02	38,577.98
2016 Nov	102,775	TSLM	113,642.76	-10,867.76
2016 Dec	100,859	TSLM	107,278.82	-6,419.82
2017 Jan	83,249	TSLM	99,176.45	-15,927.45
2017 Feb	105,210	TSLM	109,889.83	-4,679.83
2017 Mar	121,167	TSLM	131,000.16	-9,833.16
2017 Apr	217,906	TSLM	148,963.22	68,942.78
2017 May	196,622	TSLM	152,918.61	43,703.39
2017 Jun	248,582	TSLM	162,100.29	86,481.71
2017 Jul	323,496	TSLM	186,643.74	136,852.26
2017 Aug	431,571	TSLM	250,437.41	181,133.59
2017 Sep	287,242	TSLM	183,444.51	103,797.49
2017 Oct	212,357	TSLM	153,503.27	58,853.73
2017 Nov	127,745	TSLM	127,230.07	514.93
2017 Dec	132,238	TSLM	121,278.70	10,959.30
2018 Jan	95,453	TSLM	113,410.09	-17,957.09
2018 Feb	120,303	TSLM	124,719.51	-4,416.51
2018 Mar	162,886	TSLM	145,547.41	17,338.59
2018 Apr	187,186	TSLM	168,269.73	18,916.27
2018 May	239,851	TSLM	170,128.12	69,722.88
2018 Jun	264,588	TSLM	182,043.29	82,544.71
2018 Jul	339,564	TSLM	209,333.76	130,230.24
2018 Aug	446,375	TSLM	275,503.49	170,871.51
2018 Sep	304,516	TSLM	204,086.47	100,429.53
2018 Oct	230,827	TSLM	171,609.75	59,217.25
2018 Nov	149,080	TSLM	142,103.55	6,976.45
2018 Dec	135,316	TSLM	136,814.25	-1,498.25
2019 Jan	114,710	TSLM	127,677.39	-12,967.39
2019 Feb	122,635	TSLM	139,768.39	-17,133.39
2019 Mar	172,412	TSLM	161,569.54	10,842.46
2019 Apr	241,790	TSLM	184,288.11	57,501.89
2019 May	259,714	TSLM	189,328.24	70,385.76
2019 Jun	306,048	TSLM	201,927.50	104,120.50
2019 Jul	360,566	TSLM	232,005.85	128,560.15
2019 Aug	484,403	TSLM	300,296.93	184,106.07
2019 Sep	327,937	TSLM	225,343.78	102,593.22
2019 Oct	238,677	TSLM	190,728.94	47,948.06
2019 Nov	171,296	TSLM	158,338.73	12,957.27
2019 Dec	138,642	TSLM	152,675.84	-14,033.84
2020 Jan	126,349	TSLM	143,245.64	-16,896.64
2020 Feb	167,411	TSLM	155,077.65	12,333.35
2020 Mar	70,530	TSLM	178,655.67	-108,125.67
2020 Apr	13,892	TSLM	202,201.19	-188,309.19
2020 May	38,343	TSLM	204,812.88	-166,469.88
2020 Jun	159,738	TSLM	216,175.30	-56,437.30
2020 Jul	272,786	TSLM	245,519.24	27,266.76
2020 Aug	407,020	TSLM	315,370.15	91,649.85
2020 Sep	258,651	TSLM	235,246.17	23,404.83
2020 Oct	167,448	TSLM	196,971.17	-29,523.17
2020 Nov	73,734	TSLM	161,932.63	-88,198.63
2020 Dec	73,353	TSLM	153,758.10	-80,405.10
2021 Jan	48,435	TSLM	143,131.77	-94,696.77
2021 Feb	40,443	TSLM	155,395.58	-114,952.58
2021 Mar	60,251	TSLM	171,685.00	-111,434.00
2021 Apr	85,179	TSLM	191,373.19	-106,194.19
2021 May	169,690	TSLM	196,002.40	-26,312.40
2021 Jun	254,243	TSLM	214,252.22	39,990.78
2021 Jul	329,058	TSLM	248,702.57	80,355.43
2021 Aug	461,844	TSLM	322,230.10	139,613.90
2021 Sep	308,273	TSLM	239,403.76	68,869.24
2021 Oct	250,949	TSLM	199,119.95	51,829.05
2021 Nov	156,624	TSLM	162,190.16	-5,566.16
2021 Dec	115,100	TSLM	155,291.09	-40,191.09
2022 Jan	96,107	TSLM	144,547.03	-48,440.03
2022 Feb	141,508	TSLM	156,436.19	-14,928.19
2022 Mar	167,854	TSLM	174,050.10	-6,196.10
2022 Apr	248,959	TSLM	195,186.79	53,772.21
2022 May	258,413	TSLM	205,264.80	53,148.20
2022 Jun	300,520	TSLM	227,421.06	73,098.94
2010 Jan	53,653	TSLM_log	53,094.80	558.20
2010 Feb	62,257	TSLM_log	65,714.77	-3,457.77
2010 Mar	77,588	TSLM_log	85,130.39	-7,542.39
2010 Apr	99,982	TSLM_log	103,498.26	-3,516.26
2010 May	101,387	TSLM_log	100,598.71	788.29
2010 Jun	108,611	TSLM_log	102,685.20	5,925.80
2010 Jul	126,498	TSLM_log	122,039.77	4,458.23
2010 Aug	178,380	TSLM_log	175,102.99	3,277.01
2010 Sep	127,822	TSLM_log	116,284.82	11,537.18
2010 Oct	104,174	TSLM_log	92,346.34	11,827.66
2010 Nov	69,271	TSLM_log	73,979.02	-4,708.02
2010 Dec	62,935	TSLM_log	65,287.39	-2,352.39
2011 Jan	60,457	TSLM_log	54,937.08	5,519.92
2011 Feb	67,260	TSLM_log	67,740.41	-480.41
2011 Mar	83,464	TSLM_log	87,543.31	-4,079.31
2011 Apr	102,958	TSLM_log	107,106.23	-4,148.23
2011 May	101,223	TSLM_log	104,495.48	-3,272.48
2011 Jun	120,148	TSLM_log	107,037.90	13,110.10
2011 Jul	136,999	TSLM_log	127,149.12	9,849.88
2011 Aug	212,668	TSLM_log	182,300.64	30,367.36
2011 Sep	129,606	TSLM_log	122,261.34	7,344.66
2011 Oct	101,185	TSLM_log	97,249.31	3,935.69
2011 Nov	62,121	TSLM_log	76,473.08	-14,352.08
2011 Dec	65,563	TSLM_log	67,487.23	-1,924.23
2012 Jan	49,716	TSLM_log	57,465.19	-7,749.19
2012 Feb	58,638	TSLM_log	69,880.01	-11,242.01
2012 Mar	72,210	TSLM_log	89,684.68	-17,474.68
2012 Apr	87,406	TSLM_log	109,425.24	-22,019.24
2012 May	96,946	TSLM_log	106,434.06	-9,488.06
2012 Jun	115,885	TSLM_log	110,235.63	5,649.37
2012 Jul	139,695	TSLM_log	130,327.42	9,367.58
2012 Aug	194,368	TSLM_log	188,081.95	6,286.05
2012 Sep	127,610	TSLM_log	124,837.74	2,772.26
2012 Oct	89,649	TSLM_log	99,076.59	-9,427.59
2012 Nov	58,900	TSLM_log	76,125.12	-17,225.12
2012 Dec	51,122	TSLM_log	68,131.69	-17,009.69
2013 Jan	50,313	TSLM_log	57,147.13	-6,834.13
2013 Feb	58,615	TSLM_log	69,355.42	-10,740.42
2013 Mar	92,426	TSLM_log	88,742.57	3,683.43
2013 Apr	100,996	TSLM_log	108,742.62	-7,746.62
2013 May	123,431	TSLM_log	107,138.80	16,292.20
2013 Jun	143,946	TSLM_log	112,699.64	31,246.36
2013 Jul	171,016	TSLM_log	133,949.49	37,066.51
2013 Aug	252,423	TSLM_log	193,419.36	59,003.64
2013 Sep	158,839	TSLM_log	128,840.63	29,998.37
2013 Oct	109,956	TSLM_log	101,648.73	8,307.27
2013 Nov	82,040	TSLM_log	77,403.79	4,636.21
2013 Dec	72,692	TSLM_log	69,466.89	3,225.11
2014 Jan	56,872	TSLM_log	59,413.57	-2,541.57
2014 Feb	64,346	TSLM_log	72,007.49	-7,661.49
2014 Mar	102,852	TSLM_log	93,614.80	9,237.20
2014 Apr	151,151	TSLM_log	113,891.98	37,259.02
2014 May	148,593	TSLM_log	114,710.00	33,883.00
2014 Jun	154,231	TSLM_log	121,826.32	32,404.68
2014 Jul	194,227	TSLM_log	144,771.92	49,455.08
2014 Aug	303,902	TSLM_log	209,573.89	94,328.11
2014 Sep	186,247	TSLM_log	139,313.24	46,933.76
2014 Oct	133,884	TSLM_log	109,051.62	24,832.38
2014 Nov	86,161	TSLM_log	83,100.98	3,060.02
2014 Dec	81,830	TSLM_log	74,486.92	7,343.08
2015 Jan	68,436	TSLM_log	63,513.10	4,922.90
2015 Feb	84,417	TSLM_log	76,785.77	7,631.23
2015 Mar	116,291	TSLM_log	101,575.34	14,715.66
2015 Apr	145,183	TSLM_log	125,235.91	19,947.09
2015 May	172,016	TSLM_log	125,628.50	46,387.50
2015 Jun	182,765	TSLM_log	133,354.40	49,410.60
2015 Jul	238,708	TSLM_log	159,313.28	79,394.72
2015 Aug	358,044	TSLM_log	232,289.33	125,754.67
2015 Sep	216,474	TSLM_log	153,753.90	62,720.10
2015 Oct	148,376	TSLM_log	119,785.72	28,590.28
2015 Nov	99,794	TSLM_log	90,274.81	9,519.19
2015 Dec	93,804	TSLM_log	81,311.58	12,492.42
2016 Jan	74,572	TSLM_log	69,466.98	5,105.02
2016 Feb	97,522	TSLM_log	84,085.48	13,436.52
2016 Mar	144,216	TSLM_log	111,616.27	32,599.73
2016 Apr	153,386	TSLM_log	138,009.00	15,377.00
2016 May	168,235	TSLM_log	139,796.01	28,438.99
2016 Jun	215,800	TSLM_log	148,084.70	67,715.30
2016 Jul	271,212	TSLM_log	178,091.11	93,120.89
2016 Aug	380,776	TSLM_log	260,210.78	120,565.22
2016 Sep	249,098	TSLM_log	171,120.51	77,977.49
2016 Oct	175,862	TSLM_log	132,330.79	43,531.21
2016 Nov	102,775	TSLM_log	99,134.95	3,640.05
2016 Dec	100,859	TSLM_log	89,449.58	11,409.42
2017 Jan	83,249	TSLM_log	76,223.78	7,025.22
2017 Feb	105,210	TSLM_log	92,711.52	12,498.48
2017 Mar	121,167	TSLM_log	123,809.75	-2,642.75
2017 Apr	217,906	TSLM_log	151,082.49	66,823.51
2017 May	196,622	TSLM_log	154,399.47	42,222.53
2017 Jun	248,582	TSLM_log	165,555.47	83,026.53
2017 Jul	323,496	TSLM_log	199,721.58	123,774.42
2017 Aug	431,571	TSLM_log	291,436.18	140,134.82
2017 Sep	287,242	TSLM_log	191,639.63	95,602.37
2017 Oct	212,357	TSLM_log	147,480.60	64,876.40
2017 Nov	127,745	TSLM_log	109,018.97	18,726.03
2017 Dec	132,238	TSLM_log	99,025.37	33,212.63
2018 Jan	95,453	TSLM_log	84,629.79	10,823.21
2018 Feb	120,303	TSLM_log	103,207.18	17,095.82
2018 Mar	162,886	TSLM_log	136,754.94	26,131.06
2018 Apr	187,186	TSLM_log	171,004.29	16,181.71
2018 May	239,851	TSLM_log	172,840.06	67,010.94
2018 Jun	264,588	TSLM_log	187,279.67	77,308.33
2018 Jul	339,564	TSLM_log	226,677.53	112,886.47
2018 Aug	446,375	TSLM_log	328,741.46	117,633.54
2018 Sep	304,516	TSLM_log	216,044.84	88,471.16
2018 Oct	230,827	TSLM_log	165,747.26	65,079.74
2018 Nov	149,080	TSLM_log	121,073.14	28,006.86
2018 Dec	135,316	TSLM_log	110,853.31	24,462.69
2019 Jan	114,710	TSLM_log	93,913.37	20,796.63
2019 Feb	122,635	TSLM_log	114,860.98	7,774.02
2019 Mar	172,412	TSLM_log	152,183.35	20,228.65
2019 Apr	241,790	TSLM_log	189,321.53	52,468.47
2019 May	259,714	TSLM_log	194,178.67	65,535.33
2019 Jun	306,048	TSLM_log	210,491.18	95,556.82
2019 Jul	360,566	TSLM_log	255,670.03	104,895.97
2019 Aug	484,403	TSLM_log	368,564.93	115,838.07
2019 Sep	327,937	TSLM_log	242,589.12	85,347.88
2019 Oct	238,677	TSLM_log	185,891.43	52,785.57
2019 Nov	171,296	TSLM_log	134,766.26	36,529.74
2019 Dec	138,642	TSLM_log	123,388.18	15,253.82
2020 Jan	126,349	TSLM_log	104,569.29	21,779.71
2020 Feb	167,411	TSLM_log	127,017.65	40,393.35
2020 Mar	70,530	TSLM_log	169,276.24	-98,746.24
2020 Apr	13,892	TSLM_log	209,510.09	-195,618.09
2020 May	38,343	TSLM_log	210,750.15	-172,407.15
2020 Jun	159,738	TSLM_log	225,123.71	-65,385.71
2020 Jul	272,786	TSLM_log	270,665.35	2,120.65
2020 Aug	407,020	TSLM_log	387,207.93	19,812.07
2020 Sep	258,651	TSLM_log	254,547.28	4,103.72
2020 Oct	167,448	TSLM_log	193,896.52	-26,448.52
2020 Nov	73,734	TSLM_log	139,859.93	-66,125.93
2020 Dec	73,353	TSLM_log	126,081.55	-52,728.55
2021 Jan	48,435	TSLM_log	106,079.82	-57,644.82
2021 Feb	40,443	TSLM_log	127,996.67	-87,553.67
2021 Mar	60,251	TSLM_log	159,084.52	-98,833.52
2021 Apr	85,179	TSLM_log	180,263.57	-95,084.57
2021 May	169,690	TSLM_log	192,159.49	-22,469.49
2021 Jun	254,243	TSLM_log	221,904.46	32,338.54
2021 Jul	329,058	TSLM_log	272,784.36	56,273.64
2021 Aug	461,844	TSLM_log	391,887.10	69,956.90
2021 Sep	308,273	TSLM_log	257,571.26	50,701.74
2021 Oct	250,949	TSLM_log	195,070.83	55,878.17
2021 Nov	156,624	TSLM_log	138,073.83	18,550.17
2021 Dec	115,100	TSLM_log	126,034.95	-10,934.95
2022 Jan	96,107	TSLM_log	105,319.87	-9,212.87
2022 Feb	141,508	TSLM_log	125,866.22	15,641.78
2022 Mar	167,854	TSLM_log	159,713.28	8,140.72
2022 Apr	248,959	TSLM_log	184,666.35	64,292.65
2022 May	258,413	TSLM_log	204,807.24	53,605.76
2022 Jun	300,520	TSLM_log	240,316.34	60,203.66

# Show Forecast error in Plot: 2000-2022
error_fc_alentejo_stretch %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_until2022, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2000-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2010-2022
tourism_alentejo_from2010 <- tourism_alentejo_until2022 %>%
  filter(year(Month) >= 2010)

error_fc_alentejo_stretch %>%
  filter(year(Month) >= 2010) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_from2010, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2010-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2019-2022
tourism_alentejo_from2019 <- tourism_alentejo_until2022 %>%
  filter(year(Month) >= 2019)

error_fc_alentejo_stretch %>%
  filter(year(Month) >= 2019) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_from2019, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2019-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2020-2022
tourism_alentejo_from2020 <- tourism_alentejo_until2022 %>%
  filter(year(Month) >= 2020)

error_fc_alentejo_stretch %>%
  filter(year(Month) >= 2020) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_from2020, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2020-2022") +
  ylab("Overnight_Stays")

2.3.1.4 Change of RMSE: 2010-2019 vs. 2010-2022

All Models

Note: In the following, “All Models” means that all 20 models are shown. Each model appears twice: With the original & with the log-transformed variable.

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2019) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
ARIMA_d0D1_log	2	14,564.93	1	26,522.64
ARIMA_auto_log	3	14,847.27	2	26,808.36
ARIMA_auto	7	16,064.90	3	28,008.37
Drift_STL	12	22,338.22	4	28,040.79
ARIMA_d0D1	8	16,153.62	5	28,061.70
ARIMA_d1D1	5	15,731.55	6	28,349.73
Drift_STL_log	4	15,210.18	7	28,442.77
ETS_auto_log	6	15,873.19	8	29,933.59
ARIMA_d1D1_log	1	13,980.47	9	30,067.64
ETS_auto	10	17,707.32	10	32,766.78
HWA	11	17,819.80	11	34,305.99
HWA_log	9	16,901.77	12	36,259.58
Prophet_log	14	22,611.09	13	46,909.32
SNaive	15	23,520.64	14	50,152.41
SNaive_log	13	22,519.04	15	50,181.53
TSLM_log	17	47,252.29	16	52,720.38
Prophet	16	44,546.91	17	58,961.09
Naive	19	56,208.84	18	61,485.90
TSLM	18	55,439.33	19	61,588.70
Naive_log	20	57,470.65	20	62,863.34

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

Note: In the following, “Each Model once” means that each model appears only once: Either with the original or with the log-transformed variable (depending on the lowest RMSE for the 2010-2022 Forecasts).

# Save best models according to the RMSE of Forecasts from 2010-2022
best_models_fc_alentejo_stretch <- c("ARIMA_d0D1_log", "Drift_STL", "ARIMA_d1D1", "ARIMA_auto_log", "HWA", "ETS_auto_log", "Naive", "Prophet_log", "TSLM_log", "SNaive")

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2019) %>%
  filter(.model %in% best_models_fc_alentejo_stretch) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2022) %>%
  filter(.model %in% best_models_fc_alentejo_stretch) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
ARIMA_d0D1_log	1	14,564.93	1	26,522.64
ARIMA_auto_log	2	14,847.27	2	26,808.36
Drift_STL	6	22,338.22	3	28,040.79
ARIMA_d1D1	3	15,731.55	4	28,349.73
ETS_auto_log	4	15,873.19	5	29,933.59
HWA	5	17,819.80	6	34,305.99
Prophet_log	7	22,611.09	7	46,909.32
SNaive	8	23,520.64	8	50,152.41
TSLM_log	9	47,252.29	9	52,720.38
Naive	10	56,208.84	10	61,485.90

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.3.1.5 RMSE Development by including more Years in Time Series

# Compute RMSE and RMSSE for 2010 and create tibble
tourism_until_i <- tourism_alentejo_until2022 %>%
    filter(year(Month) <= 2010)

accuracy_alentejo_stretch <- accuracy(fc_alentejo_stretch, tourism_until_i) %>%
  select(c(.model, RMSE, RMSSE)) %>%
  mutate(Until_Year = 2010)

# Create tsibble of summarized RMSE and RMSSE, beginning in 2010 and including more years
for (i in 2011:2022){
  tourism_until_i <- tourism_alentejo_until2022 %>%
    filter(year(Month) <= i)

  accuracy_next_year <- accuracy(fc_alentejo_stretch, tourism_until_i) %>%
    select(c(.model, RMSE, RMSSE)) %>%
    mutate(Until_Year = i)

  accuracy_alentejo_stretch <- rbind(accuracy_alentejo_stretch, accuracy_next_year)
}

rm(accuracy_next_year, tourism_until_i) # remove variables from R environment

accuracy_alentejo_stretch <- accuracy_alentejo_stretch %>%
  rename(Model = .model) %>%
  select(c(Until_Year, Model, RMSE, RMSSE)) %>%
  as_tsibble(key = Model, index = Until_Year)

# Show table
accuracy_alentejo_stretch %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	6,200.854	0.67
2011	ARIMA_auto	9,681.848	1.03
2012	ARIMA_auto	9,210.514	0.97
2013	ARIMA_auto	11,050.463	0.93
2014	ARIMA_auto	14,460.413	1.08
2015	ARIMA_auto	14,700.788	1.01
2016	ARIMA_auto	14,918.491	0.99
2017	ARIMA_auto	16,062.132	0.93
2018	ARIMA_auto	16,357.681	0.93
2019	ARIMA_auto	16,064.895	0.88
2020	ARIMA_auto	27,322.477	0.85
2021	ARIMA_auto	26,900.044	0.75
2022	ARIMA_auto	28,008.367	0.72
2010	ARIMA_auto_log	4,525.033	0.49
2011	ARIMA_auto_log	7,602.117	0.81
2012	ARIMA_auto_log	8,466.461	0.89
2013	ARIMA_auto_log	9,402.958	0.79
2014	ARIMA_auto_log	11,927.990	0.89
2015	ARIMA_auto_log	12,082.201	0.83
2016	ARIMA_auto_log	12,683.162	0.84
2017	ARIMA_auto_log	13,906.376	0.81
2018	ARIMA_auto_log	14,556.836	0.83
2019	ARIMA_auto_log	14,847.272	0.81
2020	ARIMA_auto_log	25,834.830	0.80
2021	ARIMA_auto_log	25,457.295	0.71
2022	ARIMA_auto_log	26,808.357	0.69
2010	ARIMA_d0D1	6,200.854	0.67
2011	ARIMA_d0D1	9,681.848	1.03
2012	ARIMA_d0D1	9,210.514	0.97
2013	ARIMA_d0D1	11,050.463	0.93
2014	ARIMA_d0D1	14,216.382	1.07
2015	ARIMA_d0D1	14,515.940	0.99
2016	ARIMA_d0D1	14,761.318	0.97
2017	ARIMA_d0D1	16,002.341	0.93
2018	ARIMA_d0D1	16,340.804	0.93
2019	ARIMA_d0D1	16,153.616	0.89
2020	ARIMA_d0D1	27,384.592	0.85
2021	ARIMA_d0D1	26,957.881	0.75
2022	ARIMA_d0D1	28,061.699	0.73
2010	ARIMA_d0D1_log	4,525.033	0.49
2011	ARIMA_d0D1_log	7,602.117	0.81
2012	ARIMA_d0D1_log	8,466.461	0.89
2013	ARIMA_d0D1_log	9,402.958	0.79
2014	ARIMA_d0D1_log	11,927.990	0.89
2015	ARIMA_d0D1_log	12,061.310	0.83
2016	ARIMA_d0D1_log	12,524.064	0.83
2017	ARIMA_d0D1_log	14,135.486	0.82
2018	ARIMA_d0D1_log	14,467.014	0.82
2019	ARIMA_d0D1_log	14,564.930	0.80
2020	ARIMA_d0D1_log	25,497.508	0.79
2021	ARIMA_d0D1_log	25,143.613	0.70
2022	ARIMA_d0D1_log	26,522.638	0.69
2010	ARIMA_d1D1	7,779.810	0.85
2011	ARIMA_d1D1	10,233.124	1.08
2012	ARIMA_d1D1	9,689.376	1.02
2013	ARIMA_d1D1	11,128.814	0.94
2014	ARIMA_d1D1	13,707.859	1.03
2015	ARIMA_d1D1	14,087.159	0.96
2016	ARIMA_d1D1	14,402.078	0.95
2017	ARIMA_d1D1	15,644.272	0.91
2018	ARIMA_d1D1	15,993.654	0.91
2019	ARIMA_d1D1	15,731.554	0.86
2020	ARIMA_d1D1	27,486.413	0.86
2021	ARIMA_d1D1	27,181.928	0.76
2022	ARIMA_d1D1	28,349.730	0.73
2010	ARIMA_d1D1_log	5,650.684	0.61
2011	ARIMA_d1D1_log	8,026.343	0.85
2012	ARIMA_d1D1_log	8,429.597	0.89
2013	ARIMA_d1D1_log	9,812.299	0.83
2014	ARIMA_d1D1_log	10,682.838	0.80
2015	ARIMA_d1D1_log	10,214.354	0.70
2016	ARIMA_d1D1_log	11,187.741	0.74
2017	ARIMA_d1D1_log	12,733.907	0.74
2018	ARIMA_d1D1_log	13,569.714	0.77
2019	ARIMA_d1D1_log	13,980.471	0.77
2020	ARIMA_d1D1_log	27,309.019	0.85
2021	ARIMA_d1D1_log	28,239.741	0.79
2022	ARIMA_d1D1_log	30,067.640	0.78
2010	Drift_STL	6,379.537	0.69
2011	Drift_STL	11,007.648	1.17
2012	Drift_STL	10,309.444	1.08
2013	Drift_STL	12,515.398	1.06
2014	Drift_STL	15,969.507	1.20
2015	Drift_STL	18,631.482	1.28
2016	Drift_STL	19,861.578	1.31
2017	Drift_STL	22,193.383	1.29
2018	Drift_STL	22,403.232	1.27
2019	Drift_STL	22,338.220	1.23
2020	Drift_STL	28,160.847	0.88
2021	Drift_STL	28,172.785	0.78
2022	Drift_STL	28,040.788	0.72
2010	Drift_STL_log	5,749.181	0.62
2011	Drift_STL_log	7,992.168	0.85
2012	Drift_STL_log	7,991.590	0.84
2013	Drift_STL_log	9,064.880	0.77
2014	Drift_STL_log	10,361.515	0.78
2015	Drift_STL_log	10,657.635	0.73
2016	Drift_STL_log	11,360.205	0.75
2017	Drift_STL_log	14,493.932	0.84
2018	Drift_STL_log	15,184.068	0.86
2019	Drift_STL_log	15,210.181	0.83
2020	Drift_STL_log	25,612.191	0.80
2021	Drift_STL_log	25,517.966	0.71
2022	Drift_STL_log	28,442.772	0.74
2010	ETS_auto	10,309.567	1.12
2011	ETS_auto	11,445.615	1.21
2012	ETS_auto	11,685.690	1.23
2013	ETS_auto	13,101.111	1.11
2014	ETS_auto	13,994.203	1.05
2015	ETS_auto	14,620.493	1.00
2016	ETS_auto	15,513.290	1.02
2017	ETS_auto	17,306.514	1.01
2018	ETS_auto	17,745.525	1.01
2019	ETS_auto	17,707.316	0.97
2020	ETS_auto	28,261.026	0.88
2021	ETS_auto	31,621.262	0.88
2022	ETS_auto	32,766.781	0.85
2010	ETS_auto_log	6,397.836	0.70
2011	ETS_auto_log	9,333.524	0.99
2012	ETS_auto_log	11,113.378	1.17
2013	ETS_auto_log	12,823.819	1.08
2014	ETS_auto_log	13,759.220	1.03
2015	ETS_auto_log	14,138.577	0.97
2016	ETS_auto_log	14,136.359	0.93
2017	ETS_auto_log	15,283.000	0.89
2018	ETS_auto_log	15,815.158	0.90
2019	ETS_auto_log	15,873.189	0.87
2020	ETS_auto_log	29,804.378	0.93
2021	ETS_auto_log	30,008.928	0.83
2022	ETS_auto_log	29,933.593	0.77
2010	HWA	9,816.816	1.07
2011	HWA	13,812.607	1.46
2012	HWA	13,246.137	1.39
2013	HWA	14,686.632	1.24
2014	HWA	16,366.274	1.23
2015	HWA	16,914.591	1.16
2016	HWA	16,719.885	1.10
2017	HWA	17,768.515	1.03
2018	HWA	18,108.194	1.03
2019	HWA	17,819.799	0.98
2020	HWA	33,174.714	1.03
2021	HWA	34,519.149	0.96
2022	HWA	34,305.991	0.89
2010	HWA_log	6,273.793	0.68
2011	HWA_log	9,321.084	0.99
2012	HWA_log	10,626.887	1.12
2013	HWA_log	15,727.485	1.33
2014	HWA_log	16,568.830	1.24
2015	HWA_log	16,110.350	1.10
2016	HWA_log	15,815.612	1.04
2017	HWA_log	16,599.510	0.96
2018	HWA_log	16,958.084	0.96
2019	HWA_log	16,901.768	0.93
2020	HWA_log	36,084.207	1.12
2021	HWA_log	36,016.068	1.00
2022	HWA_log	36,259.581	0.94
2010	Naive	26,274.167	2.86
2011	Naive	32,012.238	3.39
2012	Naive	31,732.417	3.33
2013	Naive	34,711.475	2.93
2014	Naive	39,687.032	2.97
2015	Naive	44,420.789	3.04
2016	Naive	47,664.193	3.15
2017	Naive	51,569.749	3.00
2018	Naive	53,793.345	3.05
2019	Naive	56,208.838	3.08
2020	Naive	60,227.475	1.87
2021	Naive	62,111.059	1.73
2022	Naive	61,485.898	1.59
2010	Naive_log	26,843.127	2.92
2011	Naive_log	32,659.203	3.46
2012	Naive_log	32,404.379	3.40
2013	Naive_log	35,416.460	2.99
2014	Naive_log	40,492.282	3.03
2015	Naive_log	45,328.603	3.10
2016	Naive_log	48,659.867	3.21
2017	Naive_log	52,656.974	3.06
2018	Naive_log	54,967.458	3.12
2019	Naive_log	57,470.652	3.15
2020	Naive_log	61,679.953	1.92
2021	Naive_log	63,685.273	1.77
2022	Naive_log	62,863.335	1.63
2010	Prophet	9,724.106	1.06
2011	Prophet	13,926.532	1.48
2012	Prophet	15,312.300	1.61
2013	Prophet	19,843.009	1.68
2014	Prophet	25,365.063	1.90
2015	Prophet	30,652.915	2.10
2016	Prophet	34,886.875	2.30
2017	Prophet	39,590.988	2.30
2018	Prophet	42,005.635	2.38
2019	Prophet	44,546.915	2.44
2020	Prophet	55,977.994	1.74
2021	Prophet	59,524.235	1.66
2022	Prophet	58,961.087	1.52
2010	Prophet_log	7,885.291	0.86
2011	Prophet_log	10,281.057	1.09
2012	Prophet_log	11,100.268	1.17
2013	Prophet_log	16,966.068	1.43
2014	Prophet_log	20,484.443	1.53
2015	Prophet_log	21,660.951	1.48
2016	Prophet_log	21,848.126	1.44
2017	Prophet_log	23,097.839	1.34
2018	Prophet_log	22,937.074	1.30
2019	Prophet_log	22,611.087	1.24
2020	Prophet_log	39,607.199	1.23
2021	Prophet_log	45,592.436	1.27
2022	Prophet_log	46,909.315	1.21
2010	SNaive	8,030.533	0.87
2011	SNaive	9,953.632	1.05
2012	SNaive	10,097.614	1.06
2013	SNaive	16,132.891	1.36
2014	SNaive	18,504.521	1.39
2015	SNaive	20,077.454	1.37
2016	SNaive	20,306.377	1.34
2017	SNaive	23,061.290	1.34
2018	SNaive	23,138.554	1.31
2019	SNaive	23,520.644	1.29
2020	SNaive	42,516.003	1.32
2021	SNaive	46,873.597	1.30
2022	SNaive	50,152.414	1.30
2010	SNaive_log	7,601.864	0.83
2011	SNaive_log	9,536.815	1.01
2012	SNaive_log	10,019.964	1.05
2013	SNaive_log	15,817.202	1.34
2014	SNaive_log	18,021.254	1.35
2015	SNaive_log	19,441.550	1.33
2016	SNaive_log	19,572.441	1.29
2017	SNaive_log	22,198.990	1.29
2018	SNaive_log	22,245.548	1.26
2019	SNaive_log	22,519.035	1.24
2020	SNaive_log	43,684.506	1.36
2021	SNaive_log	47,363.390	1.32
2022	SNaive_log	50,181.532	1.30
2010	TSLM	9,610.826	1.04
2011	TSLM	13,479.255	1.43
2012	TSLM	14,407.164	1.51
2013	TSLM	19,415.747	1.64
2014	TSLM	26,371.609	1.98
2015	TSLM	33,930.986	2.32
2016	TSLM	39,737.672	2.62
2017	TSLM	47,109.509	2.74
2018	TSLM	51,417.802	2.92
2019	TSLM	55,439.329	3.04
2020	TSLM	59,804.947	1.86
2021	TSLM	62,099.151	1.73
2022	TSLM	61,588.699	1.59
2010	TSLM_log	6,113.985	0.66
2011	TSLM_log	9,115.047	0.97
2012	TSLM_log	10,411.619	1.09
2013	TSLM_log	15,299.809	1.29
2014	TSLM_log	22,060.215	1.65
2015	TSLM_log	29,251.057	2.00
2016	TSLM_log	34,474.151	2.28
2017	TSLM_log	41,198.920	2.39
2018	TSLM_log	44,596.250	2.53
2019	TSLM_log	47,252.294	2.59
2020	TSLM_log	52,246.690	1.63
2021	TSLM_log	53,091.141	1.48
2022	TSLM_log	52,720.381	1.36

All Models

# Plot development of RMSE for period 2010-2022
accuracy_alentejo_stretch %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_alentejo_stretch %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_alentejo_stretch %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_alentejo_stretch %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_alentejo_stretch %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	56,208.84	60,227.48	4,018.64	0.0715
Naive_log	57,470.65	61,679.95	4,209.30	0.0732
TSLM	55,439.33	59,804.95	4,365.62	0.0787
TSLM_log	47,252.29	52,246.69	4,994.40	0.1057
Prophet	44,546.91	55,977.99	11,431.08	0.2566
Drift_STL	22,338.22	28,160.85	5,822.63	0.2607
ETS_auto	17,707.32	28,261.03	10,553.71	0.5960
Drift_STL_log	15,210.18	25,612.19	10,402.01	0.6839
ARIMA_d0D1	16,153.62	27,384.59	11,230.98	0.6953
ARIMA_auto	16,064.90	27,322.48	11,257.58	0.7008
ARIMA_auto_log	14,847.27	25,834.83	10,987.56	0.7400
ARIMA_d1D1	15,731.55	27,486.41	11,754.86	0.7472
ARIMA_d0D1_log	14,564.93	25,497.51	10,932.58	0.7506
Prophet_log	22,611.09	39,607.20	16,996.11	0.7517
SNaive	23,520.64	42,516.00	18,995.36	0.8076
HWA	17,819.80	33,174.71	15,354.91	0.8617
ETS_auto_log	15,873.19	29,804.38	13,931.19	0.8777
SNaive_log	22,519.04	43,684.51	21,165.47	0.9399
ARIMA_d1D1_log	13,980.47	27,309.02	13,328.55	0.9534
HWA_log	16,901.77	36,084.21	19,182.44	1.1349

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

Each Model once

# Plot development of RMSE for period 2010-2022
accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	56,208.84	60,227.48	4,018.64	0.0715
TSLM_log	47,252.29	52,246.69	4,994.40	0.1057
Drift_STL	22,338.22	28,160.85	5,822.63	0.2607
ARIMA_auto_log	14,847.27	25,834.83	10,987.56	0.7400
ARIMA_d1D1	15,731.55	27,486.41	11,754.86	0.7472
ARIMA_d0D1_log	14,564.93	25,497.51	10,932.58	0.7506
Prophet_log	22,611.09	39,607.20	16,996.11	0.7517
SNaive	23,520.64	42,516.00	18,995.36	0.8076
HWA	17,819.80	33,174.71	15,354.91	0.8617
ETS_auto_log	15,873.19	29,804.38	13,931.19	0.8777

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

2.3.1.6 RMSE per Year

All Models

# Calculate RMSE per year and save as tsibble
rmse_pyear_alentejo_stretch <- error_fc_alentejo_stretch %>%
  mutate(Year = year(Month)) %>%
  index_by(Year) %>%
  group_by(Model) %>%
  summarise(RMSE = (mean(Forecast_Error**2))**0.5)

# Create Plot for 2010-2022
rmse_pyear_alentejo_stretch %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Create Plot for 2020-2022
rmse_pyear_alentejo_stretch %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_alentejo_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
TSLM	92,777.99	9,464.85	0.1136
Naive	91,140.01	16,636.19	0.2233
Naive_log	93,913.92	17,520.43	0.2293
TSLM_log	87,744.45	21,198.51	0.3186
Prophet	120,932.28	57,971.85	0.9208
Drift_STL	61,101.60	39,357.23	1.8100
ARIMA_auto_log	71,675.72	54,433.28	3.1569
ETS_auto	75,166.82	57,807.18	3.3300
SNaive	119,797.78	93,083.13	3.4843
Drift_STL_log	70,016.65	54,573.44	3.5338
ARIMA_d1D1_log	79,051.07	61,808.64	3.5847
ARIMA_d0D1_log	70,922.35	55,504.14	3.5999
SNaive_log	126,176.97	101,331.65	4.0785
ETS_auto_log	85,157.09	68,770.87	4.1969
ARIMA_d0D1	75,097.81	60,738.27	4.2298
Prophet_log	110,197.19	90,764.52	4.6707
ARIMA_auto	75,039.23	61,899.78	4.7110
ARIMA_d1D1	76,391.85	63,252.40	4.8139
HWA	94,502.52	79,526.13	5.3101
HWA_log	107,079.75	90,693.53	5.5347

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_alentejo_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_d0D1	21,717.59	-53,380.22	-0.7108
ARIMA_auto	21,717.59	-53,321.65	-0.7106
ARIMA_auto_log	20,858.16	-50,817.55	-0.7090
ARIMA_d0D1_log	20,858.16	-50,064.19	-0.7059
ARIMA_d1D1	23,574.45	-52,817.40	-0.6914
HWA_log	35,257.85	-71,821.90	-0.6707
Drift_STL_log	24,457.53	-45,559.12	-0.6507
ETS_auto_log	32,173.27	-52,983.82	-0.6222
Drift_STL	28,303.77	-32,797.83	-0.5368
ARIMA_d1D1_log	36,961.98	-42,089.09	-0.5324
HWA	46,826.08	-47,676.44	-0.5045
SNaive_log	76,992.16	-49,184.81	-0.3898
SNaive	80,510.21	-39,287.58	-0.3279
TSLM_log	61,621.00	-26,123.45	-0.2977
Prophet	89,714.67	-31,217.62	-0.2581
ETS_auto	56,686.06	-18,480.77	-0.2459
Prophet_log	87,681.30	-22,515.88	-0.2043
Naive	79,953.53	-11,186.48	-0.1227
Naive_log	82,590.46	-11,323.46	-0.1206
TSLM	83,262.88	-9,515.11	-0.1026

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_alentejo_stretch %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive_log	38,150.20	-44,440.26	-0.5381
Prophet	43,301.46	-46,413.21	-0.5173
Naive	43,887.16	-36,066.38	-0.4511
TSLM	47,727.20	-35,535.68	-0.4268
HWA	28,719.43	-18,106.65	-0.3867
TSLM_log	42,870.77	-18,750.23	-0.3043
Prophet_log	71,582.19	-16,099.11	-0.1836
Drift_STL	24,661.84	-3,641.93	-0.1287
ETS_auto_log	28,064.94	-4,108.33	-0.1277
ETS_auto	53,327.74	-3,358.31	-0.0592
HWA_log	41,679.23	6,421.38	0.1821
SNaive_log	95,476.05	18,483.90	0.2401
SNaive	100,749.18	20,238.97	0.2514
ARIMA_d1D1_log	58,838.62	21,876.64	0.5919
ARIMA_d1D1	48,580.93	25,006.49	1.0607
ARIMA_auto	47,381.62	25,664.03	1.1817
ARIMA_d0D1	47,381.62	25,664.03	1.1817
ARIMA_auto_log	49,126.65	28,268.48	1.3553
ARIMA_d0D1_log	49,126.65	28,268.48	1.3553
Drift_STL_log	67,799.59	43,342.06	1.7721

Each Model once

# Create Plot for 2010-2022
rmse_pyear_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022")

# Create Plot for 2020-2022
rmse_pyear_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022")

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	91,140.01	16,636.19	0.2233
TSLM_log	87,744.45	21,198.51	0.3186
Drift_STL	61,101.60	39,357.23	1.8100
ARIMA_auto_log	71,675.72	54,433.28	3.1569
SNaive	119,797.78	93,083.13	3.4843
ARIMA_d0D1_log	70,922.35	55,504.14	3.5999
ETS_auto_log	85,157.09	68,770.87	4.1969
Prophet_log	110,197.19	90,764.52	4.6707
ARIMA_d1D1	76,391.85	63,252.40	4.8139
HWA	94,502.52	79,526.13	5.3101

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_auto_log	20,858.16	-50,817.55	-0.7090
ARIMA_d0D1_log	20,858.16	-50,064.19	-0.7059
ARIMA_d1D1	23,574.45	-52,817.40	-0.6914
ETS_auto_log	32,173.27	-52,983.82	-0.6222
Drift_STL	28,303.77	-32,797.83	-0.5368
HWA	46,826.08	-47,676.44	-0.5045
SNaive	80,510.21	-39,287.58	-0.3279
TSLM_log	61,621.00	-26,123.45	-0.2977
Prophet_log	87,681.30	-22,515.88	-0.2043
Naive	79,953.53	-11,186.48	-0.1227

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	43,887.16	-36,066.38	-0.4511
HWA	28,719.43	-18,106.65	-0.3867
TSLM_log	42,870.77	-18,750.23	-0.3043
Prophet_log	71,582.19	-16,099.11	-0.1836
Drift_STL	24,661.84	-3,641.93	-0.1287
ETS_auto_log	28,064.94	-4,108.33	-0.1277
SNaive	100,749.18	20,238.97	0.2514
ARIMA_d1D1	48,580.93	25,006.49	1.0607
ARIMA_auto_log	49,126.65	28,268.48	1.3553
ARIMA_d0D1_log	49,126.65	28,268.48	1.3553

2.3.1.7 Change of RMSSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2019) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
ARIMA_d0D1_log	2	0.7990	1	0.6857
ARIMA_auto_log	3	0.8145	2	0.6931
ARIMA_auto	7	0.8813	3	0.7241
Drift_STL	12	1.2254	4	0.7249
ARIMA_d0D1	8	0.8861	5	0.7255
ARIMA_d1D1	5	0.8630	6	0.7329
Drift_STL_log	4	0.8344	7	0.7353
ETS_auto_log	6	0.8707	8	0.7739
ARIMA_d1D1_log	1	0.7669	9	0.7773
ETS_auto	10	0.9713	10	0.8471
HWA	11	0.9775	11	0.8869
HWA_log	9	0.9272	12	0.9374
Prophet_log	14	1.2403	13	1.2127
SNaive	15	1.2902	14	1.2966
SNaive_log	13	1.2353	15	1.2973
TSLM_log	17	2.5921	16	1.3629
Prophet	16	2.4437	17	1.5243
Naive	19	3.0834	18	1.5896
TSLM	18	3.0412	19	1.5922
Naive_log	20	3.1526	20	1.6252

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2019) %>%
  filter(.model %in% best_models_fc_alentejo_stretch) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_stretch, tourism_alentejo_until2022) %>%
  filter(.model %in% best_models_fc_alentejo_stretch) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
ARIMA_d0D1_log	1	0.7990	1	0.6857
ARIMA_auto_log	2	0.8145	2	0.6931
Drift_STL	6	1.2254	3	0.7249
ARIMA_d1D1	3	0.8630	4	0.7329
ETS_auto_log	4	0.8707	5	0.7739
HWA	5	0.9775	6	0.8869
Prophet_log	7	1.2403	7	1.2127
SNaive	8	1.2902	8	1.2966
TSLM_log	9	2.5921	9	1.3629
Naive	10	3.0834	10	1.5896

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.3.1.8 RMSSE Development by including more Years in Time Series

All Models

# Plot development of RMSSE for period 2010-2022
accuracy_alentejo_stretch %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_alentejo_stretch %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_alentejo_stretch %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

Each Model once

# Plot development of RMSSE for period 2010-2022
accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_alentejo_stretch %>%
  filter(Model %in% best_models_fc_alentejo_stretch) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSSE")

2.3.2 Rolling Window Cross-Validation

2.3.2.1 Time series Cross-Validation & Seasonal Strength Test

# Cross-Validation with sliding Window to create Training sets
data_slide_alentejo <- tourism_alentejo_until2022 %>%
  slide_tsibble (.size = 120, .step = 1) %>%
  filter (.id != max(.id))

# Testing for Seasonal Strength
data_slide_alentejo %>%
  features(Overnight_Stays, unitroot_nsdiffs) %>%
  group_by(Region) %>%
  summarise(Mean_nsdiffs = (mean(nsdiffs))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Seasonal Strength Test</span>", align = "lc") %>%
  column_spec(2, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover", "condensed"), full_width = F)

Seasonal Strength Test

Region	Mean_nsdiffs
Alentejo	1

2.3.2.2 Fitting Models and one-step ahead Forecasts

# Fit models
fit_alentejo_slide <- data_slide_alentejo %>%
  model(
    SNaive = SNAIVE(Overnight_Stays),
    Drift_STL = decomposition_model(STL(Overnight_Stays),RW(season_adjust ~ drift())),
    Naive = NAIVE(Overnight_Stays),
    TSLM = TSLM(Overnight_Stays ~ trend() + season()),
    ETS_auto = ETS(Overnight_Stays),
    HWA = ETS(Overnight_Stays ~ error("A") + trend("A") + season("A")),
    ARIMA_auto = ARIMA(Overnight_Stays),
    ARIMA_d1D1 = ARIMA(Overnight_Stays ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)),
    Prophet = fable.prophet::prophet(Overnight_Stays ~ season(period = 12)),
    SNaive_log = SNAIVE(log(Overnight_Stays)),
    Drift_STL_log = decomposition_model(STL(log(Overnight_Stays)),RW(season_adjust ~ drift())),
    Naive_log = NAIVE(log(Overnight_Stays)),
    TSLM_log = TSLM(log(Overnight_Stays) ~ trend() + season()),
    ETS_auto_log = ETS(log(Overnight_Stays)),
    HWA_log = ETS(log(Overnight_Stays) ~ error("A") + trend("A") + season("A")),
    ARIMA_auto_log = ARIMA(log(Overnight_Stays)),
    ARIMA_d1D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=1) + PDQ(D=1)),
    ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)),
    Prophet_log = fable.prophet::prophet(log(Overnight_Stays) ~ season(period = 12))
    )

# Perform a one-step ahead Forecast
fc_alentejo_slide <- fit_alentejo_slide %>% forecast(h=1)

2.3.2.3 Forecast Errors

# Calculate forecast error per observation and model
error_fc_alentejo_slide <- merge(tourism_alentejo_until2022, fc_alentejo_slide, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# Show table
error_fc_alentejo_slide %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Forecast Error per Observation and Model</span>", digits = 2, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Forecast Error per Observation and Model

Month	Overnight_Stays	Model	Point_Forecast	Forecast_Error
2010 Jan	53,653	ARIMA_auto	54,763.29	-1,110.29
2010 Feb	62,257	ARIMA_auto	65,300.63	-3,043.63
2010 Mar	77,588	ARIMA_auto	80,270.54	-2,682.54
2010 Apr	99,982	ARIMA_auto	96,572.52	3,409.48
2010 May	101,387	ARIMA_auto	98,595.16	2,791.84
2010 Jun	108,611	ARIMA_auto	100,957.41	7,653.59
2010 Jul	126,498	ARIMA_auto	116,384.37	10,113.63
2010 Aug	178,380	ARIMA_auto	167,620.91	10,759.09
2010 Sep	127,822	ARIMA_auto	119,068.25	8,753.75
2010 Oct	104,174	ARIMA_auto	101,220.21	2,953.79
2010 Nov	69,271	ARIMA_auto	82,442.97	-13,171.97
2010 Dec	62,935	ARIMA_auto	69,793.01	-6,858.01
2011 Jan	60,457	ARIMA_auto	55,116.69	5,340.31
2011 Feb	67,260	ARIMA_auto	68,821.42	-1,561.42
2011 Mar	83,464	ARIMA_auto	83,982.49	-518.49
2011 Apr	102,958	ARIMA_auto	101,295.44	1,662.56
2011 May	101,223	ARIMA_auto	104,111.15	-2,888.15
2011 Jun	120,148	ARIMA_auto	106,357.50	13,790.50
2011 Jul	136,999	ARIMA_auto	123,663.11	13,335.89
2011 Aug	212,668	ARIMA_auto	179,439.01	33,228.99
2011 Sep	129,606	ARIMA_auto	134,738.72	-5,132.72
2011 Oct	101,185	ARIMA_auto	110,198.24	-9,013.24
2011 Nov	62,121	ARIMA_auto	73,341.51	-11,220.51
2011 Dec	65,563	ARIMA_auto	63,821.19	1,741.81
2012 Jan	49,716	ARIMA_auto	59,818.90	-10,102.90
2012 Feb	58,638	ARIMA_auto	68,887.71	-10,249.71
2012 Mar	72,210	ARIMA_auto	80,164.90	-7,954.90
2012 Apr	87,406	ARIMA_auto	99,923.31	-12,517.31
2012 May	96,946	ARIMA_auto	99,882.00	-2,936.00
2012 Jun	115,885	ARIMA_auto	111,039.04	4,845.96
2012 Jul	139,695	ARIMA_auto	132,192.31	7,502.69
2012 Aug	194,368	ARIMA_auto	199,132.92	-4,764.92
2012 Sep	127,610	ARIMA_auto	130,322.51	-2,712.51
2012 Oct	89,649	ARIMA_auto	102,488.05	-12,839.05
2012 Nov	58,900	ARIMA_auto	67,476.34	-8,576.34
2012 Dec	51,122	ARIMA_auto	62,568.68	-11,446.68
2013 Jan	50,313	ARIMA_auto	51,914.18	-1,601.18
2013 Feb	58,615	ARIMA_auto	62,577.82	-3,962.82
2013 Mar	92,426	ARIMA_auto	77,705.73	14,720.27
2013 Apr	100,996	ARIMA_auto	101,336.32	-340.32
2013 May	123,431	ARIMA_auto	107,971.83	15,459.17
2013 Jun	143,946	ARIMA_auto	122,773.51	21,172.49
2013 Jul	171,016	ARIMA_auto	155,092.09	15,923.91
2013 Aug	252,423	ARIMA_auto	224,639.82	27,783.18
2013 Sep	158,839	ARIMA_auto	160,599.79	-1,760.79
2013 Oct	109,956	ARIMA_auto	125,189.66	-15,233.66
2013 Nov	82,040	ARIMA_auto	74,032.90	8,007.10
2013 Dec	72,692	ARIMA_auto	69,353.30	3,338.70
2014 Jan	56,872	ARIMA_auto	61,948.73	-5,076.73
2014 Feb	64,346	ARIMA_auto	66,964.00	-2,618.00
2014 Mar	102,852	ARIMA_auto	86,828.12	16,023.88
2014 Apr	151,151	ARIMA_auto	104,945.33	46,205.67
2014 May	148,593	ARIMA_auto	144,081.54	4,511.46
2014 Jun	154,231	ARIMA_auto	165,135.77	-10,904.77
2014 Jul	194,227	ARIMA_auto	177,491.97	16,735.03
2014 Aug	303,902	ARIMA_auto	251,508.21	52,393.79
2014 Sep	186,247	ARIMA_auto	193,994.96	-7,747.96
2014 Oct	133,884	ARIMA_auto	137,689.94	-3,805.94
2014 Nov	86,161	ARIMA_auto	105,231.39	-19,070.39
2014 Dec	81,830	ARIMA_auto	92,602.00	-10,772.00
2015 Jan	68,436	ARIMA_auto	78,306.90	-9,870.90
2015 Feb	84,417	ARIMA_auto	81,025.19	3,391.81
2015 Mar	116,291	ARIMA_auto	121,885.60	-5,594.60
2015 Apr	145,183	ARIMA_auto	150,125.32	-4,942.32
2015 May	172,016	ARIMA_auto	157,818.70	14,197.30
2015 Jun	182,765	ARIMA_auto	179,390.40	3,374.60
2015 Jul	238,708	ARIMA_auto	215,745.77	22,962.23
2015 Aug	358,044	ARIMA_auto	337,539.08	20,504.92
2015 Sep	216,474	ARIMA_auto	225,346.79	-8,872.79
2015 Oct	148,376	ARIMA_auto	162,460.44	-14,084.44
2015 Nov	99,794	ARIMA_auto	115,851.01	-16,057.01
2015 Dec	93,804	ARIMA_auto	103,242.39	-9,438.39
2016 Jan	74,572	ARIMA_auto	83,835.22	-9,263.22
2016 Feb	97,522	ARIMA_auto	94,936.11	2,585.89
2016 Mar	144,216	ARIMA_auto	137,153.58	7,062.42
2016 Apr	153,386	ARIMA_auto	179,811.47	-26,425.47
2016 May	168,235	ARIMA_auto	179,668.49	-11,433.49
2016 Jun	215,800	ARIMA_auto	184,724.90	31,075.10
2016 Jul	271,212	ARIMA_auto	261,793.67	9,418.33
2016 Aug	380,776	ARIMA_auto	387,827.19	-7,051.19
2016 Sep	249,098	ARIMA_auto	232,635.96	16,462.04
2016 Oct	175,862	ARIMA_auto	177,522.45	-1,660.45
2016 Nov	102,775	ARIMA_auto	123,275.69	-20,500.69
2016 Dec	100,859	ARIMA_auto	106,661.13	-5,802.13
2017 Jan	83,249	ARIMA_auto	88,262.28	-5,013.28
2017 Feb	105,210	ARIMA_auto	111,898.38	-6,688.38
2017 Mar	121,167	ARIMA_auto	153,392.92	-32,225.92
2017 Apr	217,906	ARIMA_auto	144,572.28	73,333.72
2017 May	196,622	ARIMA_auto	210,700.78	-14,078.78
2017 Jun	248,582	ARIMA_auto	237,857.65	10,724.35
2017 Jul	323,496	ARIMA_auto	280,123.42	43,372.58
2017 Aug	431,571	ARIMA_auto	414,665.03	16,905.97
2017 Sep	287,242	ARIMA_auto	287,639.09	-397.09
2017 Oct	212,357	ARIMA_auto	210,715.23	1,641.77
2017 Nov	127,745	ARIMA_auto	135,991.29	-8,246.29
2017 Dec	132,238	ARIMA_auto	128,105.15	4,132.85
2018 Jan	95,453	ARIMA_auto	111,027.84	-15,574.84
2018 Feb	120,303	ARIMA_auto	126,491.64	-6,188.64
2018 Mar	162,886	ARIMA_auto	139,646.51	23,239.49
2018 Apr	187,186	ARIMA_auto	250,847.55	-63,661.55
2018 May	239,851	ARIMA_auto	195,419.66	44,431.34
2018 Jun	264,588	ARIMA_auto	273,147.29	-8,559.29
2018 Jul	339,564	ARIMA_auto	350,692.40	-11,128.40
2018 Aug	446,375	ARIMA_auto	470,284.47	-23,909.47
2018 Sep	304,516	ARIMA_auto	304,976.72	-460.72
2018 Oct	230,827	ARIMA_auto	222,003.98	8,823.02
2018 Nov	149,080	ARIMA_auto	134,261.91	14,818.09
2018 Dec	135,316	ARIMA_auto	142,737.53	-7,421.53
2019 Jan	114,710	ARIMA_auto	113,197.85	1,512.15
2019 Feb	122,635	ARIMA_auto	138,156.58	-15,521.58
2019 Mar	172,412	ARIMA_auto	170,327.11	2,084.89
2019 Apr	241,790	ARIMA_auto	212,722.56	29,067.44
2019 May	259,714	ARIMA_auto	260,072.95	-358.95
2019 Jun	306,048	ARIMA_auto	292,643.38	13,404.62
2019 Jul	360,566	ARIMA_auto	371,391.73	-10,825.73
2019 Aug	484,403	ARIMA_auto	472,712.33	11,690.67
2019 Sep	327,937	ARIMA_auto	333,057.38	-5,120.38
2019 Oct	238,677	ARIMA_auto	257,007.08	-18,330.08
2019 Nov	171,296	ARIMA_auto	165,277.23	6,018.77
2019 Dec	138,642	ARIMA_auto	160,055.35	-21,413.35
2020 Jan	126,349	ARIMA_auto	127,858.57	-1,509.57
2020 Feb	167,411	ARIMA_auto	140,029.54	27,381.46
2020 Mar	70,530	ARIMA_auto	201,950.41	-131,420.41
2020 Apr	13,892	ARIMA_auto	258,998.70	-245,106.70
2020 May	38,343	ARIMA_auto	74,805.35	-36,462.35
2020 Jun	159,738	ARIMA_auto	90,746.76	68,991.24
2020 Jul	272,786	ARIMA_auto	243,252.51	29,533.49
2020 Aug	407,020	ARIMA_auto	421,188.91	-14,168.91
2020 Sep	258,651	ARIMA_auto	281,259.66	-22,608.66
2020 Oct	167,448	ARIMA_auto	187,567.61	-20,119.61
2020 Nov	73,734	ARIMA_auto	104,218.36	-30,484.36
2020 Dec	73,353	ARIMA_auto	66,245.72	7,107.28
2021 Jan	48,435	ARIMA_auto	57,456.76	-9,021.76
2021 Feb	40,443	ARIMA_auto	71,925.00	-31,482.00
2021 Mar	60,251	ARIMA_auto	38,286.71	21,964.29
2021 Apr	85,179	ARIMA_auto	96,979.21	-11,800.21
2021 May	169,690	ARIMA_auto	115,909.62	53,780.38
2021 Jun	254,243	ARIMA_auto	237,584.38	16,658.62
2021 Jul	329,058	ARIMA_auto	334,389.00	-5,331.00
2021 Aug	461,844	ARIMA_auto	452,909.67	8,934.33
2021 Sep	308,273	ARIMA_auto	312,189.98	-3,916.98
2021 Oct	250,949	ARIMA_auto	220,124.47	30,824.53
2021 Nov	156,624	ARIMA_auto	173,412.17	-16,788.17
2021 Dec	115,100	ARIMA_auto	128,816.43	-13,716.43
2022 Jan	96,107	ARIMA_auto	96,480.97	-373.97
2022 Feb	141,508	ARIMA_auto	116,938.44	24,569.56
2022 Mar	167,854	ARIMA_auto	104,043.55	63,810.45
2022 Apr	248,959	ARIMA_auto	163,070.66	85,888.34
2022 May	258,413	ARIMA_auto	289,307.94	-30,894.94
2022 Jun	300,520	ARIMA_auto	309,308.07	-8,788.07
2010 Jan	53,653	ARIMA_auto_log	52,479.36	1,173.64
2010 Feb	62,257	ARIMA_auto_log	66,011.45	-3,754.45
2010 Mar	77,588	ARIMA_auto_log	80,283.62	-2,695.62
2010 Apr	99,982	ARIMA_auto_log	98,285.54	1,696.46
2010 May	101,387	ARIMA_auto_log	100,749.32	637.68
2010 Jun	108,611	ARIMA_auto_log	102,323.54	6,287.46
2010 Jul	126,498	ARIMA_auto_log	119,822.37	6,675.63
2010 Aug	178,380	ARIMA_auto_log	177,325.45	1,054.55
2010 Sep	127,822	ARIMA_auto_log	118,203.87	9,618.13
2010 Oct	104,174	ARIMA_auto_log	96,552.56	7,621.44
2010 Nov	69,271	ARIMA_auto_log	77,406.54	-8,135.54
2010 Dec	62,935	ARIMA_auto_log	66,320.22	-3,385.22
2011 Jan	60,457	ARIMA_auto_log	54,232.66	6,224.34
2011 Feb	67,260	ARIMA_auto_log	67,779.39	-519.39
2011 Mar	83,464	ARIMA_auto_log	84,025.42	-561.42
2011 Apr	102,958	ARIMA_auto_log	103,503.56	-545.56
2011 May	101,223	ARIMA_auto_log	105,826.16	-4,603.16
2011 Jun	120,148	ARIMA_auto_log	107,600.27	12,547.73
2011 Jul	136,999	ARIMA_auto_log	126,784.28	10,214.72
2011 Aug	212,668	ARIMA_auto_log	188,871.52	23,796.48
2011 Sep	129,606	ARIMA_auto_log	131,129.28	-1,523.28
2011 Oct	101,185	ARIMA_auto_log	105,227.77	-4,042.77
2011 Nov	62,121	ARIMA_auto_log	77,275.30	-15,154.30
2011 Dec	65,563	ARIMA_auto_log	65,006.34	556.66
2012 Jan	49,716	ARIMA_auto_log	56,662.15	-6,946.15
2012 Feb	58,638	ARIMA_auto_log	68,286.27	-9,648.27
2012 Mar	72,210	ARIMA_auto_log	82,679.23	-10,469.23
2012 Apr	87,406	ARIMA_auto_log	97,375.57	-9,969.57
2012 May	96,946	ARIMA_auto_log	97,246.71	-300.71
2012 Jun	115,885	ARIMA_auto_log	105,083.08	10,801.92
2012 Jul	139,695	ARIMA_auto_log	128,549.74	11,145.26
2012 Aug	194,368	ARIMA_auto_log	203,262.32	-8,894.32
2012 Sep	127,610	ARIMA_auto_log	134,655.01	-7,045.01
2012 Oct	89,649	ARIMA_auto_log	104,557.80	-14,908.80
2012 Nov	58,900	ARIMA_auto_log	68,337.51	-9,437.51
2012 Dec	51,122	ARIMA_auto_log	61,870.11	-10,748.11
2013 Jan	50,313	ARIMA_auto_log	49,211.75	1,101.25
2013 Feb	58,615	ARIMA_auto_log	59,596.93	-981.93
2013 Mar	92,426	ARIMA_auto_log	75,290.67	17,135.33
2013 Apr	100,996	ARIMA_auto_log	104,818.70	-3,822.70
2013 May	123,431	ARIMA_auto_log	111,007.51	12,423.49
2013 Jun	143,946	ARIMA_auto_log	126,075.00	17,871.00
2013 Jul	171,016	ARIMA_auto_log	147,431.74	23,584.26
2013 Aug	252,423	ARIMA_auto_log	230,436.42	21,986.58
2013 Sep	158,839	ARIMA_auto_log	152,516.09	6,322.91
2013 Oct	109,956	ARIMA_auto_log	114,354.77	-4,398.77
2013 Nov	82,040	ARIMA_auto_log	72,464.24	9,575.76
2013 Dec	72,692	ARIMA_auto_log	66,927.48	5,764.52
2014 Jan	56,872	ARIMA_auto_log	62,077.20	-5,205.20
2014 Feb	64,346	ARIMA_auto_log	69,919.26	-5,573.26
2014 Mar	102,852	ARIMA_auto_log	86,590.66	16,261.34
2014 Apr	151,151	ARIMA_auto_log	106,651.43	44,499.57
2014 May	148,593	ARIMA_auto_log	140,860.67	7,732.33
2014 Jun	154,231	ARIMA_auto_log	167,001.36	-12,770.36
2014 Jul	194,227	ARIMA_auto_log	179,096.28	15,130.72
2014 Aug	303,902	ARIMA_auto_log	263,166.10	40,735.90
2014 Sep	186,247	ARIMA_auto_log	178,115.48	8,131.52
2014 Oct	133,884	ARIMA_auto_log	129,742.75	4,141.25
2014 Nov	86,161	ARIMA_auto_log	89,899.95	-3,738.95
2014 Dec	81,830	ARIMA_auto_log	78,304.01	3,525.99
2015 Jan	68,436	ARIMA_auto_log	65,086.39	3,349.61
2015 Feb	84,417	ARIMA_auto_log	76,535.23	7,881.77
2015 Mar	116,291	ARIMA_auto_log	118,514.70	-2,223.70
2015 Apr	145,183	ARIMA_auto_log	153,148.24	-7,965.24
2015 May	172,016	ARIMA_auto_log	156,135.18	15,880.82
2015 Jun	182,765	ARIMA_auto_log	176,920.61	5,844.39
2015 Jul	238,708	ARIMA_auto_log	217,936.59	20,771.41
2015 Aug	358,044	ARIMA_auto_log	340,774.76	17,269.24
2015 Sep	216,474	ARIMA_auto_log	215,470.74	1,003.26
2015 Oct	148,376	ARIMA_auto_log	153,277.30	-4,901.30
2015 Nov	99,794	ARIMA_auto_log	102,786.12	-2,992.12
2015 Dec	93,804	ARIMA_auto_log	94,421.98	-617.98
2016 Jan	74,572	ARIMA_auto_log	78,746.25	-4,174.25
2016 Feb	97,522	ARIMA_auto_log	92,426.37	5,095.63
2016 Mar	144,216	ARIMA_auto_log	135,821.56	8,394.44
2016 Apr	153,386	ARIMA_auto_log	186,830.46	-33,444.46
2016 May	168,235	ARIMA_auto_log	189,680.25	-21,445.25
2016 Jun	215,800	ARIMA_auto_log	192,901.79	22,898.21
2016 Jul	271,212	ARIMA_auto_log	258,422.29	12,789.71
2016 Aug	380,776	ARIMA_auto_log	398,393.79	-17,617.79
2016 Sep	249,098	ARIMA_auto_log	239,868.03	9,229.97
2016 Oct	175,862	ARIMA_auto_log	170,211.61	5,650.39
2016 Nov	102,775	ARIMA_auto_log	115,998.30	-13,223.30
2016 Dec	100,859	ARIMA_auto_log	103,567.61	-2,708.61
2017 Jan	83,249	ARIMA_auto_log	83,422.56	-173.56
2017 Feb	105,210	ARIMA_auto_log	104,876.22	333.78
2017 Mar	121,167	ARIMA_auto_log	153,580.21	-32,413.21
2017 Apr	217,906	ARIMA_auto_log	161,291.25	56,614.75
2017 May	196,622	ARIMA_auto_log	201,279.23	-4,657.23
2017 Jun	248,582	ARIMA_auto_log	237,015.70	11,566.30
2017 Jul	323,496	ARIMA_auto_log	304,866.02	18,629.98
2017 Aug	431,571	ARIMA_auto_log	451,684.94	-20,113.94
2017 Sep	287,242	ARIMA_auto_log	283,187.03	4,054.97
2017 Oct	212,357	ARIMA_auto_log	200,310.93	12,046.07
2017 Nov	127,745	ARIMA_auto_log	127,602.39	142.61
2017 Dec	132,238	ARIMA_auto_log	122,717.45	9,520.55
2018 Jan	95,453	ARIMA_auto_log	103,600.30	-8,147.30
2018 Feb	120,303	ARIMA_auto_log	126,830.07	-6,527.07
2018 Mar	162,886	ARIMA_auto_log	160,058.46	2,827.54
2018 Apr	187,186	ARIMA_auto_log	237,362.63	-50,176.63
2018 May	239,851	ARIMA_auto_log	215,377.53	24,473.47
2018 Jun	264,588	ARIMA_auto_log	273,593.23	-9,005.23
2018 Jul	339,564	ARIMA_auto_log	346,290.90	-6,726.90
2018 Aug	446,375	ARIMA_auto_log	480,432.10	-34,057.10
2018 Sep	304,516	ARIMA_auto_log	302,951.09	1,564.91
2018 Oct	230,827	ARIMA_auto_log	219,099.23	11,727.77
2018 Nov	149,080	ARIMA_auto_log	138,336.99	10,743.01
2018 Dec	135,316	ARIMA_auto_log	141,056.64	-5,740.64
2019 Jan	114,710	ARIMA_auto_log	108,069.21	6,640.79
2019 Feb	122,635	ARIMA_auto_log	138,934.28	-16,299.28
2019 Mar	172,412	ARIMA_auto_log	176,742.43	-4,330.43
2019 Apr	241,790	ARIMA_auto_log	226,589.57	15,200.43
2019 May	259,714	ARIMA_auto_log	259,674.18	39.82
2019 Jun	306,048	ARIMA_auto_log	302,162.19	3,885.81
2019 Jul	360,566	ARIMA_auto_log	382,993.28	-22,427.28
2019 Aug	484,403	ARIMA_auto_log	516,404.37	-32,001.37
2019 Sep	327,937	ARIMA_auto_log	328,843.11	-906.11
2019 Oct	238,677	ARIMA_auto_log	240,008.39	-1,331.39
2019 Nov	171,296	ARIMA_auto_log	152,691.50	18,604.50
2019 Dec	138,642	ARIMA_auto_log	153,357.64	-14,715.64
2020 Jan	126,349	ARIMA_auto_log	119,260.69	7,088.31
2020 Feb	167,411	ARIMA_auto_log	143,088.79	24,322.21
2020 Mar	70,530	ARIMA_auto_log	198,684.08	-128,154.08
2020 Apr	13,892	ARIMA_auto_log	207,208.20	-193,316.20
2020 May	38,343	ARIMA_auto_log	6,058.26	32,284.74
2020 Jun	159,738	ARIMA_auto_log	212,813.60	-53,075.60
2020 Jul	272,786	ARIMA_auto_log	365,073.94	-92,287.94
2020 Aug	407,020	ARIMA_auto_log	313,397.30	93,622.70
2020 Sep	258,651	ARIMA_auto_log	370,918.53	-112,267.53
2020 Oct	167,448	ARIMA_auto_log	177,670.29	-10,222.29
2020 Nov	73,734	ARIMA_auto_log	116,164.05	-42,430.05
2020 Dec	73,353	ARIMA_auto_log	60,118.56	13,234.44
2021 Jan	48,435	ARIMA_auto_log	76,233.76	-27,798.76
2021 Feb	40,443	ARIMA_auto_log	61,129.20	-20,686.20
2021 Mar	60,251	ARIMA_auto_log	41,515.60	18,735.40
2021 Apr	85,179	ARIMA_auto_log	60,753.35	24,425.65
2021 May	169,690	ARIMA_auto_log	128,432.49	41,257.51
2021 Jun	254,243	ARIMA_auto_log	307,824.83	-53,581.83
2021 Jul	329,058	ARIMA_auto_log	327,584.90	1,473.10
2021 Aug	461,844	ARIMA_auto_log	489,489.67	-27,645.67
2021 Sep	308,273	ARIMA_auto_log	307,730.90	542.10
2021 Oct	250,949	ARIMA_auto_log	227,716.33	23,232.67
2021 Nov	156,624	ARIMA_auto_log	160,293.31	-3,669.31
2021 Dec	115,100	ARIMA_auto_log	130,269.70	-15,169.70
2022 Jan	96,107	ARIMA_auto_log	91,821.96	4,285.04
2022 Feb	141,508	ARIMA_auto_log	116,395.11	25,112.89
2022 Mar	167,854	ARIMA_auto_log	92,205.95	75,648.05
2022 Apr	248,959	ARIMA_auto_log	150,490.57	98,468.43
2022 May	258,413	ARIMA_auto_log	351,993.92	-93,580.92
2022 Jun	300,520	ARIMA_auto_log	292,982.27	7,537.73
2010 Jan	53,653	ARIMA_d0D1	54,763.29	-1,110.29
2010 Feb	62,257	ARIMA_d0D1	65,300.63	-3,043.63
2010 Mar	77,588	ARIMA_d0D1	80,270.54	-2,682.54
2010 Apr	99,982	ARIMA_d0D1	96,572.52	3,409.48
2010 May	101,387	ARIMA_d0D1	98,595.16	2,791.84
2010 Jun	108,611	ARIMA_d0D1	100,957.41	7,653.59
2010 Jul	126,498	ARIMA_d0D1	116,384.37	10,113.63
2010 Aug	178,380	ARIMA_d0D1	167,620.91	10,759.09
2010 Sep	127,822	ARIMA_d0D1	119,068.25	8,753.75
2010 Oct	104,174	ARIMA_d0D1	101,220.21	2,953.79
2010 Nov	69,271	ARIMA_d0D1	82,442.97	-13,171.97
2010 Dec	62,935	ARIMA_d0D1	69,793.01	-6,858.01
2011 Jan	60,457	ARIMA_d0D1	55,116.69	5,340.31
2011 Feb	67,260	ARIMA_d0D1	68,821.42	-1,561.42
2011 Mar	83,464	ARIMA_d0D1	83,982.49	-518.49
2011 Apr	102,958	ARIMA_d0D1	101,295.44	1,662.56
2011 May	101,223	ARIMA_d0D1	104,111.15	-2,888.15
2011 Jun	120,148	ARIMA_d0D1	106,357.50	13,790.50
2011 Jul	136,999	ARIMA_d0D1	123,663.11	13,335.89
2011 Aug	212,668	ARIMA_d0D1	179,439.01	33,228.99
2011 Sep	129,606	ARIMA_d0D1	134,738.72	-5,132.72
2011 Oct	101,185	ARIMA_d0D1	110,198.24	-9,013.24
2011 Nov	62,121	ARIMA_d0D1	73,341.51	-11,220.51
2011 Dec	65,563	ARIMA_d0D1	63,821.19	1,741.81
2012 Jan	49,716	ARIMA_d0D1	59,818.90	-10,102.90
2012 Feb	58,638	ARIMA_d0D1	68,887.71	-10,249.71
2012 Mar	72,210	ARIMA_d0D1	80,164.90	-7,954.90
2012 Apr	87,406	ARIMA_d0D1	99,923.31	-12,517.31
2012 May	96,946	ARIMA_d0D1	99,882.00	-2,936.00
2012 Jun	115,885	ARIMA_d0D1	111,039.04	4,845.96
2012 Jul	139,695	ARIMA_d0D1	132,192.31	7,502.69
2012 Aug	194,368	ARIMA_d0D1	199,132.92	-4,764.92
2012 Sep	127,610	ARIMA_d0D1	130,322.51	-2,712.51
2012 Oct	89,649	ARIMA_d0D1	102,488.05	-12,839.05
2012 Nov	58,900	ARIMA_d0D1	67,476.34	-8,576.34
2012 Dec	51,122	ARIMA_d0D1	62,568.68	-11,446.68
2013 Jan	50,313	ARIMA_d0D1	51,914.18	-1,601.18
2013 Feb	58,615	ARIMA_d0D1	62,577.82	-3,962.82
2013 Mar	92,426	ARIMA_d0D1	77,705.73	14,720.27
2013 Apr	100,996	ARIMA_d0D1	101,336.32	-340.32
2013 May	123,431	ARIMA_d0D1	107,971.83	15,459.17
2013 Jun	143,946	ARIMA_d0D1	122,773.51	21,172.49
2013 Jul	171,016	ARIMA_d0D1	155,092.09	15,923.91
2013 Aug	252,423	ARIMA_d0D1	224,639.82	27,783.18
2013 Sep	158,839	ARIMA_d0D1	160,599.79	-1,760.79
2013 Oct	109,956	ARIMA_d0D1	125,189.66	-15,233.66
2013 Nov	82,040	ARIMA_d0D1	74,032.90	8,007.10
2013 Dec	72,692	ARIMA_d0D1	69,353.30	3,338.70
2014 Jan	56,872	ARIMA_d0D1	61,948.73	-5,076.73
2014 Feb	64,346	ARIMA_d0D1	66,964.00	-2,618.00
2014 Mar	102,852	ARIMA_d0D1	86,828.12	16,023.88
2014 Apr	151,151	ARIMA_d0D1	104,945.33	46,205.67
2014 May	148,593	ARIMA_d0D1	144,081.54	4,511.46
2014 Jun	154,231	ARIMA_d0D1	165,135.77	-10,904.77
2014 Jul	194,227	ARIMA_d0D1	177,491.97	16,735.03
2014 Aug	303,902	ARIMA_d0D1	251,508.21	52,393.79
2014 Sep	186,247	ARIMA_d0D1	193,994.96	-7,747.96
2014 Oct	133,884	ARIMA_d0D1	137,689.94	-3,805.94
2014 Nov	86,161	ARIMA_d0D1	102,583.06	-16,422.06
2014 Dec	81,830	ARIMA_d0D1	84,435.74	-2,605.74
2015 Jan	68,436	ARIMA_d0D1	70,031.37	-1,595.37
2015 Feb	84,417	ARIMA_d0D1	75,972.87	8,444.13
2015 Mar	116,291	ARIMA_d0D1	116,158.26	132.74
2015 Apr	145,183	ARIMA_d0D1	152,655.46	-7,472.46
2015 May	172,016	ARIMA_d0D1	152,272.12	19,743.88
2015 Jun	182,765	ARIMA_d0D1	175,763.39	7,001.61
2015 Jul	238,708	ARIMA_d0D1	217,572.27	21,135.73
2015 Aug	358,044	ARIMA_d0D1	327,680.58	30,363.42
2015 Sep	216,474	ARIMA_d0D1	225,547.13	-9,073.13
2015 Oct	148,376	ARIMA_d0D1	163,294.30	-14,918.30
2015 Nov	99,794	ARIMA_d0D1	111,068.47	-11,274.47
2015 Dec	93,804	ARIMA_d0D1	99,148.62	-5,344.62
2016 Jan	74,572	ARIMA_d0D1	79,936.20	-5,364.20
2016 Feb	97,522	ARIMA_d0D1	91,143.30	6,378.70
2016 Mar	144,216	ARIMA_d0D1	129,674.06	14,541.94
2016 Apr	153,386	ARIMA_d0D1	181,069.27	-27,683.27
2016 May	168,235	ARIMA_d0D1	181,730.22	-13,495.22
2016 Jun	215,800	ARIMA_d0D1	181,931.22	33,868.78
2016 Jul	271,212	ARIMA_d0D1	255,476.78	15,735.22
2016 Aug	380,776	ARIMA_d0D1	380,884.28	-108.28
2016 Sep	249,098	ARIMA_d0D1	236,949.39	12,148.61
2016 Oct	175,862	ARIMA_d0D1	172,429.42	3,432.58
2016 Nov	102,775	ARIMA_d0D1	123,162.98	-20,387.98
2016 Dec	100,859	ARIMA_d0D1	105,853.93	-4,994.93
2017 Jan	83,249	ARIMA_d0D1	83,870.85	-621.85
2017 Feb	105,210	ARIMA_d0D1	106,575.72	-1,365.72
2017 Mar	121,167	ARIMA_d0D1	152,750.32	-31,583.32
2017 Apr	217,906	ARIMA_d0D1	142,301.17	75,604.83
2017 May	196,622	ARIMA_d0D1	191,385.43	5,236.57
2017 Jun	248,582	ARIMA_d0D1	238,996.10	9,585.90
2017 Jul	323,496	ARIMA_d0D1	295,940.77	27,555.23
2017 Aug	431,571	ARIMA_d0D1	414,256.30	17,314.70
2017 Sep	287,242	ARIMA_d0D1	286,653.76	588.24
2017 Oct	212,357	ARIMA_d0D1	209,655.86	2,701.14
2017 Nov	127,745	ARIMA_d0D1	134,512.74	-6,767.74
2017 Dec	132,238	ARIMA_d0D1	126,462.38	5,775.62
2018 Jan	95,453	ARIMA_d0D1	109,166.92	-13,713.92
2018 Feb	120,303	ARIMA_d0D1	123,039.06	-2,736.06
2018 Mar	162,886	ARIMA_d0D1	136,879.92	26,006.08
2018 Apr	187,186	ARIMA_d0D1	243,981.25	-56,795.25
2018 May	239,851	ARIMA_d0D1	193,446.96	46,404.04
2018 Jun	264,588	ARIMA_d0D1	271,064.54	-6,476.54
2018 Jul	339,564	ARIMA_d0D1	339,443.50	120.50
2018 Aug	446,375	ARIMA_d0D1	442,985.46	3,389.54
2018 Sep	304,516	ARIMA_d0D1	302,207.57	2,308.43
2018 Oct	230,827	ARIMA_d0D1	227,169.71	3,657.29
2018 Nov	149,080	ARIMA_d0D1	145,422.37	3,657.63
2018 Dec	135,316	ARIMA_d0D1	148,902.28	-13,586.28
2019 Jan	114,710	ARIMA_d0D1	109,753.76	4,956.24
2019 Feb	122,635	ARIMA_d0D1	134,442.84	-11,807.84
2019 Mar	172,412	ARIMA_d0D1	167,612.09	4,799.91
2019 Apr	241,790	ARIMA_d0D1	208,939.51	32,850.49
2019 May	259,714	ARIMA_d0D1	259,781.12	-67.12
2019 Jun	306,048	ARIMA_d0D1	289,414.02	16,633.98
2019 Jul	360,566	ARIMA_d0D1	373,265.61	-12,699.61
2019 Aug	484,403	ARIMA_d0D1	470,810.35	13,592.65
2019 Sep	327,937	ARIMA_d0D1	331,934.11	-3,997.11
2019 Oct	238,677	ARIMA_d0D1	255,303.30	-16,626.30
2019 Nov	171,296	ARIMA_d0D1	164,340.96	6,955.04
2019 Dec	138,642	ARIMA_d0D1	157,802.91	-19,160.91
2020 Jan	126,349	ARIMA_d0D1	125,363.52	985.48
2020 Feb	167,411	ARIMA_d0D1	137,102.35	30,308.65
2020 Mar	70,530	ARIMA_d0D1	199,867.60	-129,337.60
2020 Apr	13,892	ARIMA_d0D1	258,998.70	-245,106.70
2020 May	38,343	ARIMA_d0D1	74,805.35	-36,462.35
2020 Jun	159,738	ARIMA_d0D1	90,746.76	68,991.24
2020 Jul	272,786	ARIMA_d0D1	243,252.51	29,533.49
2020 Aug	407,020	ARIMA_d0D1	421,188.91	-14,168.91
2020 Sep	258,651	ARIMA_d0D1	281,259.66	-22,608.66
2020 Oct	167,448	ARIMA_d0D1	187,567.61	-20,119.61
2020 Nov	73,734	ARIMA_d0D1	104,218.36	-30,484.36
2020 Dec	73,353	ARIMA_d0D1	66,245.72	7,107.28
2021 Jan	48,435	ARIMA_d0D1	66,682.84	-18,247.84
2021 Feb	40,443	ARIMA_d0D1	81,356.59	-40,913.59
2021 Mar	60,251	ARIMA_d0D1	45,912.09	14,338.91
2021 Apr	85,179	ARIMA_d0D1	102,886.14	-17,707.14
2021 May	169,690	ARIMA_d0D1	123,732.21	45,957.79
2021 Jun	254,243	ARIMA_d0D1	249,913.47	4,329.53
2021 Jul	329,058	ARIMA_d0D1	334,389.00	-5,331.00
2021 Aug	461,844	ARIMA_d0D1	452,909.67	8,934.33
2021 Sep	308,273	ARIMA_d0D1	312,189.98	-3,916.98
2021 Oct	250,949	ARIMA_d0D1	220,124.47	30,824.53
2021 Nov	156,624	ARIMA_d0D1	173,412.17	-16,788.17
2021 Dec	115,100	ARIMA_d0D1	128,816.43	-13,716.43
2022 Jan	96,107	ARIMA_d0D1	96,480.97	-373.97
2022 Feb	141,508	ARIMA_d0D1	116,938.44	24,569.56
2022 Mar	167,854	ARIMA_d0D1	104,043.55	63,810.45
2022 Apr	248,959	ARIMA_d0D1	163,070.66	85,888.34
2022 May	258,413	ARIMA_d0D1	289,307.94	-30,894.94
2022 Jun	300,520	ARIMA_d0D1	309,308.07	-8,788.07
2010 Jan	53,653	ARIMA_d0D1_log	52,479.36	1,173.64
2010 Feb	62,257	ARIMA_d0D1_log	66,011.45	-3,754.45
2010 Mar	77,588	ARIMA_d0D1_log	80,283.62	-2,695.62
2010 Apr	99,982	ARIMA_d0D1_log	98,285.54	1,696.46
2010 May	101,387	ARIMA_d0D1_log	100,749.32	637.68
2010 Jun	108,611	ARIMA_d0D1_log	102,323.54	6,287.46
2010 Jul	126,498	ARIMA_d0D1_log	119,822.37	6,675.63
2010 Aug	178,380	ARIMA_d0D1_log	177,325.45	1,054.55
2010 Sep	127,822	ARIMA_d0D1_log	118,203.87	9,618.13
2010 Oct	104,174	ARIMA_d0D1_log	96,552.56	7,621.44
2010 Nov	69,271	ARIMA_d0D1_log	77,406.54	-8,135.54
2010 Dec	62,935	ARIMA_d0D1_log	66,320.22	-3,385.22
2011 Jan	60,457	ARIMA_d0D1_log	54,232.66	6,224.34
2011 Feb	67,260	ARIMA_d0D1_log	67,779.39	-519.39
2011 Mar	83,464	ARIMA_d0D1_log	84,025.42	-561.42
2011 Apr	102,958	ARIMA_d0D1_log	103,503.56	-545.56
2011 May	101,223	ARIMA_d0D1_log	105,826.16	-4,603.16
2011 Jun	120,148	ARIMA_d0D1_log	107,600.27	12,547.73
2011 Jul	136,999	ARIMA_d0D1_log	126,784.28	10,214.72
2011 Aug	212,668	ARIMA_d0D1_log	188,871.52	23,796.48
2011 Sep	129,606	ARIMA_d0D1_log	131,129.28	-1,523.28
2011 Oct	101,185	ARIMA_d0D1_log	105,227.77	-4,042.77
2011 Nov	62,121	ARIMA_d0D1_log	77,275.30	-15,154.30
2011 Dec	65,563	ARIMA_d0D1_log	65,006.34	556.66
2012 Jan	49,716	ARIMA_d0D1_log	56,662.15	-6,946.15
2012 Feb	58,638	ARIMA_d0D1_log	68,286.27	-9,648.27
2012 Mar	72,210	ARIMA_d0D1_log	82,679.23	-10,469.23
2012 Apr	87,406	ARIMA_d0D1_log	97,375.57	-9,969.57
2012 May	96,946	ARIMA_d0D1_log	97,246.71	-300.71
2012 Jun	115,885	ARIMA_d0D1_log	105,083.08	10,801.92
2012 Jul	139,695	ARIMA_d0D1_log	128,549.74	11,145.26
2012 Aug	194,368	ARIMA_d0D1_log	203,262.32	-8,894.32
2012 Sep	127,610	ARIMA_d0D1_log	134,655.01	-7,045.01
2012 Oct	89,649	ARIMA_d0D1_log	104,557.80	-14,908.80
2012 Nov	58,900	ARIMA_d0D1_log	68,337.51	-9,437.51
2012 Dec	51,122	ARIMA_d0D1_log	61,870.11	-10,748.11
2013 Jan	50,313	ARIMA_d0D1_log	49,211.75	1,101.25
2013 Feb	58,615	ARIMA_d0D1_log	59,596.93	-981.93
2013 Mar	92,426	ARIMA_d0D1_log	75,290.67	17,135.33
2013 Apr	100,996	ARIMA_d0D1_log	104,818.70	-3,822.70
2013 May	123,431	ARIMA_d0D1_log	111,007.51	12,423.49
2013 Jun	143,946	ARIMA_d0D1_log	126,075.00	17,871.00
2013 Jul	171,016	ARIMA_d0D1_log	147,431.74	23,584.26
2013 Aug	252,423	ARIMA_d0D1_log	230,436.42	21,986.58
2013 Sep	158,839	ARIMA_d0D1_log	152,516.09	6,322.91
2013 Oct	109,956	ARIMA_d0D1_log	114,354.77	-4,398.77
2013 Nov	82,040	ARIMA_d0D1_log	72,464.24	9,575.76
2013 Dec	72,692	ARIMA_d0D1_log	66,927.48	5,764.52
2014 Jan	56,872	ARIMA_d0D1_log	62,077.20	-5,205.20
2014 Feb	64,346	ARIMA_d0D1_log	69,919.26	-5,573.26
2014 Mar	102,852	ARIMA_d0D1_log	86,590.66	16,261.34
2014 Apr	151,151	ARIMA_d0D1_log	106,651.43	44,499.57
2014 May	148,593	ARIMA_d0D1_log	140,860.67	7,732.33
2014 Jun	154,231	ARIMA_d0D1_log	167,001.36	-12,770.36
2014 Jul	194,227	ARIMA_d0D1_log	179,096.28	15,130.72
2014 Aug	303,902	ARIMA_d0D1_log	263,166.10	40,735.90
2014 Sep	186,247	ARIMA_d0D1_log	178,115.48	8,131.52
2014 Oct	133,884	ARIMA_d0D1_log	129,742.75	4,141.25
2014 Nov	86,161	ARIMA_d0D1_log	89,899.95	-3,738.95
2014 Dec	81,830	ARIMA_d0D1_log	78,304.01	3,525.99
2015 Jan	68,436	ARIMA_d0D1_log	65,086.39	3,349.61
2015 Feb	84,417	ARIMA_d0D1_log	76,535.23	7,881.77
2015 Mar	116,291	ARIMA_d0D1_log	118,514.70	-2,223.70
2015 Apr	145,183	ARIMA_d0D1_log	153,148.24	-7,965.24
2015 May	172,016	ARIMA_d0D1_log	156,135.18	15,880.82
2015 Jun	182,765	ARIMA_d0D1_log	176,920.61	5,844.39
2015 Jul	238,708	ARIMA_d0D1_log	217,936.59	20,771.41
2015 Aug	358,044	ARIMA_d0D1_log	340,774.76	17,269.24
2015 Sep	216,474	ARIMA_d0D1_log	215,470.74	1,003.26
2015 Oct	148,376	ARIMA_d0D1_log	153,277.30	-4,901.30
2015 Nov	99,794	ARIMA_d0D1_log	100,266.92	-472.92
2015 Dec	93,804	ARIMA_d0D1_log	92,232.96	1,571.04
2016 Jan	74,572	ARIMA_d0D1_log	77,072.28	-2,500.28
2016 Feb	97,522	ARIMA_d0D1_log	90,451.52	7,070.48
2016 Mar	144,216	ARIMA_d0D1_log	133,530.76	10,685.24
2016 Apr	153,386	ARIMA_d0D1_log	184,436.78	-31,050.78
2016 May	168,235	ARIMA_d0D1_log	184,919.34	-16,684.34
2016 Jun	215,800	ARIMA_d0D1_log	189,261.54	26,538.46
2016 Jul	271,212	ARIMA_d0D1_log	254,867.02	16,344.98
2016 Aug	380,776	ARIMA_d0D1_log	393,154.16	-12,378.16
2016 Sep	249,098	ARIMA_d0D1_log	236,279.17	12,818.83
2016 Oct	175,862	ARIMA_d0D1_log	167,849.87	8,012.13
2016 Nov	102,775	ARIMA_d0D1_log	114,337.58	-11,562.58
2016 Dec	100,859	ARIMA_d0D1_log	101,877.81	-1,018.81
2017 Jan	83,249	ARIMA_d0D1_log	82,158.18	1,090.82
2017 Feb	105,210	ARIMA_d0D1_log	103,392.08	1,817.92
2017 Mar	121,167	ARIMA_d0D1_log	151,635.07	-30,468.07
2017 Apr	217,906	ARIMA_d0D1_log	158,702.86	59,203.14
2017 May	196,622	ARIMA_d0D1_log	200,259.40	-3,637.40
2017 Jun	248,582	ARIMA_d0D1_log	234,600.78	13,981.22
2017 Jul	323,496	ARIMA_d0D1_log	301,650.27	21,845.73
2017 Aug	431,571	ARIMA_d0D1_log	446,693.02	-15,122.02
2017 Sep	287,242	ARIMA_d0D1_log	279,271.40	7,970.60
2017 Oct	212,357	ARIMA_d0D1_log	197,795.42	14,561.58
2017 Nov	127,745	ARIMA_d0D1_log	125,891.76	1,853.24
2017 Dec	132,238	ARIMA_d0D1_log	121,203.67	11,034.33
2018 Jan	95,453	ARIMA_d0D1_log	102,078.58	-6,625.58
2018 Feb	120,303	ARIMA_d0D1_log	124,599.37	-4,296.37
2018 Mar	162,886	ARIMA_d0D1_log	157,288.65	5,597.35
2018 Apr	187,186	ARIMA_d0D1_log	233,395.26	-46,209.26
2018 May	239,851	ARIMA_d0D1_log	211,461.04	28,389.96
2018 Jun	264,588	ARIMA_d0D1_log	270,416.85	-5,828.85
2018 Jul	339,564	ARIMA_d0D1_log	342,064.00	-2,500.00
2018 Aug	446,375	ARIMA_d0D1_log	476,067.54	-29,692.54
2018 Sep	304,516	ARIMA_d0D1_log	300,196.30	4,319.70
2018 Oct	230,827	ARIMA_d0D1_log	217,614.72	13,212.28
2018 Nov	149,080	ARIMA_d0D1_log	137,408.09	11,671.91
2018 Dec	135,316	ARIMA_d0D1_log	140,133.61	-4,817.61
2019 Jan	114,710	ARIMA_d0D1_log	107,210.24	7,499.76
2019 Feb	122,635	ARIMA_d0D1_log	137,758.04	-15,123.04
2019 Mar	172,412	ARIMA_d0D1_log	174,993.46	-2,581.46
2019 Apr	241,790	ARIMA_d0D1_log	224,781.56	17,008.44
2019 May	259,714	ARIMA_d0D1_log	257,504.10	2,209.90
2019 Jun	306,048	ARIMA_d0D1_log	299,766.60	6,281.40
2019 Jul	360,566	ARIMA_d0D1_log	382,993.28	-22,427.28
2019 Aug	484,403	ARIMA_d0D1_log	516,404.37	-32,001.37
2019 Sep	327,937	ARIMA_d0D1_log	328,843.11	-906.11
2019 Oct	238,677	ARIMA_d0D1_log	240,008.39	-1,331.39
2019 Nov	171,296	ARIMA_d0D1_log	152,691.50	18,604.50
2019 Dec	138,642	ARIMA_d0D1_log	153,357.64	-14,715.64
2020 Jan	126,349	ARIMA_d0D1_log	119,260.69	7,088.31
2020 Feb	167,411	ARIMA_d0D1_log	143,088.79	24,322.21
2020 Mar	70,530	ARIMA_d0D1_log	198,684.08	-128,154.08
2020 Apr	13,892	ARIMA_d0D1_log	207,208.20	-193,316.20
2020 May	38,343	ARIMA_d0D1_log	6,058.26	32,284.74
2020 Jun	159,738	ARIMA_d0D1_log	212,813.60	-53,075.60
2020 Jul	272,786	ARIMA_d0D1_log	365,073.94	-92,287.94
2020 Aug	407,020	ARIMA_d0D1_log	313,397.30	93,622.70
2020 Sep	258,651	ARIMA_d0D1_log	370,918.53	-112,267.53
2020 Oct	167,448	ARIMA_d0D1_log	177,670.29	-10,222.29
2020 Nov	73,734	ARIMA_d0D1_log	116,164.05	-42,430.05
2020 Dec	73,353	ARIMA_d0D1_log	67,796.83	5,556.17
2021 Jan	48,435	ARIMA_d0D1_log	83,785.37	-35,350.37
2021 Feb	40,443	ARIMA_d0D1_log	61,918.94	-21,475.94
2021 Mar	60,251	ARIMA_d0D1_log	45,677.83	14,573.17
2021 Apr	85,179	ARIMA_d0D1_log	62,062.43	23,116.57
2021 May	169,690	ARIMA_d0D1_log	142,509.45	27,180.55
2021 Jun	254,243	ARIMA_d0D1_log	307,824.83	-53,581.83
2021 Jul	329,058	ARIMA_d0D1_log	327,584.90	1,473.10
2021 Aug	461,844	ARIMA_d0D1_log	489,489.67	-27,645.67
2021 Sep	308,273	ARIMA_d0D1_log	307,730.90	542.10
2021 Oct	250,949	ARIMA_d0D1_log	227,716.33	23,232.67
2021 Nov	156,624	ARIMA_d0D1_log	160,293.31	-3,669.31
2021 Dec	115,100	ARIMA_d0D1_log	130,269.70	-15,169.70
2022 Jan	96,107	ARIMA_d0D1_log	91,821.96	4,285.04
2022 Feb	141,508	ARIMA_d0D1_log	116,395.11	25,112.89
2022 Mar	167,854	ARIMA_d0D1_log	92,205.95	75,648.05
2022 Apr	248,959	ARIMA_d0D1_log	150,490.57	98,468.43
2022 May	258,413	ARIMA_d0D1_log	351,993.92	-93,580.92
2022 Jun	300,520	ARIMA_d0D1_log	292,982.27	7,537.73
2010 Jan	53,653	ARIMA_d1D1	55,515.22	-1,862.22
2010 Feb	62,257	ARIMA_d1D1	66,380.34	-4,123.34
2010 Mar	77,588	ARIMA_d1D1	79,476.62	-1,888.62
2010 Apr	99,982	ARIMA_d1D1	95,877.08	4,104.92
2010 May	101,387	ARIMA_d1D1	97,918.27	3,468.73
2010 Jun	108,611	ARIMA_d1D1	99,663.88	8,947.12
2010 Jul	126,498	ARIMA_d1D1	115,342.44	11,155.56
2010 Aug	178,380	ARIMA_d1D1	167,908.19	10,471.81
2010 Sep	127,822	ARIMA_d1D1	119,002.49	8,819.51
2010 Oct	104,174	ARIMA_d1D1	102,352.84	1,821.16
2010 Nov	69,271	ARIMA_d1D1	84,200.34	-14,929.34
2010 Dec	62,935	ARIMA_d1D1	72,349.82	-9,414.82
2011 Jan	60,457	ARIMA_d1D1	59,816.69	640.31
2011 Feb	67,260	ARIMA_d1D1	70,509.42	-3,249.42
2011 Mar	83,464	ARIMA_d1D1	83,787.32	-323.32
2011 Apr	102,958	ARIMA_d1D1	102,936.86	21.14
2011 May	101,223	ARIMA_d1D1	104,501.15	-3,278.15
2011 Jun	120,148	ARIMA_d1D1	106,210.23	13,937.77
2011 Jul	136,999	ARIMA_d1D1	125,784.66	11,214.34
2011 Aug	212,668	ARIMA_d1D1	181,282.07	31,385.93
2011 Sep	129,606	ARIMA_d1D1	139,014.13	-9,408.13
2011 Oct	101,185	ARIMA_d1D1	113,800.88	-12,615.88
2011 Nov	62,121	ARIMA_d1D1	82,242.16	-20,121.16
2011 Dec	65,563	ARIMA_d1D1	65,578.12	-15.12
2012 Jan	49,716	ARIMA_d1D1	62,297.37	-12,581.37
2012 Feb	58,638	ARIMA_d1D1	67,399.01	-8,761.01
2012 Mar	72,210	ARIMA_d1D1	80,334.93	-8,124.93
2012 Apr	87,406	ARIMA_d1D1	98,271.01	-10,865.01
2012 May	96,946	ARIMA_d1D1	93,238.17	3,707.83
2012 Jun	115,885	ARIMA_d1D1	108,868.99	7,016.01
2012 Jul	139,695	ARIMA_d1D1	127,805.32	11,889.68
2012 Aug	194,368	ARIMA_d1D1	198,028.14	-3,660.14
2012 Sep	127,610	ARIMA_d1D1	126,768.36	841.64
2012 Oct	89,649	ARIMA_d1D1	101,473.49	-11,824.49
2012 Nov	58,900	ARIMA_d1D1	59,497.55	-597.55
2012 Dec	51,122	ARIMA_d1D1	58,128.55	-7,006.55
2013 Jan	50,313	ARIMA_d1D1	47,363.20	2,949.80
2013 Feb	58,615	ARIMA_d1D1	55,791.32	2,823.68
2013 Mar	92,426	ARIMA_d1D1	71,605.11	20,820.89
2013 Apr	100,996	ARIMA_d1D1	96,922.82	4,073.18
2013 May	123,431	ARIMA_d1D1	102,186.09	21,244.91
2013 Jun	143,946	ARIMA_d1D1	132,948.52	10,997.48
2013 Jul	171,016	ARIMA_d1D1	163,895.86	7,120.14
2013 Aug	252,423	ARIMA_d1D1	231,759.24	20,663.76
2013 Sep	158,839	ARIMA_d1D1	169,780.98	-10,941.98
2013 Oct	109,956	ARIMA_d1D1	134,953.27	-24,997.27
2013 Nov	82,040	ARIMA_d1D1	82,308.00	-268.00
2013 Dec	72,692	ARIMA_d1D1	76,521.14	-3,829.14
2014 Jan	56,872	ARIMA_d1D1	67,943.11	-11,071.11
2014 Feb	64,346	ARIMA_d1D1	68,910.99	-4,564.99
2014 Mar	102,852	ARIMA_d1D1	88,662.73	14,189.27
2014 Apr	151,151	ARIMA_d1D1	108,119.14	43,031.86
2014 May	148,593	ARIMA_d1D1	148,748.03	-155.03
2014 Jun	154,231	ARIMA_d1D1	168,529.84	-14,298.84
2014 Jul	194,227	ARIMA_d1D1	186,502.19	7,724.81
2014 Aug	303,902	ARIMA_d1D1	260,251.81	43,650.19
2014 Sep	186,247	ARIMA_d1D1	191,501.95	-5,254.95
2014 Oct	133,884	ARIMA_d1D1	140,610.64	-6,726.64
2014 Nov	86,161	ARIMA_d1D1	105,231.39	-19,070.39
2014 Dec	81,830	ARIMA_d1D1	92,602.00	-10,772.00
2015 Jan	68,436	ARIMA_d1D1	78,306.90	-9,870.90
2015 Feb	84,417	ARIMA_d1D1	81,025.19	3,391.81
2015 Mar	116,291	ARIMA_d1D1	121,885.60	-5,594.60
2015 Apr	145,183	ARIMA_d1D1	150,125.32	-4,942.32
2015 May	172,016	ARIMA_d1D1	157,818.70	14,197.30
2015 Jun	182,765	ARIMA_d1D1	179,390.40	3,374.60
2015 Jul	238,708	ARIMA_d1D1	215,745.77	22,962.23
2015 Aug	358,044	ARIMA_d1D1	337,539.08	20,504.92
2015 Sep	216,474	ARIMA_d1D1	225,346.79	-8,872.79
2015 Oct	148,376	ARIMA_d1D1	162,460.44	-14,084.44
2015 Nov	99,794	ARIMA_d1D1	115,851.01	-16,057.01
2015 Dec	93,804	ARIMA_d1D1	103,242.39	-9,438.39
2016 Jan	74,572	ARIMA_d1D1	83,835.22	-9,263.22
2016 Feb	97,522	ARIMA_d1D1	94,936.11	2,585.89
2016 Mar	144,216	ARIMA_d1D1	137,153.58	7,062.42
2016 Apr	153,386	ARIMA_d1D1	179,811.47	-26,425.47
2016 May	168,235	ARIMA_d1D1	179,668.49	-11,433.49
2016 Jun	215,800	ARIMA_d1D1	184,724.90	31,075.10
2016 Jul	271,212	ARIMA_d1D1	261,793.67	9,418.33
2016 Aug	380,776	ARIMA_d1D1	387,827.19	-7,051.19
2016 Sep	249,098	ARIMA_d1D1	232,635.96	16,462.04
2016 Oct	175,862	ARIMA_d1D1	177,522.45	-1,660.45
2016 Nov	102,775	ARIMA_d1D1	123,275.69	-20,500.69
2016 Dec	100,859	ARIMA_d1D1	106,661.13	-5,802.13
2017 Jan	83,249	ARIMA_d1D1	88,262.28	-5,013.28
2017 Feb	105,210	ARIMA_d1D1	111,898.38	-6,688.38
2017 Mar	121,167	ARIMA_d1D1	153,392.92	-32,225.92
2017 Apr	217,906	ARIMA_d1D1	144,572.28	73,333.72
2017 May	196,622	ARIMA_d1D1	210,700.78	-14,078.78
2017 Jun	248,582	ARIMA_d1D1	237,857.65	10,724.35
2017 Jul	323,496	ARIMA_d1D1	280,123.42	43,372.58
2017 Aug	431,571	ARIMA_d1D1	414,665.03	16,905.97
2017 Sep	287,242	ARIMA_d1D1	287,639.09	-397.09
2017 Oct	212,357	ARIMA_d1D1	210,715.23	1,641.77
2017 Nov	127,745	ARIMA_d1D1	135,991.29	-8,246.29
2017 Dec	132,238	ARIMA_d1D1	128,105.15	4,132.85
2018 Jan	95,453	ARIMA_d1D1	111,027.84	-15,574.84
2018 Feb	120,303	ARIMA_d1D1	126,491.64	-6,188.64
2018 Mar	162,886	ARIMA_d1D1	139,646.51	23,239.49
2018 Apr	187,186	ARIMA_d1D1	250,847.55	-63,661.55
2018 May	239,851	ARIMA_d1D1	195,419.66	44,431.34
2018 Jun	264,588	ARIMA_d1D1	273,147.29	-8,559.29
2018 Jul	339,564	ARIMA_d1D1	350,692.40	-11,128.40
2018 Aug	446,375	ARIMA_d1D1	470,284.47	-23,909.47
2018 Sep	304,516	ARIMA_d1D1	304,976.72	-460.72
2018 Oct	230,827	ARIMA_d1D1	222,003.98	8,823.02
2018 Nov	149,080	ARIMA_d1D1	134,261.91	14,818.09
2018 Dec	135,316	ARIMA_d1D1	142,737.53	-7,421.53
2019 Jan	114,710	ARIMA_d1D1	113,197.85	1,512.15
2019 Feb	122,635	ARIMA_d1D1	138,156.58	-15,521.58
2019 Mar	172,412	ARIMA_d1D1	170,327.11	2,084.89
2019 Apr	241,790	ARIMA_d1D1	212,722.56	29,067.44
2019 May	259,714	ARIMA_d1D1	260,072.95	-358.95
2019 Jun	306,048	ARIMA_d1D1	292,643.38	13,404.62
2019 Jul	360,566	ARIMA_d1D1	371,391.73	-10,825.73
2019 Aug	484,403	ARIMA_d1D1	472,712.33	11,690.67
2019 Sep	327,937	ARIMA_d1D1	333,057.38	-5,120.38
2019 Oct	238,677	ARIMA_d1D1	257,007.08	-18,330.08
2019 Nov	171,296	ARIMA_d1D1	165,277.23	6,018.77
2019 Dec	138,642	ARIMA_d1D1	160,055.35	-21,413.35
2020 Jan	126,349	ARIMA_d1D1	127,858.57	-1,509.57
2020 Feb	167,411	ARIMA_d1D1	140,029.54	27,381.46
2020 Mar	70,530	ARIMA_d1D1	201,950.41	-131,420.41
2020 Apr	13,892	ARIMA_d1D1	234,655.97	-220,763.97
2020 May	38,343	ARIMA_d1D1	50,443.79	-12,100.79
2020 Jun	159,738	ARIMA_d1D1	73,251.32	86,486.68
2020 Jul	272,786	ARIMA_d1D1	224,237.55	48,548.45
2020 Aug	407,020	ARIMA_d1D1	415,191.45	-8,171.45
2020 Sep	258,651	ARIMA_d1D1	265,559.90	-6,908.90
2020 Oct	167,448	ARIMA_d1D1	176,927.75	-9,479.75
2020 Nov	73,734	ARIMA_d1D1	84,840.71	-11,106.71
2020 Dec	73,353	ARIMA_d1D1	56,334.40	17,018.60
2021 Jan	48,435	ARIMA_d1D1	57,456.76	-9,021.76
2021 Feb	40,443	ARIMA_d1D1	71,925.00	-31,482.00
2021 Mar	60,251	ARIMA_d1D1	38,286.71	21,964.29
2021 Apr	85,179	ARIMA_d1D1	96,979.21	-11,800.21
2021 May	169,690	ARIMA_d1D1	115,909.62	53,780.38
2021 Jun	254,243	ARIMA_d1D1	237,584.38	16,658.62
2021 Jul	329,058	ARIMA_d1D1	321,849.74	7,208.26
2021 Aug	461,844	ARIMA_d1D1	437,241.15	24,602.85
2021 Sep	308,273	ARIMA_d1D1	300,899.76	7,373.24
2021 Oct	250,949	ARIMA_d1D1	210,146.97	40,802.03
2021 Nov	156,624	ARIMA_d1D1	164,549.00	-7,925.00
2021 Dec	115,100	ARIMA_d1D1	120,376.41	-5,276.41
2022 Jan	96,107	ARIMA_d1D1	87,460.25	8,646.75
2022 Feb	141,508	ARIMA_d1D1	112,229.96	29,278.04
2022 Mar	167,854	ARIMA_d1D1	104,389.29	63,464.71
2022 Apr	248,959	ARIMA_d1D1	176,953.69	72,005.31
2022 May	258,413	ARIMA_d1D1	303,732.56	-45,319.56
2022 Jun	300,520	ARIMA_d1D1	305,065.75	-4,545.75
2010 Jan	53,653	ARIMA_d1D1_log	51,747.40	1,905.60
2010 Feb	62,257	ARIMA_d1D1_log	64,456.77	-2,199.77
2010 Mar	77,588	ARIMA_d1D1_log	78,134.56	-546.56
2010 Apr	99,982	ARIMA_d1D1_log	96,562.29	3,419.71
2010 May	101,387	ARIMA_d1D1_log	99,314.05	2,072.95
2010 Jun	108,611	ARIMA_d1D1_log	100,728.94	7,882.06
2010 Jul	126,498	ARIMA_d1D1_log	117,349.94	9,148.06
2010 Aug	178,380	ARIMA_d1D1_log	175,418.05	2,961.95
2010 Sep	127,822	ARIMA_d1D1_log	118,285.34	9,536.66
2010 Oct	104,174	ARIMA_d1D1_log	98,234.80	5,939.20
2010 Nov	69,271	ARIMA_d1D1_log	78,102.03	-8,831.03
2010 Dec	62,935	ARIMA_d1D1_log	67,611.21	-4,676.21
2011 Jan	60,457	ARIMA_d1D1_log	55,714.66	4,742.34
2011 Feb	67,260	ARIMA_d1D1_log	68,390.52	-1,130.52
2011 Mar	83,464	ARIMA_d1D1_log	83,467.79	-3.79
2011 Apr	102,958	ARIMA_d1D1_log	104,949.68	-1,991.68
2011 May	101,223	ARIMA_d1D1_log	107,248.64	-6,025.64
2011 Jun	120,148	ARIMA_d1D1_log	109,946.31	10,201.69
2011 Jul	136,999	ARIMA_d1D1_log	128,498.43	8,500.57
2011 Aug	212,668	ARIMA_d1D1_log	189,212.42	23,455.58
2011 Sep	129,606	ARIMA_d1D1_log	133,783.82	-4,177.82
2011 Oct	101,185	ARIMA_d1D1_log	108,779.45	-7,594.45
2011 Nov	62,121	ARIMA_d1D1_log	78,658.32	-16,537.32
2011 Dec	65,563	ARIMA_d1D1_log	66,531.22	-968.22
2012 Jan	49,716	ARIMA_d1D1_log	58,961.09	-9,245.09
2012 Feb	58,638	ARIMA_d1D1_log	65,596.34	-6,958.34
2012 Mar	72,210	ARIMA_d1D1_log	78,022.73	-5,812.73
2012 Apr	87,406	ARIMA_d1D1_log	93,979.78	-6,573.78
2012 May	96,946	ARIMA_d1D1_log	92,511.04	4,434.96
2012 Jun	115,885	ARIMA_d1D1_log	102,300.15	13,584.85
2012 Jul	139,695	ARIMA_d1D1_log	122,907.62	16,787.38
2012 Aug	194,368	ARIMA_d1D1_log	191,797.65	2,570.35
2012 Sep	127,610	ARIMA_d1D1_log	126,251.62	1,358.38
2012 Oct	89,649	ARIMA_d1D1_log	102,060.06	-12,411.06
2012 Nov	58,900	ARIMA_d1D1_log	65,868.82	-6,968.82
2012 Dec	51,122	ARIMA_d1D1_log	61,061.22	-9,939.22
2013 Jan	50,313	ARIMA_d1D1_log	47,846.03	2,466.97
2013 Feb	58,615	ARIMA_d1D1_log	57,076.04	1,538.96
2013 Mar	92,426	ARIMA_d1D1_log	70,733.30	21,692.70
2013 Apr	100,996	ARIMA_d1D1_log	94,436.24	6,559.76
2013 May	123,431	ARIMA_d1D1_log	101,904.42	21,526.58
2013 Jun	143,946	ARIMA_d1D1_log	126,311.63	17,634.37
2013 Jul	171,016	ARIMA_d1D1_log	168,050.53	2,965.47
2013 Aug	252,423	ARIMA_d1D1_log	246,779.96	5,643.04
2013 Sep	158,839	ARIMA_d1D1_log	158,432.26	406.74
2013 Oct	109,956	ARIMA_d1D1_log	118,953.41	-8,997.41
2013 Nov	82,040	ARIMA_d1D1_log	76,026.29	6,013.71
2013 Dec	72,692	ARIMA_d1D1_log	70,936.98	1,755.02
2014 Jan	56,872	ARIMA_d1D1_log	67,005.54	-10,133.54
2014 Feb	64,346	ARIMA_d1D1_log	71,553.76	-7,207.76
2014 Mar	102,852	ARIMA_d1D1_log	90,027.95	12,824.05
2014 Apr	151,151	ARIMA_d1D1_log	114,762.81	36,388.19
2014 May	148,593	ARIMA_d1D1_log	147,398.64	1,194.36
2014 Jun	154,231	ARIMA_d1D1_log	172,609.55	-18,378.55
2014 Jul	194,227	ARIMA_d1D1_log	194,634.56	-407.56
2014 Aug	303,902	ARIMA_d1D1_log	284,838.18	19,063.82
2014 Sep	186,247	ARIMA_d1D1_log	187,107.03	-860.03
2014 Oct	133,884	ARIMA_d1D1_log	133,804.06	79.94
2014 Nov	86,161	ARIMA_d1D1_log	94,418.05	-8,257.05
2014 Dec	81,830	ARIMA_d1D1_log	82,154.17	-324.17
2015 Jan	68,436	ARIMA_d1D1_log	68,633.95	-197.95
2015 Feb	84,417	ARIMA_d1D1_log	78,711.40	5,705.60
2015 Mar	116,291	ARIMA_d1D1_log	122,709.78	-6,418.78
2015 Apr	145,183	ARIMA_d1D1_log	159,255.45	-14,072.45
2015 May	172,016	ARIMA_d1D1_log	161,539.64	10,476.36
2015 Jun	182,765	ARIMA_d1D1_log	181,174.98	1,590.02
2015 Jul	238,708	ARIMA_d1D1_log	223,348.95	15,359.05
2015 Aug	358,044	ARIMA_d1D1_log	349,187.82	8,856.18
2015 Sep	216,474	ARIMA_d1D1_log	220,284.70	-3,810.70
2015 Oct	148,376	ARIMA_d1D1_log	156,824.19	-8,448.19
2015 Nov	99,794	ARIMA_d1D1_log	102,786.12	-2,992.12
2015 Dec	93,804	ARIMA_d1D1_log	94,421.98	-617.98
2016 Jan	74,572	ARIMA_d1D1_log	78,746.25	-4,174.25
2016 Feb	97,522	ARIMA_d1D1_log	92,426.37	5,095.63
2016 Mar	144,216	ARIMA_d1D1_log	135,821.56	8,394.44
2016 Apr	153,386	ARIMA_d1D1_log	186,830.46	-33,444.46
2016 May	168,235	ARIMA_d1D1_log	189,680.25	-21,445.25
2016 Jun	215,800	ARIMA_d1D1_log	192,901.79	22,898.21
2016 Jul	271,212	ARIMA_d1D1_log	258,422.29	12,789.71
2016 Aug	380,776	ARIMA_d1D1_log	398,393.79	-17,617.79
2016 Sep	249,098	ARIMA_d1D1_log	239,868.03	9,229.97
2016 Oct	175,862	ARIMA_d1D1_log	170,211.61	5,650.39
2016 Nov	102,775	ARIMA_d1D1_log	115,998.30	-13,223.30
2016 Dec	100,859	ARIMA_d1D1_log	103,567.61	-2,708.61
2017 Jan	83,249	ARIMA_d1D1_log	83,422.56	-173.56
2017 Feb	105,210	ARIMA_d1D1_log	104,876.22	333.78
2017 Mar	121,167	ARIMA_d1D1_log	153,580.21	-32,413.21
2017 Apr	217,906	ARIMA_d1D1_log	161,291.25	56,614.75
2017 May	196,622	ARIMA_d1D1_log	201,279.23	-4,657.23
2017 Jun	248,582	ARIMA_d1D1_log	237,015.70	11,566.30
2017 Jul	323,496	ARIMA_d1D1_log	304,866.02	18,629.98
2017 Aug	431,571	ARIMA_d1D1_log	451,684.94	-20,113.94
2017 Sep	287,242	ARIMA_d1D1_log	283,187.03	4,054.97
2017 Oct	212,357	ARIMA_d1D1_log	200,310.93	12,046.07
2017 Nov	127,745	ARIMA_d1D1_log	127,602.39	142.61
2017 Dec	132,238	ARIMA_d1D1_log	122,717.45	9,520.55
2018 Jan	95,453	ARIMA_d1D1_log	103,600.30	-8,147.30
2018 Feb	120,303	ARIMA_d1D1_log	126,830.07	-6,527.07
2018 Mar	162,886	ARIMA_d1D1_log	160,058.46	2,827.54
2018 Apr	187,186	ARIMA_d1D1_log	237,362.63	-50,176.63
2018 May	239,851	ARIMA_d1D1_log	215,377.53	24,473.47
2018 Jun	264,588	ARIMA_d1D1_log	273,593.23	-9,005.23
2018 Jul	339,564	ARIMA_d1D1_log	346,290.90	-6,726.90
2018 Aug	446,375	ARIMA_d1D1_log	480,432.10	-34,057.10
2018 Sep	304,516	ARIMA_d1D1_log	302,951.09	1,564.91
2018 Oct	230,827	ARIMA_d1D1_log	219,099.23	11,727.77
2018 Nov	149,080	ARIMA_d1D1_log	138,336.99	10,743.01
2018 Dec	135,316	ARIMA_d1D1_log	141,056.64	-5,740.64
2019 Jan	114,710	ARIMA_d1D1_log	108,069.21	6,640.79
2019 Feb	122,635	ARIMA_d1D1_log	138,934.28	-16,299.28
2019 Mar	172,412	ARIMA_d1D1_log	176,742.43	-4,330.43
2019 Apr	241,790	ARIMA_d1D1_log	226,589.57	15,200.43
2019 May	259,714	ARIMA_d1D1_log	259,674.18	39.82
2019 Jun	306,048	ARIMA_d1D1_log	302,162.19	3,885.81
2019 Jul	360,566	ARIMA_d1D1_log	387,233.88	-26,667.88
2019 Aug	484,403	ARIMA_d1D1_log	519,045.45	-34,642.45
2019 Sep	327,937	ARIMA_d1D1_log	331,996.31	-4,059.31
2019 Oct	238,677	ARIMA_d1D1_log	241,410.46	-2,733.46
2019 Nov	171,296	ARIMA_d1D1_log	152,892.44	18,403.56
2019 Dec	138,642	ARIMA_d1D1_log	153,122.21	-14,480.21
2020 Jan	126,349	ARIMA_d1D1_log	119,435.46	6,913.54
2020 Feb	167,411	ARIMA_d1D1_log	145,982.55	21,428.45
2020 Mar	70,530	ARIMA_d1D1_log	213,636.01	-143,106.01
2020 Apr	13,892	ARIMA_d1D1_log	207,911.99	-194,019.99
2020 May	38,343	ARIMA_d1D1_log	4,236.25	34,106.75
2020 Jun	159,738	ARIMA_d1D1_log	172,233.91	-12,495.91
2020 Jul	272,786	ARIMA_d1D1_log	188,942.19	83,843.81
2020 Aug	407,020	ARIMA_d1D1_log	211,347.86	195,672.14
2020 Sep	258,651	ARIMA_d1D1_log	208,065.09	50,585.91
2020 Oct	167,448	ARIMA_d1D1_log	170,301.12	-2,853.12
2020 Nov	73,734	ARIMA_d1D1_log	111,326.39	-37,592.39
2020 Dec	73,353	ARIMA_d1D1_log	60,118.56	13,234.44
2021 Jan	48,435	ARIMA_d1D1_log	76,233.76	-27,798.76
2021 Feb	40,443	ARIMA_d1D1_log	61,129.20	-20,686.20
2021 Mar	60,251	ARIMA_d1D1_log	41,515.60	18,735.40
2021 Apr	85,179	ARIMA_d1D1_log	60,753.35	24,425.65
2021 May	169,690	ARIMA_d1D1_log	128,432.49	41,257.51
2021 Jun	254,243	ARIMA_d1D1_log	239,326.91	14,916.09
2021 Jul	329,058	ARIMA_d1D1_log	243,531.03	85,526.97
2021 Aug	461,844	ARIMA_d1D1_log	380,024.30	81,819.70
2021 Sep	308,273	ARIMA_d1D1_log	285,344.75	22,928.25
2021 Oct	250,949	ARIMA_d1D1_log	195,853.20	55,095.80
2021 Nov	156,624	ARIMA_d1D1_log	151,083.50	5,540.50
2021 Dec	115,100	ARIMA_d1D1_log	116,907.98	-1,807.98
2022 Jan	96,107	ARIMA_d1D1_log	85,374.31	10,732.69
2022 Feb	141,508	ARIMA_d1D1_log	113,684.09	27,823.91
2022 Mar	167,854	ARIMA_d1D1_log	86,021.91	81,832.09
2022 Apr	248,959	ARIMA_d1D1_log	138,699.41	110,259.59
2022 May	258,413	ARIMA_d1D1_log	354,663.82	-96,250.82
2022 Jun	300,520	ARIMA_d1D1_log	295,733.49	4,786.51
2010 Jan	53,653	Drift_STL	48,728.64	4,924.36
2010 Feb	62,257	Drift_STL	65,131.74	-2,874.74
2010 Mar	77,588	Drift_STL	77,021.78	566.22
2010 Apr	99,982	Drift_STL	94,578.22	5,403.78
2010 May	101,387	Drift_STL	101,203.05	183.95
2010 Jun	108,611	Drift_STL	100,501.50	8,109.50
2010 Jul	126,498	Drift_STL	121,135.76	5,362.24
2010 Aug	178,380	Drift_STL	174,729.66	3,650.34
2010 Sep	127,822	Drift_STL	125,846.91	1,975.09
2010 Oct	104,174	Drift_STL	107,151.29	-2,977.29
2010 Nov	69,271	Drift_STL	86,224.77	-16,953.77
2010 Dec	62,935	Drift_STL	65,222.58	-2,287.58
2011 Jan	60,457	Drift_STL	53,319.46	7,137.54
2011 Feb	67,260	Drift_STL	71,662.35	-4,402.35
2011 Mar	83,464	Drift_STL	82,412.12	1,051.88
2011 Apr	102,958	Drift_STL	101,633.60	1,324.40
2011 May	101,223	Drift_STL	104,725.39	-3,502.39
2011 Jun	120,148	Drift_STL	102,451.43	17,696.57
2011 Jul	136,999	Drift_STL	131,912.92	5,086.08
2011 Aug	212,668	Drift_STL	185,375.53	27,292.47
2011 Sep	129,606	Drift_STL	156,403.02	-26,797.02
2011 Oct	101,185	Drift_STL	109,743.48	-8,558.48
2011 Nov	62,121	Drift_STL	81,681.79	-19,560.79
2011 Dec	65,563	Drift_STL	60,155.60	5,407.40
2012 Jan	49,716	Drift_STL	57,590.86	-7,874.86
2012 Feb	58,638	Drift_STL	61,936.06	-3,298.06
2012 Mar	72,210	Drift_STL	74,920.35	-2,710.35
2012 Apr	87,406	Drift_STL	91,791.07	-4,385.07
2012 May	96,946	Drift_STL	89,645.51	7,300.49
2012 Jun	115,885	Drift_STL	100,837.35	15,047.65
2012 Jul	139,695	Drift_STL	127,036.84	12,658.16
2012 Aug	194,368	Drift_STL	190,978.35	3,389.65
2012 Sep	127,610	Drift_STL	133,171.14	-5,561.14
2012 Oct	89,649	Drift_STL	104,623.58	-14,974.58
2012 Nov	58,900	Drift_STL	66,099.44	-7,199.44
2012 Dec	51,122	Drift_STL	57,416.57	-6,294.57
2013 Jan	50,313	Drift_STL	43,171.11	7,141.89
2013 Feb	58,615	Drift_STL	60,953.22	-2,338.22
2013 Mar	92,426	Drift_STL	74,130.29	18,295.71
2013 Apr	100,996	Drift_STL	108,686.41	-7,690.41
2013 May	123,431	Drift_STL	103,722.58	19,708.42
2013 Jun	143,946	Drift_STL	128,840.55	15,105.45
2013 Jul	171,016	Drift_STL	155,515.91	15,500.09
2013 Aug	252,423	Drift_STL	222,322.98	30,100.02
2013 Sep	158,839	Drift_STL	184,531.97	-25,692.97
2013 Oct	109,956	Drift_STL	133,618.42	-23,662.42
2013 Nov	82,040	Drift_STL	86,720.07	-4,680.07
2013 Dec	72,692	Drift_STL	81,985.40	-9,293.40
2014 Jan	56,872	Drift_STL	68,887.22	-12,015.22
2014 Feb	64,346	Drift_STL	70,696.14	-6,350.14
2014 Mar	102,852	Drift_STL	86,132.02	16,719.98
2014 Apr	151,151	Drift_STL	118,986.48	32,164.52
2014 May	148,593	Drift_STL	153,445.40	-4,852.40
2014 Jun	154,231	Drift_STL	157,391.77	-3,160.77
2014 Jul	194,227	Drift_STL	169,867.99	24,359.01
2014 Aug	303,902	Drift_STL	250,300.03	53,601.97
2014 Sep	186,247	Drift_STL	224,144.28	-37,897.28
2014 Oct	133,884	Drift_STL	155,278.08	-21,394.08
2014 Nov	86,161	Drift_STL	109,025.12	-22,864.12
2014 Dec	81,830	Drift_STL	87,435.78	-5,605.78
2015 Jan	68,436	Drift_STL	78,319.74	-9,883.74
2015 Feb	84,417	Drift_STL	82,430.31	1,986.69
2015 Mar	116,291	Drift_STL	109,744.17	6,546.83
2015 Apr	145,183	Drift_STL	138,412.91	6,770.09
2015 May	172,016	Drift_STL	149,230.90	22,785.10
2015 Jun	182,765	Drift_STL	179,402.55	3,362.45
2015 Jul	238,708	Drift_STL	201,062.82	37,645.18
2015 Aug	358,044	Drift_STL	301,226.50	56,817.50
2015 Sep	216,474	Drift_STL	263,263.72	-46,789.72
2015 Oct	148,376	Drift_STL	179,766.58	-31,390.58
2015 Nov	99,794	Drift_STL	120,683.00	-20,889.00
2015 Dec	93,804	Drift_STL	102,313.06	-8,509.06
2016 Jan	74,572	Drift_STL	90,932.60	-16,360.60
2016 Feb	97,522	Drift_STL	91,497.90	6,024.10
2016 Mar	144,216	Drift_STL	126,365.53	17,850.47
2016 Apr	153,386	Drift_STL	166,848.52	-13,462.52
2016 May	168,235	Drift_STL	163,162.45	5,072.55
2016 Jun	215,800	Drift_STL	179,086.65	36,713.35
2016 Jul	271,212	Drift_STL	238,721.30	32,490.70
2016 Aug	380,776	Drift_STL	342,814.24	37,961.76
2016 Sep	249,098	Drift_STL	271,215.69	-22,117.69
2016 Oct	175,862	Drift_STL	201,928.32	-26,066.32
2016 Nov	102,775	Drift_STL	142,445.16	-39,670.16
2016 Dec	100,859	Drift_STL	106,530.19	-5,671.19
2017 Jan	83,249	Drift_STL	96,788.20	-13,539.20
2017 Feb	105,210	Drift_STL	103,037.15	2,172.85
2017 Mar	121,167	Drift_STL	139,747.88	-18,580.88
2017 Apr	217,906	Drift_STL	146,626.87	71,279.13
2017 May	196,622	Drift_STL	221,750.08	-25,128.08
2017 Jun	248,582	Drift_STL	213,010.65	35,571.35
2017 Jul	323,496	Drift_STL	277,343.83	46,152.17
2017 Aug	431,571	Drift_STL	400,662.06	30,908.94
2017 Sep	287,242	Drift_STL	309,549.71	-22,307.71
2017 Oct	212,357	Drift_STL	231,771.27	-19,414.27
2017 Nov	127,745	Drift_STL	170,776.05	-43,031.05
2017 Dec	132,238	Drift_STL	133,070.51	-832.51
2018 Jan	95,453	Drift_STL	126,697.35	-31,244.35
2018 Feb	120,303	Drift_STL	120,285.02	17.98
2018 Mar	162,886	Drift_STL	156,135.44	6,750.56
2018 Apr	187,186	Drift_STL	200,730.71	-13,544.71
2018 May	239,851	Drift_STL	194,433.04	45,417.96
2018 Jun	264,588	Drift_STL	259,824.84	4,763.16
2018 Jul	339,564	Drift_STL	303,725.93	35,838.07
2018 Aug	446,375	Drift_STL	424,545.03	21,829.97
2018 Sep	304,516	Drift_STL	313,647.20	-9,131.20
2018 Oct	230,827	Drift_STL	240,292.79	-9,465.79
2018 Nov	149,080	Drift_STL	177,525.17	-28,445.17
2018 Dec	135,316	Drift_STL	152,960.57	-17,644.57
2019 Jan	114,710	Drift_STL	124,661.30	-9,951.30
2019 Feb	122,635	Drift_STL	139,827.67	-17,192.67
2019 Mar	172,412	Drift_STL	162,549.93	9,862.07
2019 Apr	241,790	Drift_STL	210,933.85	30,856.15
2019 May	259,714	Drift_STL	251,978.18	7,735.82
2019 Jun	306,048	Drift_STL	282,358.36	23,689.64
2019 Jul	360,566	Drift_STL	352,248.60	8,317.40
2019 Aug	484,403	Drift_STL	453,405.32	30,997.68
2019 Sep	327,937	Drift_STL	343,894.69	-15,957.69
2019 Oct	238,677	Drift_STL	259,353.39	-20,676.39
2019 Nov	171,296	Drift_STL	179,244.54	-7,948.54
2019 Dec	138,642	Drift_STL	172,254.96	-33,612.96
2020 Jan	126,349	Drift_STL	127,429.04	-1,080.04
2020 Feb	167,411	Drift_STL	150,275.86	17,135.14
2020 Mar	70,530	Drift_STL	206,489.20	-135,959.20
2020 Apr	13,892	Drift_STL	132,870.56	-118,978.56
2020 May	38,343	Drift_STL	53,639.21	-15,296.21
2020 Jun	159,738	Drift_STL	84,883.44	74,854.56
2020 Jul	272,786	Drift_STL	211,661.25	61,124.75
2020 Aug	407,020	Drift_STL	364,653.48	42,366.52
2020 Sep	258,651	Drift_STL	248,947.66	9,703.34
2020 Oct	167,448	Drift_STL	172,420.92	-4,972.92
2020 Nov	73,734	Drift_STL	93,400.78	-19,666.78
2020 Dec	73,353	Drift_STL	63,731.19	9,621.81
2021 Jan	48,435	Drift_STL	53,066.78	-4,631.78
2021 Feb	40,443	Drift_STL	71,338.68	-30,895.68
2021 Mar	60,251	Drift_STL	58,994.59	1,256.41
2021 Apr	85,179	Drift_STL	95,675.20	-10,496.20
2021 May	169,690	Drift_STL	111,351.92	58,338.08
2021 Jun	254,243	Drift_STL	217,743.64	36,499.36
2021 Jul	329,058	Drift_STL	315,310.87	13,747.13
2021 Aug	461,844	Drift_STL	434,604.88	27,239.12
2021 Sep	308,273	Drift_STL	308,316.09	-43.09
2021 Oct	250,949	Drift_STL	225,255.67	25,693.33
2021 Nov	156,624	Drift_STL	172,170.04	-15,546.04
2021 Dec	115,100	Drift_STL	149,772.02	-34,672.02
2022 Jan	96,107	Drift_STL	101,263.82	-5,156.82
2022 Feb	141,508	Drift_STL	120,266.45	21,241.55
2022 Mar	167,854	Drift_STL	155,731.93	12,122.07
2022 Apr	248,959	Drift_STL	199,417.90	49,541.10
2022 May	258,413	Drift_STL	280,092.24	-21,679.24
2022 Jun	300,520	Drift_STL	321,141.36	-20,621.36
2010 Jan	53,653	Drift_STL_log	48,562.60	5,090.40
2010 Feb	62,257	Drift_STL_log	65,545.83	-3,288.83
2010 Mar	77,588	Drift_STL_log	77,352.66	235.34
2010 Apr	99,982	Drift_STL_log	96,342.34	3,639.66
2010 May	101,387	Drift_STL_log	102,286.64	-899.64
2010 Jun	108,611	Drift_STL_log	101,000.76	7,610.24
2010 Jul	126,498	Drift_STL_log	124,763.17	1,734.83
2010 Aug	178,380	Drift_STL_log	185,688.50	-7,308.50
2010 Sep	127,822	Drift_STL_log	120,739.85	7,082.15
2010 Oct	104,174	Drift_STL_log	103,476.37	697.63
2010 Nov	69,271	Drift_STL_log	82,279.31	-13,008.31
2010 Dec	62,935	Drift_STL_log	63,752.29	-817.29
2011 Jan	60,457	Drift_STL_log	52,121.14	8,335.86
2011 Feb	67,260	Drift_STL_log	72,740.66	-5,480.66
2011 Mar	83,464	Drift_STL_log	83,405.88	58.12
2011 Apr	102,958	Drift_STL_log	104,456.80	-1,498.80
2011 May	101,223	Drift_STL_log	105,932.69	-4,709.69
2011 Jun	120,148	Drift_STL_log	103,005.61	17,142.39
2011 Jul	136,999	Drift_STL_log	136,341.79	657.21
2011 Aug	212,668	Drift_STL_log	198,666.63	14,001.37
2011 Sep	129,606	Drift_STL_log	143,604.02	-13,998.02
2011 Oct	101,185	Drift_STL_log	106,346.85	-5,161.85
2011 Nov	62,121	Drift_STL_log	78,435.61	-16,314.61
2011 Dec	65,563	Drift_STL_log	58,768.10	6,794.90
2012 Jan	49,716	Drift_STL_log	55,652.43	-5,936.43
2012 Feb	58,638	Drift_STL_log	60,359.33	-1,721.33
2012 Mar	72,210	Drift_STL_log	73,196.74	-986.74
2012 Apr	87,406	Drift_STL_log	90,743.17	-3,337.17
2012 May	96,946	Drift_STL_log	89,599.39	7,346.61
2012 Jun	115,885	Drift_STL_log	100,325.41	15,559.59
2012 Jul	139,695	Drift_STL_log	128,769.96	10,925.04
2012 Aug	194,368	Drift_STL_log	199,908.85	-5,540.85
2012 Sep	127,610	Drift_STL_log	128,487.94	-877.94
2012 Oct	89,649	Drift_STL_log	102,862.21	-13,213.21
2012 Nov	58,900	Drift_STL_log	66,682.72	-7,782.72
2012 Dec	51,122	Drift_STL_log	57,033.16	-5,911.16
2013 Jan	50,313	Drift_STL_log	43,990.19	6,322.81
2013 Feb	58,615	Drift_STL_log	59,988.60	-1,373.60
2013 Mar	92,426	Drift_STL_log	72,596.31	19,829.69
2013 Apr	100,996	Drift_STL_log	111,457.31	-10,461.31
2013 May	123,431	Drift_STL_log	103,951.28	19,479.72
2013 Jun	143,946	Drift_STL_log	129,864.11	14,081.89
2013 Jul	171,016	Drift_STL_log	160,044.65	10,971.35
2013 Aug	252,423	Drift_STL_log	242,343.59	10,079.41
2013 Sep	158,839	Drift_STL_log	164,977.85	-6,138.85
2013 Oct	109,956	Drift_STL_log	125,292.02	-15,336.02
2013 Nov	82,040	Drift_STL_log	79,761.67	2,278.33
2013 Dec	72,692	Drift_STL_log	77,995.76	-5,303.76
2014 Jan	56,872	Drift_STL_log	64,702.06	-7,830.06
2014 Feb	64,346	Drift_STL_log	69,429.45	-5,083.45
2014 Mar	102,852	Drift_STL_log	85,675.64	17,176.36
2014 Apr	151,151	Drift_STL_log	123,771.08	27,379.92
2014 May	148,593	Drift_STL_log	156,981.32	-8,388.32
2014 Jun	154,231	Drift_STL_log	161,928.22	-7,697.22
2014 Jul	194,227	Drift_STL_log	176,091.40	18,135.60
2014 Aug	303,902	Drift_STL_log	276,988.65	26,913.35
2014 Sep	186,247	Drift_STL_log	194,306.10	-8,059.10
2014 Oct	133,884	Drift_STL_log	141,970.10	-8,086.10
2014 Nov	86,161	Drift_STL_log	95,315.88	-9,154.88
2014 Dec	81,830	Drift_STL_log	81,683.45	146.55
2015 Jan	68,436	Drift_STL_log	71,860.92	-3,424.92
2015 Feb	84,417	Drift_STL_log	81,802.68	2,614.32
2015 Mar	116,291	Drift_STL_log	115,267.95	1,023.05
2015 Apr	145,183	Drift_STL_log	145,253.61	-70.61
2015 May	172,016	Drift_STL_log	153,233.27	18,782.73
2015 Jun	182,765	Drift_STL_log	186,887.74	-4,122.74
2015 Jul	238,708	Drift_STL_log	211,425.34	27,282.66
2015 Aug	358,044	Drift_STL_log	341,695.84	16,348.16
2015 Sep	216,474	Drift_STL_log	224,373.20	-7,899.20
2015 Oct	148,376	Drift_STL_log	161,400.40	-13,024.40
2015 Nov	99,794	Drift_STL_log	102,899.50	-3,105.50
2015 Dec	93,804	Drift_STL_log	94,161.85	-357.85
2016 Jan	74,572	Drift_STL_log	81,813.67	-7,241.67
2016 Feb	97,522	Drift_STL_log	89,933.35	7,588.65
2016 Mar	144,216	Drift_STL_log	134,937.76	9,278.24
2016 Apr	153,386	Drift_STL_log	178,152.44	-24,766.44
2016 May	168,235	Drift_STL_log	167,786.81	448.19
2016 Jun	215,800	Drift_STL_log	186,565.51	29,234.49
2016 Jul	271,212	Drift_STL_log	254,005.87	17,206.13
2016 Aug	380,776	Drift_STL_log	390,173.00	-9,397.00
2016 Sep	249,098	Drift_STL_log	235,957.26	13,140.74
2016 Oct	175,862	Drift_STL_log	179,128.66	-3,266.66
2016 Nov	102,775	Drift_STL_log	118,843.52	-16,068.52
2016 Dec	100,859	Drift_STL_log	97,430.80	3,428.20
2017 Jan	83,249	Drift_STL_log	86,271.25	-3,022.25
2017 Feb	105,210	Drift_STL_log	101,380.16	3,829.84
2017 Mar	121,167	Drift_STL_log	148,959.62	-27,792.62
2017 Apr	217,906	Drift_STL_log	150,413.88	67,492.12
2017 May	196,622	Drift_STL_log	230,103.43	-33,481.43
2017 Jun	248,582	Drift_STL_log	222,668.08	25,913.92
2017 Jul	323,496	Drift_STL_log	297,740.39	25,755.61
2017 Aug	431,571	Drift_STL_log	461,371.40	-29,800.40
2017 Sep	287,242	Drift_STL_log	269,315.96	17,926.04
2017 Oct	212,357	Drift_STL_log	203,267.64	9,089.36
2017 Nov	127,745	Drift_STL_log	138,094.12	-10,349.12
2017 Dec	132,238	Drift_STL_log	121,008.12	11,229.88
2018 Jan	95,453	Drift_STL_log	110,395.60	-14,942.60
2018 Feb	120,303	Drift_STL_log	118,577.58	1,725.42
2018 Mar	162,886	Drift_STL_log	167,661.14	-4,775.14
2018 Apr	187,186	Drift_STL_log	214,121.71	-26,935.71
2018 May	239,851	Drift_STL_log	201,722.66	38,128.34
2018 Jun	264,588	Drift_STL_log	275,617.94	-11,029.94
2018 Jul	339,564	Drift_STL_log	327,374.08	12,189.92
2018 Aug	446,375	Drift_STL_log	482,416.22	-36,041.22
2018 Sep	304,516	Drift_STL_log	282,790.01	21,725.99
2018 Oct	230,827	Drift_STL_log	214,502.77	16,324.23
2018 Nov	149,080	Drift_STL_log	145,684.10	3,395.90
2018 Dec	135,316	Drift_STL_log	141,015.37	-5,699.37
2019 Jan	114,710	Drift_STL_log	109,205.65	5,504.35
2019 Feb	122,635	Drift_STL_log	140,691.83	-18,056.83
2019 Mar	172,412	Drift_STL_log	171,411.89	1,000.11
2019 Apr	241,790	Drift_STL_log	223,840.92	17,949.08
2019 May	259,714	Drift_STL_log	262,720.31	-3,006.31
2019 Jun	306,048	Drift_STL_log	299,007.36	7,040.64
2019 Jul	360,566	Drift_STL_log	383,403.18	-22,837.18
2019 Aug	484,403	Drift_STL_log	509,672.32	-25,269.32
2019 Sep	327,937	Drift_STL_log	314,432.68	13,504.32
2019 Oct	238,677	Drift_STL_log	234,484.57	4,192.43
2019 Nov	171,296	Drift_STL_log	150,982.38	20,313.62
2019 Dec	138,642	Drift_STL_log	159,643.75	-21,001.75
2020 Jan	126,349	Drift_STL_log	112,365.00	13,984.00
2020 Feb	167,411	Drift_STL_log	150,813.30	16,597.70
2020 Mar	70,530	Drift_STL_log	226,013.74	-155,483.74
2020 Apr	13,892	Drift_STL_log	107,240.35	-93,348.35
2020 May	38,343	Drift_STL_log	21,700.29	16,642.71
2020 Jun	159,738	Drift_STL_log	51,295.02	108,442.98
2020 Jul	272,786	Drift_STL_log	185,501.00	87,285.00
2020 Aug	407,020	Drift_STL_log	339,026.96	67,993.04
2020 Sep	258,651	Drift_STL_log	240,000.12	18,650.88
2020 Oct	167,448	Drift_STL_log	172,104.45	-4,656.45
2020 Nov	73,734	Drift_STL_log	103,374.57	-29,640.57
2020 Dec	73,353	Drift_STL_log	69,702.31	3,650.69
2021 Jan	48,435	Drift_STL_log	60,969.76	-12,534.76
2021 Feb	40,443	Drift_STL_log	61,979.93	-21,536.93
2021 Mar	60,251	Drift_STL_log	48,944.05	11,306.95
2021 Apr	85,179	Drift_STL_log	61,357.84	23,821.16
2021 May	169,690	Drift_STL_log	117,333.83	52,356.17
2021 Jun	254,243	Drift_STL_log	246,572.63	7,670.37
2021 Jul	329,058	Drift_STL_log	327,821.25	1,236.75
2021 Aug	461,844	Drift_STL_log	453,746.29	8,097.71
2021 Sep	308,273	Drift_STL_log	302,011.36	6,261.64
2021 Oct	250,949	Drift_STL_log	219,592.75	31,356.25
2021 Nov	156,624	Drift_STL_log	150,540.31	6,083.69
2021 Dec	115,100	Drift_STL_log	148,098.22	-32,998.22
2022 Jan	96,107	Drift_STL_log	96,025.05	81.95
2022 Feb	141,508	Drift_STL_log	116,073.55	25,434.45
2022 Mar	167,854	Drift_STL_log	163,825.50	4,028.50
2022 Apr	248,959	Drift_STL_log	172,312.11	76,646.89
2022 May	258,413	Drift_STL_log	376,756.78	-118,343.78
2022 Jun	300,520	Drift_STL_log	425,500.02	-124,980.02
2010 Jan	53,653	ETS_auto	55,527.88	-1,874.88
2010 Feb	62,257	ETS_auto	65,478.14	-3,221.14
2010 Mar	77,588	ETS_auto	81,980.02	-4,392.02
2010 Apr	99,982	ETS_auto	98,879.22	1,102.78
2010 May	101,387	ETS_auto	97,893.82	3,493.18
2010 Jun	108,611	ETS_auto	100,720.02	7,890.98
2010 Jul	126,498	ETS_auto	118,192.31	8,305.69
2010 Aug	178,380	ETS_auto	169,742.08	8,637.92
2010 Sep	127,822	ETS_auto	115,379.88	12,442.12
2010 Oct	104,174	ETS_auto	93,058.87	11,115.13
2010 Nov	69,271	ETS_auto	76,280.63	-7,009.63
2010 Dec	62,935	ETS_auto	65,841.00	-2,906.00
2011 Jan	60,457	ETS_auto	54,012.81	6,444.19
2011 Feb	67,260	ETS_auto	69,690.33	-2,430.33
2011 Mar	83,464	ETS_auto	86,185.87	-2,721.87
2011 Apr	102,958	ETS_auto	104,101.74	-1,143.74
2011 May	101,223	ETS_auto	104,067.09	-2,844.09
2011 Jun	120,148	ETS_auto	103,569.46	16,578.54
2011 Jul	136,999	ETS_auto	127,022.16	9,976.84
2011 Aug	212,668	ETS_auto	186,201.10	26,466.90
2011 Sep	129,606	ETS_auto	127,534.10	2,071.90
2011 Oct	101,185	ETS_auto	103,795.94	-2,610.94
2011 Nov	62,121	ETS_auto	78,281.33	-16,160.33
2011 Dec	65,563	ETS_auto	67,769.34	-2,206.34
2012 Jan	49,716	ETS_auto	55,880.26	-6,164.26
2012 Feb	58,638	ETS_auto	66,811.33	-8,173.33
2012 Mar	72,210	ETS_auto	82,463.03	-10,253.03
2012 Apr	87,406	ETS_auto	92,146.42	-4,740.42
2012 May	96,946	ETS_auto	93,275.14	3,670.86
2012 Jun	115,885	ETS_auto	96,986.22	18,898.78
2012 Jul	139,695	ETS_auto	117,272.77	22,422.23
2012 Aug	194,368	ETS_auto	186,736.10	7,631.90
2012 Sep	127,610	ETS_auto	126,761.15	848.85
2012 Oct	89,649	ETS_auto	101,774.93	-12,125.93
2012 Nov	58,900	ETS_auto	73,413.31	-14,513.31
2012 Dec	51,122	ETS_auto	60,943.23	-9,821.23
2013 Jan	50,313	ETS_auto	45,688.90	4,624.10
2013 Feb	58,615	ETS_auto	58,484.84	130.16
2013 Mar	92,426	ETS_auto	72,705.64	19,720.36
2013 Apr	100,996	ETS_auto	101,460.23	-464.23
2013 May	123,431	ETS_auto	100,025.12	23,405.88
2013 Jun	143,946	ETS_auto	114,509.52	29,436.48
2013 Jul	171,016	ETS_auto	155,185.53	15,830.47
2013 Aug	252,423	ETS_auto	240,754.83	11,668.17
2013 Sep	158,839	ETS_auto	160,565.90	-1,726.90
2013 Oct	109,956	ETS_auto	124,364.22	-14,408.22
2013 Nov	82,040	ETS_auto	86,942.37	-4,902.37
2013 Dec	72,692	ETS_auto	75,563.23	-2,871.23
2014 Jan	56,872	ETS_auto	61,497.12	-4,625.12
2014 Feb	64,346	ETS_auto	68,940.86	-4,594.86
2014 Mar	102,852	ETS_auto	83,495.08	19,356.92
2014 Apr	151,151	ETS_auto	113,034.89	38,116.11
2014 May	148,593	ETS_auto	152,219.95	-3,626.95
2014 Jun	154,231	ETS_auto	155,443.03	-1,212.03
2014 Jul	194,227	ETS_auto	178,971.56	15,255.44
2014 Aug	303,902	ETS_auto	276,320.56	27,581.44
2014 Sep	186,247	ETS_auto	188,963.15	-2,716.15
2014 Oct	133,884	ETS_auto	147,673.21	-13,789.21
2014 Nov	86,161	ETS_auto	102,139.66	-15,978.66
2014 Dec	81,830	ETS_auto	81,960.99	-130.99
2015 Jan	68,436	ETS_auto	67,196.13	1,239.87
2015 Feb	84,417	ETS_auto	79,215.23	5,201.77
2015 Mar	116,291	ETS_auto	109,708.53	6,582.47
2015 Apr	145,183	ETS_auto	144,378.05	804.95
2015 May	172,016	ETS_auto	149,112.10	22,903.90
2015 Jun	182,765	ETS_auto	179,025.70	3,739.30
2015 Jul	238,708	ETS_auto	210,290.32	28,417.68
2015 Aug	358,044	ETS_auto	335,410.58	22,633.42
2015 Sep	216,474	ETS_auto	205,497.55	10,976.45
2015 Oct	148,376	ETS_auto	146,107.38	2,268.62
2015 Nov	99,794	ETS_auto	110,401.42	-10,607.42
2015 Dec	93,804	ETS_auto	91,363.01	2,440.99
2016 Jan	74,572	ETS_auto	76,901.61	-2,329.61
2016 Feb	97,522	ETS_auto	92,017.55	5,504.45
2016 Mar	144,216	ETS_auto	135,340.64	8,875.36
2016 Apr	153,386	ETS_auto	179,657.63	-26,271.63
2016 May	168,235	ETS_auto	195,984.57	-27,749.57
2016 Jun	215,800	ETS_auto	180,128.66	35,671.34
2016 Jul	271,212	ETS_auto	253,789.31	17,422.69
2016 Aug	380,776	ETS_auto	386,419.45	-5,643.45
2016 Sep	249,098	ETS_auto	224,569.07	24,528.93
2016 Oct	175,862	ETS_auto	186,213.12	-10,351.12
2016 Nov	102,775	ETS_auto	125,211.35	-22,436.35
2016 Dec	100,859	ETS_auto	99,533.88	1,325.12
2017 Jan	83,249	ETS_auto	83,274.40	-25.40
2017 Feb	105,210	ETS_auto	98,777.09	6,432.91
2017 Mar	121,167	ETS_auto	139,620.88	-18,453.88
2017 Apr	217,906	ETS_auto	151,833.51	66,072.49
2017 May	196,622	ETS_auto	201,089.15	-4,467.15
2017 Jun	248,582	ETS_auto	239,929.74	8,652.26
2017 Jul	323,496	ETS_auto	302,442.49	21,053.51
2017 Aug	431,571	ETS_auto	440,610.12	-9,039.12
2017 Sep	287,242	ETS_auto	268,810.82	18,431.18
2017 Oct	212,357	ETS_auto	193,450.60	18,906.40
2017 Nov	127,745	ETS_auto	144,019.85	-16,274.85
2017 Dec	132,238	ETS_auto	121,576.98	10,661.02
2018 Jan	95,453	ETS_auto	100,991.65	-5,538.65
2018 Feb	120,303	ETS_auto	126,371.16	-6,068.16
2018 Mar	162,886	ETS_auto	167,174.40	-4,288.40
2018 Apr	187,186	ETS_auto	246,022.69	-58,836.69
2018 May	239,851	ETS_auto	201,740.26	38,110.74
2018 Jun	264,588	ETS_auto	253,673.16	10,914.84
2018 Jul	339,564	ETS_auto	311,219.81	28,344.19
2018 Aug	446,375	ETS_auto	465,722.09	-19,347.09
2018 Sep	304,516	ETS_auto	291,258.26	13,257.74
2018 Oct	230,827	ETS_auto	219,999.97	10,827.03
2018 Nov	149,080	ETS_auto	149,395.16	-315.16
2018 Dec	135,316	ETS_auto	138,385.98	-3,069.98
2019 Jan	114,710	ETS_auto	113,627.40	1,082.60
2019 Feb	122,635	ETS_auto	134,514.55	-11,879.55
2019 Mar	172,412	ETS_auto	173,311.99	-899.99
2019 Apr	241,790	ETS_auto	219,886.43	21,903.57
2019 May	259,714	ETS_auto	245,705.24	14,008.76
2019 Jun	306,048	ETS_auto	291,068.44	14,979.56
2019 Jul	360,566	ETS_auto	357,818.40	2,747.60
2019 Aug	484,403	ETS_auto	501,525.79	-17,122.79
2019 Sep	327,937	ETS_auto	319,804.96	8,132.04
2019 Oct	238,677	ETS_auto	241,266.58	-2,589.58
2019 Nov	171,296	ETS_auto	153,380.74	17,915.26
2019 Dec	138,642	ETS_auto	150,750.72	-12,108.72
2020 Jan	126,349	ETS_auto	119,672.22	6,676.78
2020 Feb	167,411	ETS_auto	144,941.77	22,469.23
2020 Mar	70,530	ETS_auto	214,401.72	-143,871.72
2020 Apr	13,892	ETS_auto	221,256.37	-207,364.37
2020 May	38,343	ETS_auto	167,152.33	-128,809.33
2020 Jun	159,738	ETS_auto	43,746.22	115,991.78
2020 Jul	272,786	ETS_auto	168,370.37	104,415.63
2020 Aug	407,020	ETS_auto	312,676.11	94,343.89
2020 Sep	258,651	ETS_auto	209,561.35	49,089.65
2020 Oct	167,448	ETS_auto	159,970.79	7,477.21
2020 Nov	73,734	ETS_auto	104,187.44	-30,453.44
2020 Dec	73,353	ETS_auto	89,432.07	-16,079.07
2021 Jan	48,435	ETS_auto	71,825.81	-23,390.81
2021 Feb	40,443	ETS_auto	82,641.94	-42,198.94
2021 Mar	60,251	ETS_auto	92,013.12	-31,762.12
2021 Apr	85,179	ETS_auto	79,096.39	6,082.61
2021 May	169,690	ETS_auto	71,750.42	97,939.58
2021 Jun	254,243	ETS_auto	147,892.01	106,350.99
2021 Jul	329,058	ETS_auto	217,250.28	111,807.72
2021 Aug	461,844	ETS_auto	374,552.73	87,291.27
2021 Sep	308,273	ETS_auto	335,055.33	-26,782.33
2021 Oct	250,949	ETS_auto	240,608.24	10,340.76
2021 Nov	156,624	ETS_auto	188,898.35	-32,274.35
2021 Dec	115,100	ETS_auto	147,688.79	-32,588.79
2022 Jan	96,107	ETS_auto	95,647.30	459.70
2022 Feb	141,508	ETS_auto	109,827.39	31,680.61
2022 Mar	167,854	ETS_auto	159,666.29	8,187.71
2022 Apr	248,959	ETS_auto	194,450.80	54,508.20
2022 May	258,413	ETS_auto	272,176.35	-13,763.35
2022 Jun	300,520	ETS_auto	303,598.67	-3,078.67
2010 Jan	53,653	ETS_auto_log	52,753.15	899.85
2010 Feb	62,257	ETS_auto_log	65,374.69	-3,117.69
2010 Mar	77,588	ETS_auto_log	84,075.32	-6,487.32
2010 Apr	99,982	ETS_auto_log	97,916.66	2,065.34
2010 May	101,387	ETS_auto_log	95,689.84	5,697.16
2010 Jun	108,611	ETS_auto_log	97,404.55	11,206.45
2010 Jul	126,498	ETS_auto_log	118,615.73	7,882.27
2010 Aug	178,380	ETS_auto_log	170,268.69	8,111.31
2010 Sep	127,822	ETS_auto_log	113,945.39	13,876.61
2010 Oct	104,174	ETS_auto_log	93,550.91	10,623.09
2010 Nov	69,271	ETS_auto_log	76,215.59	-6,944.59
2010 Dec	62,935	ETS_auto_log	64,920.41	-1,985.41
2011 Jan	60,457	ETS_auto_log	54,712.92	5,744.08
2011 Feb	67,260	ETS_auto_log	69,298.00	-2,038.00
2011 Mar	83,464	ETS_auto_log	87,219.02	-3,755.02
2011 Apr	102,958	ETS_auto_log	104,019.33	-1,061.33
2011 May	101,223	ETS_auto_log	104,782.48	-3,559.48
2011 Jun	120,148	ETS_auto_log	105,137.07	15,010.93
2011 Jul	136,999	ETS_auto_log	126,980.36	10,018.64
2011 Aug	212,668	ETS_auto_log	186,874.74	25,793.26
2011 Sep	129,606	ETS_auto_log	127,084.12	2,521.88
2011 Oct	101,185	ETS_auto_log	104,918.18	-3,733.18
2011 Nov	62,121	ETS_auto_log	79,993.18	-17,872.18
2011 Dec	65,563	ETS_auto_log	66,329.67	-766.67
2012 Jan	49,716	ETS_auto_log	57,307.54	-7,591.54
2012 Feb	58,638	ETS_auto_log	67,951.90	-9,313.90
2012 Mar	72,210	ETS_auto_log	80,111.08	-7,901.08
2012 Apr	87,406	ETS_auto_log	92,664.03	-5,258.03
2012 May	96,946	ETS_auto_log	94,276.95	2,669.05
2012 Jun	115,885	ETS_auto_log	97,162.03	18,722.97
2012 Jul	139,695	ETS_auto_log	118,634.60	21,060.40
2012 Aug	194,368	ETS_auto_log	182,182.83	12,185.17
2012 Sep	127,610	ETS_auto_log	124,373.54	3,236.46
2012 Oct	89,649	ETS_auto_log	102,327.08	-12,678.08
2012 Nov	58,900	ETS_auto_log	72,913.09	-14,013.09
2012 Dec	51,122	ETS_auto_log	60,023.43	-8,901.43
2013 Jan	50,313	ETS_auto_log	49,637.08	675.92
2013 Feb	58,615	ETS_auto_log	59,097.55	-482.55
2013 Mar	92,426	ETS_auto_log	71,095.40	21,330.60
2013 Apr	100,996	ETS_auto_log	96,857.80	4,138.20
2013 May	123,431	ETS_auto_log	100,230.92	23,200.08
2013 Jun	143,946	ETS_auto_log	115,619.97	28,326.03
2013 Jul	171,016	ETS_auto_log	157,444.89	13,571.11
2013 Aug	252,423	ETS_auto_log	237,642.51	14,780.49
2013 Sep	158,839	ETS_auto_log	162,381.35	-3,542.35
2013 Oct	109,956	ETS_auto_log	127,798.15	-17,842.15
2013 Nov	82,040	ETS_auto_log	88,464.03	-6,424.03
2013 Dec	72,692	ETS_auto_log	77,199.17	-4,507.17
2014 Jan	56,872	ETS_auto_log	60,981.28	-4,109.28
2014 Feb	64,346	ETS_auto_log	71,658.97	-7,312.97
2014 Mar	102,852	ETS_auto_log	84,958.23	17,893.77
2014 Apr	151,151	ETS_auto_log	117,344.00	33,807.00
2014 May	148,593	ETS_auto_log	143,821.36	4,771.64
2014 Jun	154,231	ETS_auto_log	156,861.88	-2,630.88
2014 Jul	194,227	ETS_auto_log	181,113.40	13,113.60
2014 Aug	303,902	ETS_auto_log	282,727.68	21,174.32
2014 Sep	186,247	ETS_auto_log	208,951.71	-22,704.71
2014 Oct	133,884	ETS_auto_log	150,495.42	-16,611.42
2014 Nov	86,161	ETS_auto_log	102,331.54	-16,170.54
2014 Dec	81,830	ETS_auto_log	78,714.89	3,115.11
2015 Jan	68,436	ETS_auto_log	68,354.56	81.44
2015 Feb	84,417	ETS_auto_log	81,364.62	3,052.38
2015 Mar	116,291	ETS_auto_log	124,483.60	-8,192.60
2015 Apr	145,183	ETS_auto_log	162,947.76	-17,764.76
2015 May	172,016	ETS_auto_log	161,171.99	10,844.01
2015 Jun	182,765	ETS_auto_log	176,068.11	6,696.89
2015 Jul	238,708	ETS_auto_log	214,333.33	24,374.67
2015 Aug	358,044	ETS_auto_log	327,382.31	30,661.69
2015 Sep	216,474	ETS_auto_log	208,363.62	8,110.38
2015 Oct	148,376	ETS_auto_log	147,897.33	478.67
2015 Nov	99,794	ETS_auto_log	109,523.50	-9,729.50
2015 Dec	93,804	ETS_auto_log	91,867.83	1,936.17
2016 Jan	74,572	ETS_auto_log	77,084.04	-2,512.04
2016 Feb	97,522	ETS_auto_log	92,354.42	5,167.58
2016 Mar	144,216	ETS_auto_log	135,909.58	8,306.42
2016 Apr	153,386	ETS_auto_log	176,872.48	-23,486.48
2016 May	168,235	ETS_auto_log	167,868.64	366.36
2016 Jun	215,800	ETS_auto_log	182,832.96	32,967.04
2016 Jul	271,212	ETS_auto_log	240,723.07	30,488.93
2016 Aug	380,776	ETS_auto_log	385,996.92	-5,220.92
2016 Sep	249,098	ETS_auto_log	235,831.18	13,266.82
2016 Oct	175,862	ETS_auto_log	184,922.62	-9,060.62
2016 Nov	102,775	ETS_auto_log	125,347.37	-22,572.37
2016 Dec	100,859	ETS_auto_log	99,904.57	954.43
2017 Jan	83,249	ETS_auto_log	84,027.18	-778.18
2017 Feb	105,210	ETS_auto_log	100,900.84	4,309.16
2017 Mar	121,167	ETS_auto_log	141,147.99	-19,980.99
2017 Apr	217,906	ETS_auto_log	156,344.18	61,561.82
2017 May	196,622	ETS_auto_log	209,010.77	-12,388.77
2017 Jun	248,582	ETS_auto_log	222,978.74	25,603.26
2017 Jul	323,496	ETS_auto_log	282,911.76	40,584.24
2017 Aug	431,571	ETS_auto_log	460,375.98	-28,804.98
2017 Sep	287,242	ETS_auto_log	278,701.64	8,540.36
2017 Oct	212,357	ETS_auto_log	206,888.79	5,468.21
2017 Nov	127,745	ETS_auto_log	140,972.75	-13,227.75
2017 Dec	132,238	ETS_auto_log	122,446.02	9,791.98
2018 Jan	95,453	ETS_auto_log	106,839.08	-11,386.08
2018 Feb	120,303	ETS_auto_log	121,516.38	-1,213.38
2018 Mar	162,886	ETS_auto_log	160,795.60	2,090.40
2018 Apr	187,186	ETS_auto_log	212,306.71	-25,120.71
2018 May	239,851	ETS_auto_log	210,097.07	29,753.93
2018 Jun	264,588	ETS_auto_log	257,043.77	7,544.23
2018 Jul	339,564	ETS_auto_log	315,779.12	23,784.88
2018 Aug	446,375	ETS_auto_log	475,893.95	-29,518.95
2018 Sep	304,516	ETS_auto_log	290,122.54	14,393.46
2018 Oct	230,827	ETS_auto_log	216,272.31	14,554.69
2018 Nov	149,080	ETS_auto_log	144,926.11	4,153.89
2018 Dec	135,316	ETS_auto_log	139,948.81	-4,632.81
2019 Jan	114,710	ETS_auto_log	113,337.00	1,373.00
2019 Feb	122,635	ETS_auto_log	137,256.26	-14,621.26
2019 Mar	172,412	ETS_auto_log	178,064.15	-5,652.15
2019 Apr	241,790	ETS_auto_log	224,937.33	16,852.67
2019 May	259,714	ETS_auto_log	250,798.96	8,915.04
2019 Jun	306,048	ETS_auto_log	293,238.18	12,809.82
2019 Jul	360,566	ETS_auto_log	367,982.05	-7,416.05
2019 Aug	484,403	ETS_auto_log	531,011.33	-46,608.33
2019 Sep	327,937	ETS_auto_log	319,864.04	8,072.96
2019 Oct	238,677	ETS_auto_log	234,598.91	4,078.09
2019 Nov	171,296	ETS_auto_log	154,366.82	16,929.18
2019 Dec	138,642	ETS_auto_log	154,900.74	-16,258.74
2020 Jan	126,349	ETS_auto_log	120,025.02	6,323.98
2020 Feb	167,411	ETS_auto_log	147,453.80	19,957.20
2020 Mar	70,530	ETS_auto_log	212,740.28	-142,210.28
2020 Apr	13,892	ETS_auto_log	171,416.34	-157,524.34
2020 May	38,343	ETS_auto_log	11,757.99	26,585.01
2020 Jun	159,738	ETS_auto_log	40,392.78	119,345.22
2020 Jul	272,786	ETS_auto_log	110,305.31	162,480.69
2020 Aug	407,020	ETS_auto_log	389,174.66	17,845.34
2020 Sep	258,651	ETS_auto_log	270,210.96	-11,559.96
2020 Oct	167,448	ETS_auto_log	179,880.03	-12,432.03
2020 Nov	73,734	ETS_auto_log	101,845.52	-28,111.52
2020 Dec	73,353	ETS_auto_log	66,452.75	6,900.25
2021 Jan	48,435	ETS_auto_log	59,796.79	-11,361.79
2021 Feb	40,443	ETS_auto_log	58,013.03	-17,570.03
2021 Mar	60,251	ETS_auto_log	51,290.40	8,960.60
2021 Apr	85,179	ETS_auto_log	65,029.27	20,149.73
2021 May	169,690	ETS_auto_log	108,656.78	61,033.22
2021 Jun	254,243	ETS_auto_log	231,144.83	23,098.17
2021 Jul	329,058	ETS_auto_log	348,046.67	-18,988.67
2021 Aug	461,844	ETS_auto_log	496,953.66	-35,109.66
2021 Sep	308,273	ETS_auto_log	308,987.66	-714.66
2021 Oct	250,949	ETS_auto_log	225,905.40	25,043.60
2021 Nov	156,624	ETS_auto_log	165,846.79	-9,222.79
2021 Dec	115,100	ETS_auto_log	147,150.91	-32,050.91
2022 Jan	96,107	ETS_auto_log	98,932.21	-2,825.21
2022 Feb	141,508	ETS_auto_log	122,118.36	19,389.64
2022 Mar	167,854	ETS_auto_log	186,673.69	-18,819.69
2022 Apr	248,959	ETS_auto_log	182,769.23	66,189.77
2022 May	258,413	ETS_auto_log	328,973.04	-70,560.04
2022 Jun	300,520	ETS_auto_log	371,814.83	-71,294.83
2010 Jan	53,653	HWA	57,017.89	-3,364.89
2010 Feb	62,257	HWA	67,035.83	-4,778.83
2010 Mar	77,588	HWA	81,678.14	-4,090.14
2010 Apr	99,982	HWA	96,168.68	3,813.32
2010 May	101,387	HWA	96,671.69	4,715.31
2010 Jun	108,611	HWA	99,023.57	9,587.43
2010 Jul	126,498	HWA	115,831.76	10,666.24
2010 Aug	178,380	HWA	163,058.79	15,321.21
2010 Sep	127,822	HWA	116,940.47	10,881.53
2010 Oct	104,174	HWA	100,469.67	3,704.33
2010 Nov	69,271	HWA	85,352.51	-16,081.51
2010 Dec	62,935	HWA	72,812.71	-9,877.71
2011 Jan	60,457	HWA	61,174.79	-717.79
2011 Feb	67,260	HWA	71,413.54	-4,153.54
2011 Mar	83,464	HWA	85,619.31	-2,155.31
2011 Apr	102,958	HWA	100,332.05	2,625.95
2011 May	101,223	HWA	102,335.38	-1,112.38
2011 Jun	120,148	HWA	103,396.12	16,751.88
2011 Jul	136,999	HWA	122,422.85	14,576.15
2011 Aug	212,668	HWA	177,541.45	35,126.55
2011 Sep	129,606	HWA	144,122.24	-14,516.24
2011 Oct	101,185	HWA	113,395.36	-12,210.36
2011 Nov	62,121	HWA	89,114.24	-26,993.24
2011 Dec	65,563	HWA	74,112.17	-8,549.17
2012 Jan	49,716	HWA	57,385.81	-7,669.81
2012 Feb	58,638	HWA	61,553.83	-2,915.83
2012 Mar	72,210	HWA	74,986.93	-2,776.93
2012 Apr	87,406	HWA	91,554.31	-4,148.31
2012 May	96,946	HWA	90,827.16	6,118.84
2012 Jun	115,885	HWA	96,965.46	18,919.54
2012 Jul	139,695	HWA	123,172.25	16,522.75
2012 Aug	194,368	HWA	185,754.99	8,613.01
2012 Sep	127,610	HWA	137,868.10	-10,258.10
2012 Oct	89,649	HWA	109,185.72	-19,536.72
2012 Nov	58,900	HWA	62,552.89	-3,652.89
2012 Dec	51,122	HWA	61,930.26	-10,808.26
2013 Jan	50,313	HWA	49,277.61	1,035.39
2013 Feb	58,615	HWA	59,387.65	-772.65
2013 Mar	92,426	HWA	74,597.90	17,828.10
2013 Apr	100,996	HWA	95,798.33	5,197.67
2013 May	123,431	HWA	103,540.04	19,890.96
2013 Jun	143,946	HWA	124,991.64	18,954.36
2013 Jul	171,016	HWA	150,038.99	20,977.01
2013 Aug	252,423	HWA	213,228.99	39,194.01
2013 Sep	158,839	HWA	153,552.44	5,286.56
2013 Oct	109,956	HWA	118,629.28	-8,673.28
2013 Nov	82,040	HWA	84,739.12	-2,699.12
2013 Dec	72,692	HWA	78,969.42	-6,277.42
2014 Jan	56,872	HWA	75,199.18	-18,327.18
2014 Feb	64,346	HWA	79,219.36	-14,873.36
2014 Mar	102,852	HWA	104,860.39	-2,008.39
2014 Apr	151,151	HWA	112,451.60	38,699.40
2014 May	148,593	HWA	139,197.41	9,395.59
2014 Jun	154,231	HWA	158,528.26	-4,297.26
2014 Jul	194,227	HWA	180,616.67	13,610.33
2014 Aug	303,902	HWA	255,429.59	48,472.41
2014 Sep	186,247	HWA	173,012.12	13,234.88
2014 Oct	133,884	HWA	128,882.55	5,001.45
2014 Nov	86,161	HWA	103,055.55	-16,894.55
2014 Dec	81,830	HWA	90,834.19	-9,004.19
2015 Jan	68,436	HWA	76,363.80	-7,927.80
2015 Feb	84,417	HWA	84,245.61	171.39
2015 Mar	116,291	HWA	124,324.35	-8,033.35
2015 Apr	145,183	HWA	166,300.14	-21,117.14
2015 May	172,016	HWA	158,941.26	13,074.74
2015 Jun	182,765	HWA	168,222.87	14,542.13
2015 Jul	238,708	HWA	208,884.79	29,823.21
2015 Aug	358,044	HWA	297,776.40	60,267.60
2015 Sep	216,474	HWA	204,171.57	12,302.43
2015 Oct	148,376	HWA	153,123.14	-4,747.14
2015 Nov	99,794	HWA	106,956.84	-7,162.84
2015 Dec	93,804	HWA	102,443.87	-8,639.87
2016 Jan	74,572	HWA	87,214.30	-12,642.30
2016 Feb	97,522	HWA	102,003.40	-4,481.40
2016 Mar	144,216	HWA	118,731.31	25,484.69
2016 Apr	153,386	HWA	165,522.97	-12,136.97
2016 May	168,235	HWA	161,524.73	6,710.27
2016 Jun	215,800	HWA	178,342.77	37,457.23
2016 Jul	271,212	HWA	239,506.26	31,705.74
2016 Aug	380,776	HWA	369,719.80	11,056.20
2016 Sep	249,098	HWA	289,467.62	-40,369.62
2016 Oct	175,862	HWA	207,343.15	-31,481.15
2016 Nov	102,775	HWA	138,988.74	-36,213.74
2016 Dec	100,859	HWA	92,100.93	8,758.07
2017 Jan	83,249	HWA	85,223.62	-1,974.62
2017 Feb	105,210	HWA	91,586.89	13,623.11
2017 Mar	121,167	HWA	128,949.39	-7,782.39
2017 Apr	217,906	HWA	140,269.49	77,636.51
2017 May	196,622	HWA	226,606.86	-29,984.86
2017 Jun	248,582	HWA	209,537.20	39,044.80
2017 Jul	323,496	HWA	274,012.23	49,483.77
2017 Aug	431,571	HWA	403,326.75	28,244.25
2017 Sep	287,242	HWA	330,981.83	-43,739.83
2017 Oct	212,357	HWA	239,007.16	-26,650.16
2017 Nov	127,745	HWA	168,063.04	-40,318.04
2017 Dec	132,238	HWA	117,717.70	14,520.30
2018 Jan	95,453	HWA	116,184.78	-20,731.78
2018 Feb	120,303	HWA	105,779.61	14,523.39
2018 Mar	162,886	HWA	143,094.91	19,791.09
2018 Apr	187,186	HWA	193,342.63	-6,156.63
2018 May	239,851	HWA	193,418.65	46,432.35
2018 Jun	264,588	HWA	261,011.96	3,576.04
2018 Jul	339,564	HWA	297,167.71	42,396.29
2018 Aug	446,375	HWA	447,259.00	-884.00
2018 Sep	304,516	HWA	301,050.06	3,465.94
2018 Oct	230,827	HWA	251,801.20	-20,974.20
2018 Nov	149,080	HWA	181,244.33	-32,164.33
2018 Dec	135,316	HWA	146,013.92	-10,697.92
2019 Jan	114,710	HWA	109,767.47	4,942.53
2019 Feb	122,635	HWA	127,564.96	-4,929.96
2019 Mar	172,412	HWA	175,244.08	-2,832.08
2019 Apr	241,790	HWA	206,578.10	35,211.90
2019 May	259,714	HWA	262,285.32	-2,571.32
2019 Jun	306,048	HWA	287,643.20	18,404.80
2019 Jul	360,566	HWA	363,768.05	-3,202.05
2019 Aug	484,403	HWA	468,822.42	15,580.58
2019 Sep	327,937	HWA	328,944.38	-1,007.38
2019 Oct	238,677	HWA	255,007.70	-16,330.70
2019 Nov	171,296	HWA	170,238.05	1,057.95
2019 Dec	138,642	HWA	159,043.12	-20,401.12
2020 Jan	126,349	HWA	135,297.61	-8,948.61
2020 Feb	167,411	HWA	144,706.25	22,704.75
2020 Mar	70,530	HWA	193,243.29	-122,713.29
2020 Apr	13,892	HWA	250,782.97	-236,890.97
2020 May	38,343	HWA	27,485.99	10,857.01
2020 Jun	159,738	HWA	66,194.34	93,543.66
2020 Jul	272,786	HWA	204,736.20	68,049.80
2020 Aug	407,020	HWA	363,487.75	43,532.25
2020 Sep	258,651	HWA	286,636.81	-27,985.81
2020 Oct	167,448	HWA	199,209.54	-31,761.54
2020 Nov	73,734	HWA	113,794.87	-40,060.87
2020 Dec	73,353	HWA	67,748.77	5,604.23
2021 Jan	48,435	HWA	57,256.37	-8,821.37
2021 Feb	40,443	HWA	66,471.13	-26,028.13
2021 Mar	60,251	HWA	60,574.04	-323.04
2021 Apr	85,179	HWA	88,743.71	-3,564.71
2021 May	169,690	HWA	103,401.78	66,288.22
2021 Jun	254,243	HWA	210,852.73	43,390.27
2021 Jul	329,058	HWA	308,578.36	20,479.64
2021 Aug	461,844	HWA	424,550.46	37,293.54
2021 Sep	308,273	HWA	325,882.83	-17,609.83
2021 Oct	250,949	HWA	237,979.29	12,969.71
2021 Nov	156,624	HWA	189,348.05	-32,724.05
2021 Dec	115,100	HWA	149,116.09	-34,016.09
2022 Jan	96,107	HWA	97,741.99	-1,634.99
2022 Feb	141,508	HWA	112,206.79	29,301.21
2022 Mar	167,854	HWA	162,454.51	5,399.49
2022 Apr	248,959	HWA	197,304.27	51,654.73
2022 May	258,413	HWA	275,936.76	-17,523.76
2022 Jun	300,520	HWA	307,526.92	-7,006.92
2010 Jan	53,653	HWA_log	52,753.15	899.85
2010 Feb	62,257	HWA_log	65,374.69	-3,117.69
2010 Mar	77,588	HWA_log	84,075.32	-6,487.32
2010 Apr	99,982	HWA_log	100,132.14	-150.14
2010 May	101,387	HWA_log	99,530.80	1,856.20
2010 Jun	108,611	HWA_log	101,970.87	6,640.13
2010 Jul	126,498	HWA_log	121,292.37	5,205.63
2010 Aug	178,380	HWA_log	172,485.02	5,894.98
2010 Sep	127,822	HWA_log	115,049.57	12,772.43
2010 Oct	104,174	HWA_log	91,570.55	12,603.45
2010 Nov	69,271	HWA_log	73,613.23	-4,342.23
2010 Dec	62,935	HWA_log	63,311.41	-376.41
2011 Jan	60,457	HWA_log	54,457.99	5,999.01
2011 Feb	67,260	HWA_log	65,688.04	1,571.96
2011 Mar	83,464	HWA_log	85,748.41	-2,284.41
2011 Apr	102,958	HWA_log	102,240.05	717.95
2011 May	101,223	HWA_log	105,040.29	-3,817.29
2011 Jun	120,148	HWA_log	104,931.01	15,216.99
2011 Jul	136,999	HWA_log	126,630.68	10,368.32
2011 Aug	212,668	HWA_log	184,166.72	28,501.28
2011 Sep	129,606	HWA_log	124,980.67	4,625.33
2011 Oct	101,185	HWA_log	99,158.10	2,026.90
2011 Nov	62,121	HWA_log	76,127.16	-14,006.16
2011 Dec	65,563	HWA_log	66,329.67	-766.67
2012 Jan	49,716	HWA_log	57,307.54	-7,591.54
2012 Feb	58,638	HWA_log	68,773.92	-10,135.92
2012 Mar	72,210	HWA_log	87,112.03	-14,902.03
2012 Apr	87,406	HWA_log	101,658.15	-14,252.15
2012 May	96,946	HWA_log	97,542.98	-596.98
2012 Jun	115,885	HWA_log	100,817.02	15,067.98
2012 Jul	139,695	HWA_log	112,565.70	27,129.30
2012 Aug	194,368	HWA_log	181,325.85	13,042.15
2012 Sep	127,610	HWA_log	121,976.68	5,633.32
2012 Oct	89,649	HWA_log	98,862.78	-9,213.78
2012 Nov	58,900	HWA_log	74,053.28	-15,153.28
2012 Dec	51,122	HWA_log	63,745.60	-12,623.60
2013 Jan	50,313	HWA_log	50,613.47	-300.47
2013 Feb	58,615	HWA_log	60,531.47	-1,916.47
2013 Mar	92,426	HWA_log	74,491.59	17,934.41
2013 Apr	100,996	HWA_log	96,023.96	4,972.04
2013 May	123,431	HWA_log	101,837.44	21,593.56
2013 Jun	143,946	HWA_log	116,409.91	27,536.09
2013 Jul	171,016	HWA_log	143,727.31	27,288.69
2013 Aug	252,423	HWA_log	216,820.54	35,602.46
2013 Sep	158,839	HWA_log	146,657.46	12,181.54
2013 Oct	109,956	HWA_log	110,730.46	-774.46
2013 Nov	82,040	HWA_log	72,729.71	9,310.29
2013 Dec	72,692	HWA_log	71,674.59	1,017.41
2014 Jan	56,872	HWA_log	67,206.89	-10,334.89
2014 Feb	64,346	HWA_log	76,004.33	-11,658.33
2014 Mar	102,852	HWA_log	100,166.29	2,685.71
2014 Apr	151,151	HWA_log	116,665.94	34,485.06
2014 May	148,593	HWA_log	142,046.60	6,546.40
2014 Jun	154,231	HWA_log	164,612.54	-10,381.54
2014 Jul	194,227	HWA_log	187,063.70	7,163.30
2014 Aug	303,902	HWA_log	271,059.18	32,842.82
2014 Sep	186,247	HWA_log	173,754.73	12,492.27
2014 Oct	133,884	HWA_log	124,470.81	9,413.19
2014 Nov	86,161	HWA_log	89,962.16	-3,801.16
2014 Dec	81,830	HWA_log	79,608.39	2,221.61
2015 Jan	68,436	HWA_log	66,684.30	1,751.70
2015 Feb	84,417	HWA_log	78,346.37	6,070.63
2015 Mar	116,291	HWA_log	124,483.60	-8,192.60
2015 Apr	145,183	HWA_log	164,343.83	-19,160.83
2015 May	172,016	HWA_log	161,171.99	10,844.01
2015 Jun	182,765	HWA_log	176,068.11	6,696.89
2015 Jul	238,708	HWA_log	220,416.07	18,291.93
2015 Aug	358,044	HWA_log	338,346.58	19,697.42
2015 Sep	216,474	HWA_log	208,363.62	8,110.38
2015 Oct	148,376	HWA_log	150,957.89	-2,581.89
2015 Nov	99,794	HWA_log	97,665.58	2,128.42
2015 Dec	93,804	HWA_log	92,323.87	1,480.13
2016 Jan	74,572	HWA_log	77,084.04	-2,512.04
2016 Feb	97,522	HWA_log	92,354.42	5,167.58
2016 Mar	144,216	HWA_log	133,675.62	10,540.38
2016 Apr	153,386	HWA_log	179,347.37	-25,961.37
2016 May	168,235	HWA_log	198,532.85	-30,297.85
2016 Jun	215,800	HWA_log	202,292.85	13,507.15
2016 Jul	271,212	HWA_log	255,286.72	15,925.28
2016 Aug	380,776	HWA_log	394,765.33	-13,989.33
2016 Sep	249,098	HWA_log	235,831.18	13,266.82
2016 Oct	175,862	HWA_log	165,182.78	10,679.22
2016 Nov	102,775	HWA_log	128,213.57	-25,438.57
2016 Dec	100,859	HWA_log	102,884.75	-2,025.75
2017 Jan	83,249	HWA_log	82,588.85	660.15
2017 Feb	105,210	HWA_log	104,699.41	510.59
2017 Mar	121,167	HWA_log	154,222.03	-33,055.03
2017 Apr	217,906	HWA_log	163,480.46	54,425.54
2017 May	196,622	HWA_log	200,266.56	-3,644.56
2017 Jun	248,582	HWA_log	238,602.26	9,979.74
2017 Jul	323,496	HWA_log	305,375.81	18,120.19
2017 Aug	431,571	HWA_log	443,078.57	-11,507.57
2017 Sep	287,242	HWA_log	279,714.95	7,527.05
2017 Oct	212,357	HWA_log	202,743.54	9,613.46
2017 Nov	127,745	HWA_log	146,424.50	-18,679.50
2017 Dec	132,238	HWA_log	127,787.71	4,450.29
2018 Jan	95,453	HWA_log	101,338.08	-5,885.08
2018 Feb	120,303	HWA_log	126,993.45	-6,690.45
2018 Mar	162,886	HWA_log	161,967.54	918.46
2018 Apr	187,186	HWA_log	245,653.71	-58,467.71
2018 May	239,851	HWA_log	224,308.65	15,542.35
2018 Jun	264,588	HWA_log	279,122.72	-14,534.72
2018 Jul	339,564	HWA_log	349,189.72	-9,625.72
2018 Aug	446,375	HWA_log	475,943.75	-29,568.75
2018 Sep	304,516	HWA_log	296,163.61	8,352.39
2018 Oct	230,827	HWA_log	212,239.12	18,587.88
2018 Nov	149,080	HWA_log	146,533.80	2,546.20
2018 Dec	135,316	HWA_log	139,402.20	-4,086.20
2019 Jan	114,710	HWA_log	118,360.51	-3,650.51
2019 Feb	122,635	HWA_log	141,881.74	-19,246.74
2019 Mar	172,412	HWA_log	180,821.32	-8,409.32
2019 Apr	241,790	HWA_log	229,301.84	12,488.16
2019 May	259,714	HWA_log	254,526.49	5,187.51
2019 Jun	306,048	HWA_log	292,440.77	13,607.23
2019 Jul	360,566	HWA_log	357,584.59	2,981.41
2019 Aug	484,403	HWA_log	508,275.08	-23,872.08
2019 Sep	327,937	HWA_log	315,958.86	11,978.14
2019 Oct	238,677	HWA_log	236,742.35	1,934.65
2019 Nov	171,296	HWA_log	151,071.52	20,224.48
2019 Dec	138,642	HWA_log	149,371.02	-10,729.02
2020 Jan	126,349	HWA_log	120,808.19	5,540.81
2020 Feb	167,411	HWA_log	147,453.80	19,957.20
2020 Mar	70,530	HWA_log	201,940.86	-131,410.86
2020 Apr	13,892	HWA_log	208,378.28	-194,486.28
2020 May	38,343	HWA_log	11,757.99	26,585.01
2020 Jun	159,738	HWA_log	42,599.60	117,138.40
2020 Jul	272,786	HWA_log	112,270.37	160,515.63
2020 Aug	407,020	HWA_log	387,043.09	19,976.91
2020 Sep	258,651	HWA_log	270,210.96	-11,559.96
2020 Oct	167,448	HWA_log	179,880.03	-12,432.03
2020 Nov	73,734	HWA_log	117,240.66	-43,506.66
2020 Dec	73,353	HWA_log	62,175.57	11,177.43
2021 Jan	48,435	HWA_log	59,796.79	-11,361.79
2021 Feb	40,443	HWA_log	58,013.03	-17,570.03
2021 Mar	60,251	HWA_log	47,938.96	12,312.04
2021 Apr	85,179	HWA_log	65,029.27	20,149.73
2021 May	169,690	HWA_log	104,886.41	64,803.59
2021 Jun	254,243	HWA_log	235,485.98	18,757.02
2021 Jul	329,058	HWA_log	321,978.32	7,079.68
2021 Aug	461,844	HWA_log	457,594.06	4,249.94
2021 Sep	308,273	HWA_log	316,291.54	-8,018.54
2021 Oct	250,949	HWA_log	221,325.75	29,623.25
2021 Nov	156,624	HWA_log	162,141.91	-5,517.91
2021 Dec	115,100	HWA_log	147,150.91	-32,050.91
2022 Jan	96,107	HWA_log	86,840.43	9,266.57
2022 Feb	141,508	HWA_log	101,241.23	40,266.77
2022 Mar	167,854	HWA_log	175,804.34	-7,950.34
2022 Apr	248,959	HWA_log	184,408.85	64,550.15
2022 May	258,413	HWA_log	316,388.99	-57,975.99
2022 Jun	300,520	HWA_log	380,873.82	-80,353.82
2010 Jan	53,653	Naive	59,473.00	-5,820.00
2010 Feb	62,257	Naive	53,653.00	8,604.00
2010 Mar	77,588	Naive	62,257.00	15,331.00
2010 Apr	99,982	Naive	77,588.00	22,394.00
2010 May	101,387	Naive	99,982.00	1,405.00
2010 Jun	108,611	Naive	101,387.00	7,224.00
2010 Jul	126,498	Naive	108,611.00	17,887.00
2010 Aug	178,380	Naive	126,498.00	51,882.00
2010 Sep	127,822	Naive	178,380.00	-50,558.00
2010 Oct	104,174	Naive	127,822.00	-23,648.00
2010 Nov	69,271	Naive	104,174.00	-34,903.00
2010 Dec	62,935	Naive	69,271.00	-6,336.00
2011 Jan	60,457	Naive	62,935.00	-2,478.00
2011 Feb	67,260	Naive	60,457.00	6,803.00
2011 Mar	83,464	Naive	67,260.00	16,204.00
2011 Apr	102,958	Naive	83,464.00	19,494.00
2011 May	101,223	Naive	102,958.00	-1,735.00
2011 Jun	120,148	Naive	101,223.00	18,925.00
2011 Jul	136,999	Naive	120,148.00	16,851.00
2011 Aug	212,668	Naive	136,999.00	75,669.00
2011 Sep	129,606	Naive	212,668.00	-83,062.00
2011 Oct	101,185	Naive	129,606.00	-28,421.00
2011 Nov	62,121	Naive	101,185.00	-39,064.00
2011 Dec	65,563	Naive	62,121.00	3,442.00
2012 Jan	49,716	Naive	65,563.00	-15,847.00
2012 Feb	58,638	Naive	49,716.00	8,922.00
2012 Mar	72,210	Naive	58,638.00	13,572.00
2012 Apr	87,406	Naive	72,210.00	15,196.00
2012 May	96,946	Naive	87,406.00	9,540.00
2012 Jun	115,885	Naive	96,946.00	18,939.00
2012 Jul	139,695	Naive	115,885.00	23,810.00
2012 Aug	194,368	Naive	139,695.00	54,673.00
2012 Sep	127,610	Naive	194,368.00	-66,758.00
2012 Oct	89,649	Naive	127,610.00	-37,961.00
2012 Nov	58,900	Naive	89,649.00	-30,749.00
2012 Dec	51,122	Naive	58,900.00	-7,778.00
2013 Jan	50,313	Naive	51,122.00	-809.00
2013 Feb	58,615	Naive	50,313.00	8,302.00
2013 Mar	92,426	Naive	58,615.00	33,811.00
2013 Apr	100,996	Naive	92,426.00	8,570.00
2013 May	123,431	Naive	100,996.00	22,435.00
2013 Jun	143,946	Naive	123,431.00	20,515.00
2013 Jul	171,016	Naive	143,946.00	27,070.00
2013 Aug	252,423	Naive	171,016.00	81,407.00
2013 Sep	158,839	Naive	252,423.00	-93,584.00
2013 Oct	109,956	Naive	158,839.00	-48,883.00
2013 Nov	82,040	Naive	109,956.00	-27,916.00
2013 Dec	72,692	Naive	82,040.00	-9,348.00
2014 Jan	56,872	Naive	72,692.00	-15,820.00
2014 Feb	64,346	Naive	56,872.00	7,474.00
2014 Mar	102,852	Naive	64,346.00	38,506.00
2014 Apr	151,151	Naive	102,852.00	48,299.00
2014 May	148,593	Naive	151,151.00	-2,558.00
2014 Jun	154,231	Naive	148,593.00	5,638.00
2014 Jul	194,227	Naive	154,231.00	39,996.00
2014 Aug	303,902	Naive	194,227.00	109,675.00
2014 Sep	186,247	Naive	303,902.00	-117,655.00
2014 Oct	133,884	Naive	186,247.00	-52,363.00
2014 Nov	86,161	Naive	133,884.00	-47,723.00
2014 Dec	81,830	Naive	86,161.00	-4,331.00
2015 Jan	68,436	Naive	81,830.00	-13,394.00
2015 Feb	84,417	Naive	68,436.00	15,981.00
2015 Mar	116,291	Naive	84,417.00	31,874.00
2015 Apr	145,183	Naive	116,291.00	28,892.00
2015 May	172,016	Naive	145,183.00	26,833.00
2015 Jun	182,765	Naive	172,016.00	10,749.00
2015 Jul	238,708	Naive	182,765.00	55,943.00
2015 Aug	358,044	Naive	238,708.00	119,336.00
2015 Sep	216,474	Naive	358,044.00	-141,570.00
2015 Oct	148,376	Naive	216,474.00	-68,098.00
2015 Nov	99,794	Naive	148,376.00	-48,582.00
2015 Dec	93,804	Naive	99,794.00	-5,990.00
2016 Jan	74,572	Naive	93,804.00	-19,232.00
2016 Feb	97,522	Naive	74,572.00	22,950.00
2016 Mar	144,216	Naive	97,522.00	46,694.00
2016 Apr	153,386	Naive	144,216.00	9,170.00
2016 May	168,235	Naive	153,386.00	14,849.00
2016 Jun	215,800	Naive	168,235.00	47,565.00
2016 Jul	271,212	Naive	215,800.00	55,412.00
2016 Aug	380,776	Naive	271,212.00	109,564.00
2016 Sep	249,098	Naive	380,776.00	-131,678.00
2016 Oct	175,862	Naive	249,098.00	-73,236.00
2016 Nov	102,775	Naive	175,862.00	-73,087.00
2016 Dec	100,859	Naive	102,775.00	-1,916.00
2017 Jan	83,249	Naive	100,859.00	-17,610.00
2017 Feb	105,210	Naive	83,249.00	21,961.00
2017 Mar	121,167	Naive	105,210.00	15,957.00
2017 Apr	217,906	Naive	121,167.00	96,739.00
2017 May	196,622	Naive	217,906.00	-21,284.00
2017 Jun	248,582	Naive	196,622.00	51,960.00
2017 Jul	323,496	Naive	248,582.00	74,914.00
2017 Aug	431,571	Naive	323,496.00	108,075.00
2017 Sep	287,242	Naive	431,571.00	-144,329.00
2017 Oct	212,357	Naive	287,242.00	-74,885.00
2017 Nov	127,745	Naive	212,357.00	-84,612.00
2017 Dec	132,238	Naive	127,745.00	4,493.00
2018 Jan	95,453	Naive	132,238.00	-36,785.00
2018 Feb	120,303	Naive	95,453.00	24,850.00
2018 Mar	162,886	Naive	120,303.00	42,583.00
2018 Apr	187,186	Naive	162,886.00	24,300.00
2018 May	239,851	Naive	187,186.00	52,665.00
2018 Jun	264,588	Naive	239,851.00	24,737.00
2018 Jul	339,564	Naive	264,588.00	74,976.00
2018 Aug	446,375	Naive	339,564.00	106,811.00
2018 Sep	304,516	Naive	446,375.00	-141,859.00
2018 Oct	230,827	Naive	304,516.00	-73,689.00
2018 Nov	149,080	Naive	230,827.00	-81,747.00
2018 Dec	135,316	Naive	149,080.00	-13,764.00
2019 Jan	114,710	Naive	135,316.00	-20,606.00
2019 Feb	122,635	Naive	114,710.00	7,925.00
2019 Mar	172,412	Naive	122,635.00	49,777.00
2019 Apr	241,790	Naive	172,412.00	69,378.00
2019 May	259,714	Naive	241,790.00	17,924.00
2019 Jun	306,048	Naive	259,714.00	46,334.00
2019 Jul	360,566	Naive	306,048.00	54,518.00
2019 Aug	484,403	Naive	360,566.00	123,837.00
2019 Sep	327,937	Naive	484,403.00	-156,466.00
2019 Oct	238,677	Naive	327,937.00	-89,260.00
2019 Nov	171,296	Naive	238,677.00	-67,381.00
2019 Dec	138,642	Naive	171,296.00	-32,654.00
2020 Jan	126,349	Naive	138,642.00	-12,293.00
2020 Feb	167,411	Naive	126,349.00	41,062.00
2020 Mar	70,530	Naive	167,411.00	-96,881.00
2020 Apr	13,892	Naive	70,530.00	-56,638.00
2020 May	38,343	Naive	13,892.00	24,451.00
2020 Jun	159,738	Naive	38,343.00	121,395.00
2020 Jul	272,786	Naive	159,738.00	113,048.00
2020 Aug	407,020	Naive	272,786.00	134,234.00
2020 Sep	258,651	Naive	407,020.00	-148,369.00
2020 Oct	167,448	Naive	258,651.00	-91,203.00
2020 Nov	73,734	Naive	167,448.00	-93,714.00
2020 Dec	73,353	Naive	73,734.00	-381.00
2021 Jan	48,435	Naive	73,353.00	-24,918.00
2021 Feb	40,443	Naive	48,435.00	-7,992.00
2021 Mar	60,251	Naive	40,443.00	19,808.00
2021 Apr	85,179	Naive	60,251.00	24,928.00
2021 May	169,690	Naive	85,179.00	84,511.00
2021 Jun	254,243	Naive	169,690.00	84,553.00
2021 Jul	329,058	Naive	254,243.00	74,815.00
2021 Aug	461,844	Naive	329,058.00	132,786.00
2021 Sep	308,273	Naive	461,844.00	-153,571.00
2021 Oct	250,949	Naive	308,273.00	-57,324.00
2021 Nov	156,624	Naive	250,949.00	-94,325.00
2021 Dec	115,100	Naive	156,624.00	-41,524.00
2022 Jan	96,107	Naive	115,100.00	-18,993.00
2022 Feb	141,508	Naive	96,107.00	45,401.00
2022 Mar	167,854	Naive	141,508.00	26,346.00
2022 Apr	248,959	Naive	167,854.00	81,105.00
2022 May	258,413	Naive	248,959.00	9,454.00
2022 Jun	300,520	Naive	258,413.00	42,107.00
2010 Jan	53,653	Naive_log	61,333.28	-7,680.28
2010 Feb	62,257	Naive_log	55,323.69	6,933.31
2010 Mar	77,588	Naive_log	64,144.12	13,443.88
2010 Apr	99,982	Naive_log	79,936.76	20,045.24
2010 May	101,387	Naive_log	103,004.28	-1,617.28
2010 Jun	108,611	Naive_log	104,448.63	4,162.37
2010 Jul	126,498	Naive_log	111,859.27	14,638.73
2010 Aug	178,380	Naive_log	130,229.38	48,150.62
2010 Sep	127,822	Naive_log	183,598.60	-55,776.60
2010 Oct	104,174	Naive_log	131,573.52	-27,399.52
2010 Nov	69,271	Naive_log	107,225.93	-37,954.93
2010 Dec	62,935	Naive_log	71,348.67	-8,413.67
2011 Jan	60,457	Naive_log	64,816.40	-4,359.40
2011 Feb	67,260	Naive_log	62,251.01	5,008.99
2011 Mar	83,464	Naive_log	69,241.97	14,222.03
2011 Apr	102,958	Naive_log	85,906.80	17,051.20
2011 May	101,223	Naive_log	105,971.24	-4,748.24
2011 Jun	120,148	Naive_log	104,179.59	15,968.41
2011 Jul	136,999	Naive_log	123,644.91	13,354.09
2011 Aug	212,668	Naive_log	140,957.36	71,710.64
2011 Sep	129,606	Naive_log	218,796.28	-89,190.28
2011 Oct	101,185	Naive_log	133,440.17	-32,255.17
2011 Nov	62,121	Naive_log	104,175.74	-42,054.74
2011 Dec	65,563	Naive_log	64,007.18	1,555.82
2012 Jan	49,716	Naive_log	67,553.69	-17,837.69
2012 Feb	58,638	Naive_log	51,218.27	7,419.73
2012 Mar	72,210	Naive_log	60,374.15	11,835.85
2012 Apr	87,406	Naive_log	74,355.49	13,050.51
2012 May	96,946	Naive_log	90,015.43	6,930.57
2012 Jun	115,885	Naive_log	99,841.58	16,043.42
2012 Jul	139,695	Naive_log	119,342.02	20,352.98
2012 Aug	194,368	Naive_log	143,825.87	50,542.13
2012 Sep	127,610	Naive_log	200,044.07	-72,434.07
2012 Oct	89,649	Naive_log	131,369.37	-41,720.37
2012 Nov	58,900	Naive_log	92,330.68	-33,430.68
2012 Dec	51,122	Naive_log	60,686.30	-9,564.30
2013 Jan	50,313	Naive_log	52,676.67	-2,363.67
2013 Feb	58,615	Naive_log	51,840.69	6,774.31
2013 Mar	92,426	Naive_log	60,373.81	32,052.19
2013 Apr	100,996	Naive_log	95,247.63	5,748.37
2013 May	123,431	Naive_log	104,082.21	19,348.79
2013 Jun	143,946	Naive_log	127,223.39	16,722.61
2013 Jul	171,016	Naive_log	148,369.47	22,646.53
2013 Aug	252,423	Naive_log	176,234.37	76,188.63
2013 Sep	158,839	Naive_log	260,122.78	-101,283.78
2013 Oct	109,956	Naive_log	163,785.86	-53,829.86
2013 Nov	82,040	Naive_log	113,429.01	-31,389.01
2013 Dec	72,692	Naive_log	84,650.11	-11,958.11
2014 Jan	56,872	Naive_log	75,004.83	-18,132.83
2014 Feb	64,346	Naive_log	58,669.61	5,676.39
2014 Mar	102,852	Naive_log	66,382.90	36,469.10
2014 Apr	151,151	Naive_log	106,169.31	44,981.69
2014 May	148,593	Naive_log	156,120.24	-7,527.24
2014 Jun	154,231	Naive_log	153,478.23	752.77
2014 Jul	194,227	Naive_log	159,292.28	34,934.72
2014 Aug	303,902	Naive_log	200,501.25	103,400.75
2014 Sep	186,247	Naive_log	313,725.53	-127,478.53
2014 Oct	133,884	Naive_log	192,428.91	-58,544.91
2014 Nov	86,161	Naive_log	138,299.05	-52,138.05
2014 Dec	81,830	Naive_log	89,069.96	-7,239.96
2015 Jan	68,436	Naive_log	84,589.36	-16,153.36
2015 Feb	84,417	Naive_log	70,749.32	13,667.68
2015 Mar	116,291	Naive_log	87,246.58	29,044.42
2015 Apr	145,183	Naive_log	120,237.52	24,945.48
2015 May	172,016	Naive_log	150,126.01	21,889.99
2015 Jun	182,765	Naive_log	177,887.00	4,878.00
2015 Jul	238,708	Naive_log	188,994.06	49,713.94
2015 Aug	358,044	Naive_log	246,679.41	111,364.59
2015 Sep	216,474	Naive_log	369,928.14	-153,454.14
2015 Oct	148,376	Naive_log	223,836.61	-75,460.61
2015 Nov	99,794	Naive_log	153,502.36	-53,708.36
2015 Dec	93,804	Naive_log	103,302.97	-9,498.97
2016 Jan	74,572	Naive_log	97,085.43	-22,513.43
2016 Feb	97,522	Naive_log	77,186.04	20,335.96
2016 Mar	144,216	Naive_log	100,966.96	43,249.04
2016 Apr	153,386	Naive_log	149,299.81	4,086.19
2016 May	168,235	Naive_log	158,786.47	9,448.53
2016 Jun	215,800	Naive_log	174,162.92	41,637.08
2016 Jul	271,212	Naive_log	223,414.46	47,797.54
2016 Aug	380,776	Naive_log	280,723.08	100,052.92
2016 Sep	249,098	Naive_log	394,145.65	-145,047.65
2016 Oct	175,862	Naive_log	258,003.08	-82,141.08
2016 Nov	102,775	Naive_log	182,208.67	-79,433.67
2016 Dec	100,859	Naive_log	106,607.03	-5,748.03
2017 Jan	83,249	Naive_log	104,569.83	-21,320.83
2017 Feb	105,210	Naive_log	86,315.64	18,894.36
2017 Mar	121,167	Naive_log	109,078.86	12,088.14
2017 Apr	217,906	Naive_log	125,606.47	92,299.53
2017 May	196,622	Naive_log	226,195.49	-29,573.49
2017 Jun	248,582	Naive_log	204,105.81	44,476.19
2017 Jul	323,496	Naive_log	258,074.02	65,421.98
2017 Aug	431,571	Naive_log	335,750.28	95,820.72
2017 Sep	287,242	Naive_log	447,764.46	-160,522.46
2017 Oct	212,357	Naive_log	298,168.82	-85,811.82
2017 Nov	127,745	Naive_log	220,498.87	-92,753.87
2017 Dec	132,238	Naive_log	132,774.89	-536.89
2018 Jan	95,453	Naive_log	137,397.16	-41,944.16
2018 Feb	120,303	Naive_log	99,201.00	21,102.00
2018 Mar	162,886	Naive_log	124,998.61	37,887.39
2018 Apr	187,186	Naive_log	169,304.78	17,881.22
2018 May	239,851	Naive_log	194,551.19	45,299.81
2018 Jun	264,588	Naive_log	249,338.57	15,249.43
2018 Jul	339,564	Naive_log	275,035.30	64,528.70
2018 Aug	446,375	Naive_log	352,875.98	93,499.02
2018 Sep	304,516	Naive_log	463,878.85	-159,362.85
2018 Oct	230,827	Naive_log	316,582.05	-85,755.05
2018 Nov	149,080	Naive_log	239,967.00	-90,887.00
2018 Dec	135,316	Naive_log	155,087.72	-19,771.72
2019 Jan	114,710	Naive_log	140,754.91	-26,044.91
2019 Feb	122,635	Naive_log	119,306.76	3,328.24
2019 Mar	172,412	Naive_log	127,549.45	44,862.55
2019 Apr	241,790	Naive_log	179,315.56	62,474.44
2019 May	259,714	Naive_log	251,587.54	8,126.46
2019 Jun	306,048	Naive_log	270,234.33	35,813.67
2019 Jul	360,566	Naive_log	318,475.01	42,090.99
2019 Aug	484,403	Naive_log	374,959.48	109,443.52
2019 Sep	327,937	Naive_log	503,455.61	-175,518.61
2019 Oct	238,677	Naive_log	341,004.87	-102,327.87
2019 Nov	171,296	Naive_log	248,200.56	-76,904.56
2019 Dec	138,642	Naive_log	178,195.48	-39,553.48
2020 Jan	126,349	Naive_log	144,246.12	-17,897.12
2020 Feb	167,411	Naive_log	131,449.05	35,961.95
2020 Mar	70,530	Naive_log	174,190.12	-103,660.12
2020 Apr	13,892	Naive_log	73,588.41	-59,696.41
2020 May	38,343	Naive_log	14,648.47	23,694.53
2020 Jun	159,738	Naive_log	40,596.22	119,141.78
2020 Jul	272,786	Naive_log	170,476.01	102,309.99
2020 Aug	407,020	Naive_log	291,316.25	115,703.75
2020 Sep	258,651	Naive_log	434,752.62	-176,101.62
2020 Oct	167,448	Naive_log	276,452.30	-109,004.30
2020 Nov	73,734	Naive_log	178,988.25	-105,254.25
2020 Dec	73,353	Naive_log	79,021.20	-5,668.20
2021 Jan	48,435	Naive_log	78,612.39	-30,177.39
2021 Feb	40,443	Naive_log	51,940.52	-11,497.52
2021 Mar	60,251	Naive_log	43,367.70	16,883.30
2021 Apr	85,179	Naive_log	64,637.22	20,541.78
2021 May	169,690	Naive_log	91,422.76	78,267.24
2021 Jun	254,243	Naive_log	182,446.30	71,796.70
2021 Jul	329,058	Naive_log	273,511.73	55,546.27
2021 Aug	461,844	Naive_log	353,821.47	108,022.53
2021 Sep	308,273	Naive_log	496,347.43	-188,074.43
2021 Oct	250,949	Naive_log	331,435.74	-80,486.74
2021 Nov	156,624	Naive_log	269,598.25	-112,974.25
2021 Dec	115,100	Naive_log	168,407.82	-53,307.82
2022 Jan	96,107	Naive_log	123,768.57	-27,661.57
2022 Feb	141,508	Naive_log	103,347.28	38,160.72
2022 Mar	167,854	Naive_log	152,231.82	15,622.18
2022 Apr	248,959	Naive_log	180,569.22	68,389.78
2022 May	258,413	Naive_log	267,969.37	-9,556.37
2022 Jun	300,520	Naive_log	278,112.21	22,407.79
2010 Jan	53,653	Prophet	59,893.49	-6,240.49
2010 Feb	62,257	Prophet	69,707.64	-7,450.64
2010 Mar	77,588	Prophet	84,895.50	-7,307.50
2010 Apr	99,982	Prophet	100,698.76	-716.76
2010 May	101,387	Prophet	98,275.29	3,111.71
2010 Jun	108,611	Prophet	101,075.81	7,535.19
2010 Jul	126,498	Prophet	117,773.27	8,724.73
2010 Aug	178,380	Prophet	162,241.78	16,138.22
2010 Sep	127,822	Prophet	112,585.72	15,236.28
2010 Oct	104,174	Prophet	93,280.36	10,893.64
2010 Nov	69,271	Prophet	79,678.98	-10,407.98
2010 Dec	62,935	Prophet	72,415.66	-9,480.66
2011 Jan	60,457	Prophet	62,250.43	-1,793.43
2011 Feb	67,260	Prophet	73,749.53	-6,489.53
2011 Mar	83,464	Prophet	87,318.66	-3,854.66
2011 Apr	102,958	Prophet	104,927.46	-1,969.46
2011 May	101,223	Prophet	102,092.81	-869.81
2011 Jun	120,148	Prophet	107,057.40	13,090.60
2011 Jul	136,999	Prophet	124,323.41	12,675.59
2011 Aug	212,668	Prophet	167,427.75	45,240.25
2011 Sep	129,606	Prophet	119,221.31	10,384.69
2011 Oct	101,185	Prophet	100,858.38	326.62
2011 Nov	62,121	Prophet	86,402.16	-24,281.16
2011 Dec	65,563	Prophet	78,197.70	-12,634.70
2012 Jan	49,716	Prophet	67,714.22	-17,998.22
2012 Feb	58,638	Prophet	79,059.42	-20,421.42
2012 Mar	72,210	Prophet	92,344.47	-20,134.47
2012 Apr	87,406	Prophet	104,525.28	-17,119.28
2012 May	96,946	Prophet	113,641.18	-16,695.18
2012 Jun	115,885	Prophet	109,749.30	6,135.70
2012 Jul	139,695	Prophet	122,284.07	17,410.93
2012 Aug	194,368	Prophet	173,931.00	20,437.00
2012 Sep	127,610	Prophet	122,707.56	4,902.44
2012 Oct	89,649	Prophet	102,506.44	-12,857.44
2012 Nov	58,900	Prophet	81,232.22	-22,332.22
2012 Dec	51,122	Prophet	73,448.97	-22,326.97
2013 Jan	50,313	Prophet	66,631.23	-16,318.23
2013 Feb	58,615	Prophet	74,121.17	-15,506.17
2013 Mar	92,426	Prophet	85,211.46	7,214.54
2013 Apr	100,996	Prophet	102,587.39	-1,591.39
2013 May	123,431	Prophet	106,403.93	17,027.07
2013 Jun	143,946	Prophet	111,088.18	32,857.82
2013 Jul	171,016	Prophet	128,526.94	42,489.06
2013 Aug	252,423	Prophet	182,013.63	70,409.37
2013 Sep	158,839	Prophet	129,325.84	29,513.16
2013 Oct	109,956	Prophet	108,952.74	1,003.26
2013 Nov	82,040	Prophet	86,559.59	-4,519.59
2013 Dec	72,692	Prophet	80,876.10	-8,184.10
2014 Jan	56,872	Prophet	71,124.61	-14,252.61
2014 Feb	64,346	Prophet	79,886.49	-15,540.49
2014 Mar	102,852	Prophet	95,243.65	7,608.35
2014 Apr	151,151	Prophet	112,953.59	38,197.41
2014 May	148,593	Prophet	118,498.48	30,094.52
2014 Jun	154,231	Prophet	129,327.74	24,903.26
2014 Jul	194,227	Prophet	148,328.40	45,898.60
2014 Aug	303,902	Prophet	209,181.29	94,720.71
2014 Sep	186,247	Prophet	159,299.99	26,947.01
2014 Oct	133,884	Prophet	138,561.13	-4,677.13
2014 Nov	86,161	Prophet	117,134.42	-30,973.42
2014 Dec	81,830	Prophet	107,824.04	-25,994.04
2015 Jan	68,436	Prophet	96,070.25	-27,634.25
2015 Feb	84,417	Prophet	102,153.29	-17,736.29
2015 Mar	116,291	Prophet	119,023.25	-2,732.25
2015 Apr	145,183	Prophet	142,106.37	3,076.63
2015 May	172,016	Prophet	143,117.13	28,898.87
2015 Jun	182,765	Prophet	153,133.72	29,631.28
2015 Jul	238,708	Prophet	175,665.47	63,042.53
2015 Aug	358,044	Prophet	246,168.51	111,875.49
2015 Sep	216,474	Prophet	185,709.83	30,764.17
2015 Oct	148,376	Prophet	162,637.62	-14,261.62
2015 Nov	99,794	Prophet	137,657.91	-37,863.91
2015 Dec	93,804	Prophet	133,499.97	-39,695.97
2016 Jan	74,572	Prophet	117,072.85	-42,500.85
2016 Feb	97,522	Prophet	128,172.15	-30,650.15
2016 Mar	144,216	Prophet	143,993.35	222.65
2016 Apr	153,386	Prophet	161,300.10	-7,914.10
2016 May	168,235	Prophet	174,811.29	-6,576.29
2016 Jun	215,800	Prophet	183,657.59	32,142.41
2016 Jul	271,212	Prophet	204,464.62	66,747.38
2016 Aug	380,776	Prophet	271,680.98	109,095.02
2016 Sep	249,098	Prophet	210,310.68	38,787.32
2016 Oct	175,862	Prophet	181,644.35	-5,782.35
2016 Nov	102,775	Prophet	153,098.37	-50,323.37
2016 Dec	100,859	Prophet	143,832.37	-42,973.37
2017 Jan	83,249	Prophet	132,507.90	-49,258.90
2017 Feb	105,210	Prophet	142,368.17	-37,158.17
2017 Mar	121,167	Prophet	163,148.25	-41,981.25
2017 Apr	217,906	Prophet	180,315.14	37,590.86
2017 May	196,622	Prophet	191,134.23	5,487.77
2017 Jun	248,582	Prophet	205,946.45	42,635.55
2017 Jul	323,496	Prophet	236,566.59	86,929.41
2017 Aug	431,571	Prophet	318,403.32	113,167.68
2017 Sep	287,242	Prophet	241,429.49	45,812.51
2017 Oct	212,357	Prophet	206,441.69	5,915.31
2017 Nov	127,745	Prophet	169,834.06	-42,089.06
2017 Dec	132,238	Prophet	162,926.10	-30,688.10
2018 Jan	95,453	Prophet	150,038.15	-54,585.15
2018 Feb	120,303	Prophet	159,999.63	-39,696.63
2018 Mar	162,886	Prophet	182,349.21	-19,463.21
2018 Apr	187,186	Prophet	210,776.89	-23,590.89
2018 May	239,851	Prophet	216,761.96	23,089.04
2018 Jun	264,588	Prophet	235,857.38	28,730.62
2018 Jul	339,564	Prophet	272,146.59	67,417.41
2018 Aug	446,375	Prophet	359,489.73	86,885.27
2018 Sep	304,516	Prophet	267,800.96	36,715.04
2018 Oct	230,827	Prophet	226,237.86	4,589.14
2018 Nov	149,080	Prophet	184,334.64	-35,254.64
2018 Dec	135,316	Prophet	179,632.03	-44,316.03
2019 Jan	114,710	Prophet	163,890.56	-49,180.56
2019 Feb	122,635	Prophet	175,231.81	-52,596.81
2019 Mar	172,412	Prophet	197,615.67	-25,203.67
2019 Apr	241,790	Prophet	227,968.15	13,821.85
2019 May	259,714	Prophet	241,830.68	17,883.32
2019 Jun	306,048	Prophet	262,784.06	43,263.94
2019 Jul	360,566	Prophet	306,325.98	54,240.02
2019 Aug	484,403	Prophet	397,050.56	87,352.44
2019 Sep	327,937	Prophet	293,356.44	34,580.56
2019 Oct	238,677	Prophet	247,143.67	-8,466.67
2019 Nov	171,296	Prophet	200,256.92	-28,960.92
2019 Dec	138,642	Prophet	195,756.35	-57,114.35
2020 Jan	126,349	Prophet	178,633.41	-52,284.41
2020 Feb	167,411	Prophet	190,996.46	-23,585.46
2020 Mar	70,530	Prophet	221,105.26	-150,575.26
2020 Apr	13,892	Prophet	251,249.48	-237,357.48
2020 May	38,343	Prophet	258,212.15	-219,869.15
2020 Jun	159,738	Prophet	280,827.82	-121,089.82
2020 Jul	272,786	Prophet	311,363.27	-38,577.27
2020 Aug	407,020	Prophet	399,941.26	7,078.74
2020 Sep	258,651	Prophet	286,704.80	-28,053.80
2020 Oct	167,448	Prophet	227,239.25	-59,791.25
2020 Nov	73,734	Prophet	166,582.75	-92,848.75
2020 Dec	73,353	Prophet	148,134.31	-74,781.31
2021 Jan	48,435	Prophet	123,590.81	-75,155.81
2021 Feb	40,443	Prophet	134,309.34	-93,866.34
2021 Mar	60,251	Prophet	138,623.00	-78,372.00
2021 Apr	85,179	Prophet	151,828.47	-66,649.47
2021 May	169,690	Prophet	157,412.58	12,277.42
2021 Jun	254,243	Prophet	192,572.31	61,670.69
2021 Jul	329,058	Prophet	255,121.57	73,936.43
2021 Aug	461,844	Prophet	356,005.18	105,838.82
2021 Sep	308,273	Prophet	239,090.46	69,182.54
2021 Oct	250,949	Prophet	186,158.70	64,790.30
2021 Nov	156,624	Prophet	132,579.73	24,044.27
2021 Dec	115,100	Prophet	122,560.44	-7,460.44
2022 Jan	96,107	Prophet	104,553.14	-8,446.14
2022 Feb	141,508	Prophet	113,310.28	28,197.72
2022 Mar	167,854	Prophet	137,990.44	29,863.56
2022 Apr	248,959	Prophet	164,441.09	84,517.91
2022 May	258,413	Prophet	193,384.55	65,028.45
2022 Jun	300,520	Prophet	239,993.05	60,526.95
2010 Jan	53,653	Prophet_log	51,638.17	2,014.83
2010 Feb	62,257	Prophet_log	64,043.41	-1,786.41
2010 Mar	77,588	Prophet_log	81,036.26	-3,448.26
2010 Apr	99,982	Prophet_log	99,864.68	117.32
2010 May	101,387	Prophet_log	96,370.48	5,016.52
2010 Jun	108,611	Prophet_log	99,544.53	9,066.47
2010 Jul	126,498	Prophet_log	118,535.29	7,962.71
2010 Aug	178,380	Prophet_log	168,898.64	9,481.36
2010 Sep	127,822	Prophet_log	111,855.19	15,966.81
2010 Oct	104,174	Prophet_log	89,537.24	14,636.76
2010 Nov	69,271	Prophet_log	75,585.66	-6,314.66
2010 Dec	62,935	Prophet_log	65,539.72	-2,604.72
2011 Jan	60,457	Prophet_log	55,060.06	5,396.94
2011 Feb	67,260	Prophet_log	69,105.03	-1,845.03
2011 Mar	83,464	Prophet_log	84,684.12	-1,220.12
2011 Apr	102,958	Prophet_log	109,222.91	-6,264.91
2011 May	101,223	Prophet_log	103,578.16	-2,355.16
2011 Jun	120,148	Prophet_log	109,803.52	10,344.48
2011 Jul	136,999	Prophet_log	132,569.25	4,429.75
2011 Aug	212,668	Prophet_log	183,622.57	29,045.43
2011 Sep	129,606	Prophet_log	124,895.98	4,710.02
2011 Oct	101,185	Prophet_log	98,946.08	2,238.92
2011 Nov	62,121	Prophet_log	83,696.74	-21,575.74
2011 Dec	65,563	Prophet_log	71,553.30	-5,990.30
2012 Jan	49,716	Prophet_log	59,542.03	-9,826.03
2012 Feb	58,638	Prophet_log	72,296.12	-13,658.12
2012 Mar	72,210	Prophet_log	89,217.73	-17,007.73
2012 Apr	87,406	Prophet_log	101,207.73	-13,801.73
2012 May	96,946	Prophet_log	110,364.50	-13,418.50
2012 Jun	115,885	Prophet_log	103,093.99	12,791.01
2012 Jul	139,695	Prophet_log	117,090.95	22,604.05
2012 Aug	194,368	Prophet_log	177,240.61	17,127.39
2012 Sep	127,610	Prophet_log	120,284.27	7,325.73
2012 Oct	89,649	Prophet_log	97,531.81	-7,882.81
2012 Nov	58,900	Prophet_log	72,231.37	-13,331.37
2012 Dec	51,122	Prophet_log	62,462.18	-11,340.18
2013 Jan	50,313	Prophet_log	54,156.23	-3,843.23
2013 Feb	58,615	Prophet_log	61,719.16	-3,104.16
2013 Mar	92,426	Prophet_log	75,011.65	17,414.35
2013 Apr	100,996	Prophet_log	92,591.36	8,404.64
2013 May	123,431	Prophet_log	97,842.44	25,588.56
2013 Jun	143,946	Prophet_log	102,948.46	40,997.54
2013 Jul	171,016	Prophet_log	123,761.19	47,254.81
2013 Aug	252,423	Prophet_log	188,059.07	64,363.93
2013 Sep	158,839	Prophet_log	130,210.84	28,628.16
2013 Oct	109,956	Prophet_log	106,950.96	3,005.04
2013 Nov	82,040	Prophet_log	80,285.71	1,754.29
2013 Dec	72,692	Prophet_log	74,250.04	-1,558.04
2014 Jan	56,872	Prophet_log	64,755.49	-7,883.49
2014 Feb	64,346	Prophet_log	76,551.42	-12,205.42
2014 Mar	102,852	Prophet_log	93,424.76	9,427.24
2014 Apr	151,151	Prophet_log	121,721.35	29,429.65
2014 May	148,593	Prophet_log	126,845.34	21,747.66
2014 Jun	154,231	Prophet_log	141,109.81	13,121.19
2014 Jul	194,227	Prophet_log	168,727.33	25,499.67
2014 Aug	303,902	Prophet_log	255,612.56	48,289.44
2014 Sep	186,247	Prophet_log	176,430.75	9,816.25
2014 Oct	133,884	Prophet_log	143,847.99	-9,963.99
2014 Nov	86,161	Prophet_log	108,101.40	-21,940.40
2014 Dec	81,830	Prophet_log	101,085.80	-19,255.80
2015 Jan	68,436	Prophet_log	79,895.77	-11,459.77
2015 Feb	84,417	Prophet_log	93,092.96	-8,675.96
2015 Mar	116,291	Prophet_log	117,134.33	-843.33
2015 Apr	145,183	Prophet_log	164,132.83	-18,949.83
2015 May	172,016	Prophet_log	152,384.77	19,631.23
2015 Jun	182,765	Prophet_log	170,507.83	12,257.17
2015 Jul	238,708	Prophet_log	203,638.51	35,069.49
2015 Aug	358,044	Prophet_log	310,690.96	47,353.04
2015 Sep	216,474	Prophet_log	202,524.50	13,949.50
2015 Oct	148,376	Prophet_log	164,784.48	-16,408.48
2015 Nov	99,794	Prophet_log	119,702.05	-19,908.05
2015 Dec	93,804	Prophet_log	118,250.86	-24,446.86
2016 Jan	74,572	Prophet_log	90,361.31	-15,789.31
2016 Feb	97,522	Prophet_log	106,244.56	-8,722.56
2016 Mar	144,216	Prophet_log	142,653.35	1,562.65
2016 Apr	153,386	Prophet_log	165,106.47	-11,720.47
2016 May	168,235	Prophet_log	186,806.47	-18,571.47
2016 Jun	215,800	Prophet_log	194,528.90	21,271.10
2016 Jul	271,212	Prophet_log	228,848.61	42,363.39
2016 Aug	380,776	Prophet_log	335,881.27	44,894.73
2016 Sep	249,098	Prophet_log	235,126.58	13,971.42
2016 Oct	175,862	Prophet_log	180,104.73	-4,242.73
2016 Nov	102,775	Prophet_log	129,858.30	-27,083.30
2016 Dec	100,859	Prophet_log	110,927.28	-10,068.28
2017 Jan	83,249	Prophet_log	99,657.72	-16,408.72
2017 Feb	105,210	Prophet_log	115,935.39	-10,725.39
2017 Mar	121,167	Prophet_log	153,713.00	-32,546.00
2017 Apr	217,906	Prophet_log	176,540.22	41,365.78
2017 May	196,622	Prophet_log	196,769.74	-147.74
2017 Jun	248,582	Prophet_log	217,228.90	31,353.10
2017 Jul	323,496	Prophet_log	263,961.40	59,534.60
2017 Aug	431,571	Prophet_log	396,697.56	34,873.44
2017 Sep	287,242	Prophet_log	264,927.99	22,314.01
2017 Oct	212,357	Prophet_log	200,410.69	11,946.31
2017 Nov	127,745	Prophet_log	137,717.58	-9,972.58
2017 Dec	132,238	Prophet_log	125,383.68	6,854.32
2018 Jan	95,453	Prophet_log	108,288.81	-12,835.81
2018 Feb	120,303	Prophet_log	129,583.53	-9,280.53
2018 Mar	162,886	Prophet_log	169,560.21	-6,674.21
2018 Apr	187,186	Prophet_log	221,493.66	-34,307.66
2018 May	239,851	Prophet_log	228,676.21	11,174.79
2018 Jun	264,588	Prophet_log	256,641.81	7,946.19
2018 Jul	339,564	Prophet_log	312,419.74	27,144.26
2018 Aug	446,375	Prophet_log	472,083.57	-25,708.57
2018 Sep	304,516	Prophet_log	299,848.55	4,667.45
2018 Oct	230,827	Prophet_log	225,090.15	5,736.85
2018 Nov	149,080	Prophet_log	148,809.73	270.27
2018 Dec	135,316	Prophet_log	141,917.86	-6,601.86
2019 Jan	114,710	Prophet_log	116,333.28	-1,623.28
2019 Feb	122,635	Prophet_log	140,751.00	-18,116.00
2019 Mar	172,412	Prophet_log	183,704.67	-11,292.67
2019 Apr	241,790	Prophet_log	243,708.41	-1,918.41
2019 May	259,714	Prophet_log	264,218.57	-4,504.57
2019 Jun	306,048	Prophet_log	285,374.46	20,673.54
2019 Jul	360,566	Prophet_log	353,311.52	7,254.48
2019 Aug	484,403	Prophet_log	529,548.97	-45,145.97
2019 Sep	327,937	Prophet_log	329,632.25	-1,695.25
2019 Oct	238,677	Prophet_log	247,414.81	-8,737.81
2019 Nov	171,296	Prophet_log	160,510.37	10,785.63
2019 Dec	138,642	Prophet_log	154,900.69	-16,258.69
2020 Jan	126,349	Prophet_log	123,465.83	2,883.17
2020 Feb	167,411	Prophet_log	146,926.91	20,484.09
2020 Mar	70,530	Prophet_log	216,013.22	-145,483.22
2020 Apr	13,892	Prophet_log	244,743.74	-230,851.74
2020 May	38,343	Prophet_log	230,156.61	-191,813.61
2020 Jun	159,738	Prophet_log	234,138.93	-74,400.93
2020 Jul	272,786	Prophet_log	249,596.42	23,189.58
2020 Aug	407,020	Prophet_log	314,722.82	92,297.18
2020 Sep	258,651	Prophet_log	194,921.83	63,729.17
2020 Oct	167,448	Prophet_log	133,162.58	34,285.42
2020 Nov	73,734	Prophet_log	86,598.92	-12,864.92
2020 Dec	73,353	Prophet_log	82,676.23	-9,323.23
2021 Jan	48,435	Prophet_log	71,566.36	-23,131.36
2021 Feb	40,443	Prophet_log	85,282.68	-44,839.68
2021 Mar	60,251	Prophet_log	87,950.73	-27,699.73
2021 Apr	85,179	Prophet_log	74,476.10	10,702.90
2021 May	169,690	Prophet_log	91,823.63	77,866.37
2021 Jun	254,243	Prophet_log	130,369.97	123,873.03
2021 Jul	329,058	Prophet_log	175,499.12	153,558.88
2021 Aug	461,844	Prophet_log	262,872.39	198,971.61
2021 Sep	308,273	Prophet_log	175,651.47	132,621.53
2021 Oct	250,949	Prophet_log	130,515.35	120,433.65
2021 Nov	156,624	Prophet_log	83,371.31	73,252.69
2021 Dec	115,100	Prophet_log	83,475.22	31,624.78
2022 Jan	96,107	Prophet_log	70,788.83	25,318.17
2022 Feb	141,508	Prophet_log	84,499.63	57,008.37
2022 Mar	167,854	Prophet_log	99,072.86	68,781.14
2022 Apr	248,959	Prophet_log	134,491.04	114,467.96
2022 May	258,413	Prophet_log	181,305.85	77,107.15
2022 Jun	300,520	Prophet_log	244,251.43	56,268.57
2010 Jan	53,653	SNaive	50,256.00	3,397.00
2010 Feb	62,257	SNaive	63,694.00	-1,437.00
2010 Mar	77,588	SNaive	67,975.00	9,613.00
2010 Apr	99,982	SNaive	96,647.00	3,335.00
2010 May	101,387	SNaive	97,936.00	3,451.00
2010 Jun	108,611	SNaive	107,295.00	1,316.00
2010 Jul	126,498	SNaive	114,085.00	12,413.00
2010 Aug	178,380	SNaive	176,426.00	1,954.00
2010 Sep	127,822	SNaive	109,573.00	18,249.00
2010 Oct	104,174	SNaive	92,353.00	11,821.00
2010 Nov	69,271	SNaive	68,602.00	669.00
2010 Dec	62,935	SNaive	59,473.00	3,462.00
2011 Jan	60,457	SNaive	53,653.00	6,804.00
2011 Feb	67,260	SNaive	62,257.00	5,003.00
2011 Mar	83,464	SNaive	77,588.00	5,876.00
2011 Apr	102,958	SNaive	99,982.00	2,976.00
2011 May	101,223	SNaive	101,387.00	-164.00
2011 Jun	120,148	SNaive	108,611.00	11,537.00
2011 Jul	136,999	SNaive	126,498.00	10,501.00
2011 Aug	212,668	SNaive	178,380.00	34,288.00
2011 Sep	129,606	SNaive	127,822.00	1,784.00
2011 Oct	101,185	SNaive	104,174.00	-2,989.00
2011 Nov	62,121	SNaive	69,271.00	-7,150.00
2011 Dec	65,563	SNaive	62,935.00	2,628.00
2012 Jan	49,716	SNaive	60,457.00	-10,741.00
2012 Feb	58,638	SNaive	67,260.00	-8,622.00
2012 Mar	72,210	SNaive	83,464.00	-11,254.00
2012 Apr	87,406	SNaive	102,958.00	-15,552.00
2012 May	96,946	SNaive	101,223.00	-4,277.00
2012 Jun	115,885	SNaive	120,148.00	-4,263.00
2012 Jul	139,695	SNaive	136,999.00	2,696.00
2012 Aug	194,368	SNaive	212,668.00	-18,300.00
2012 Sep	127,610	SNaive	129,606.00	-1,996.00
2012 Oct	89,649	SNaive	101,185.00	-11,536.00
2012 Nov	58,900	SNaive	62,121.00	-3,221.00
2012 Dec	51,122	SNaive	65,563.00	-14,441.00
2013 Jan	50,313	SNaive	49,716.00	597.00
2013 Feb	58,615	SNaive	58,638.00	-23.00
2013 Mar	92,426	SNaive	72,210.00	20,216.00
2013 Apr	100,996	SNaive	87,406.00	13,590.00
2013 May	123,431	SNaive	96,946.00	26,485.00
2013 Jun	143,946	SNaive	115,885.00	28,061.00
2013 Jul	171,016	SNaive	139,695.00	31,321.00
2013 Aug	252,423	SNaive	194,368.00	58,055.00
2013 Sep	158,839	SNaive	127,610.00	31,229.00
2013 Oct	109,956	SNaive	89,649.00	20,307.00
2013 Nov	82,040	SNaive	58,900.00	23,140.00
2013 Dec	72,692	SNaive	51,122.00	21,570.00
2014 Jan	56,872	SNaive	50,313.00	6,559.00
2014 Feb	64,346	SNaive	58,615.00	5,731.00
2014 Mar	102,852	SNaive	92,426.00	10,426.00
2014 Apr	151,151	SNaive	100,996.00	50,155.00
2014 May	148,593	SNaive	123,431.00	25,162.00
2014 Jun	154,231	SNaive	143,946.00	10,285.00
2014 Jul	194,227	SNaive	171,016.00	23,211.00
2014 Aug	303,902	SNaive	252,423.00	51,479.00
2014 Sep	186,247	SNaive	158,839.00	27,408.00
2014 Oct	133,884	SNaive	109,956.00	23,928.00
2014 Nov	86,161	SNaive	82,040.00	4,121.00
2014 Dec	81,830	SNaive	72,692.00	9,138.00
2015 Jan	68,436	SNaive	56,872.00	11,564.00
2015 Feb	84,417	SNaive	64,346.00	20,071.00
2015 Mar	116,291	SNaive	102,852.00	13,439.00
2015 Apr	145,183	SNaive	151,151.00	-5,968.00
2015 May	172,016	SNaive	148,593.00	23,423.00
2015 Jun	182,765	SNaive	154,231.00	28,534.00
2015 Jul	238,708	SNaive	194,227.00	44,481.00
2015 Aug	358,044	SNaive	303,902.00	54,142.00
2015 Sep	216,474	SNaive	186,247.00	30,227.00
2015 Oct	148,376	SNaive	133,884.00	14,492.00
2015 Nov	99,794	SNaive	86,161.00	13,633.00
2015 Dec	93,804	SNaive	81,830.00	11,974.00
2016 Jan	74,572	SNaive	68,436.00	6,136.00
2016 Feb	97,522	SNaive	84,417.00	13,105.00
2016 Mar	144,216	SNaive	116,291.00	27,925.00
2016 Apr	153,386	SNaive	145,183.00	8,203.00
2016 May	168,235	SNaive	172,016.00	-3,781.00
2016 Jun	215,800	SNaive	182,765.00	33,035.00
2016 Jul	271,212	SNaive	238,708.00	32,504.00
2016 Aug	380,776	SNaive	358,044.00	22,732.00
2016 Sep	249,098	SNaive	216,474.00	32,624.00
2016 Oct	175,862	SNaive	148,376.00	27,486.00
2016 Nov	102,775	SNaive	99,794.00	2,981.00
2016 Dec	100,859	SNaive	93,804.00	7,055.00
2017 Jan	83,249	SNaive	74,572.00	8,677.00
2017 Feb	105,210	SNaive	97,522.00	7,688.00
2017 Mar	121,167	SNaive	144,216.00	-23,049.00
2017 Apr	217,906	SNaive	153,386.00	64,520.00
2017 May	196,622	SNaive	168,235.00	28,387.00
2017 Jun	248,582	SNaive	215,800.00	32,782.00
2017 Jul	323,496	SNaive	271,212.00	52,284.00
2017 Aug	431,571	SNaive	380,776.00	50,795.00
2017 Sep	287,242	SNaive	249,098.00	38,144.00
2017 Oct	212,357	SNaive	175,862.00	36,495.00
2017 Nov	127,745	SNaive	102,775.00	24,970.00
2017 Dec	132,238	SNaive	100,859.00	31,379.00
2018 Jan	95,453	SNaive	83,249.00	12,204.00
2018 Feb	120,303	SNaive	105,210.00	15,093.00
2018 Mar	162,886	SNaive	121,167.00	41,719.00
2018 Apr	187,186	SNaive	217,906.00	-30,720.00
2018 May	239,851	SNaive	196,622.00	43,229.00
2018 Jun	264,588	SNaive	248,582.00	16,006.00
2018 Jul	339,564	SNaive	323,496.00	16,068.00
2018 Aug	446,375	SNaive	431,571.00	14,804.00
2018 Sep	304,516	SNaive	287,242.00	17,274.00
2018 Oct	230,827	SNaive	212,357.00	18,470.00
2018 Nov	149,080	SNaive	127,745.00	21,335.00
2018 Dec	135,316	SNaive	132,238.00	3,078.00
2019 Jan	114,710	SNaive	95,453.00	19,257.00
2019 Feb	122,635	SNaive	120,303.00	2,332.00
2019 Mar	172,412	SNaive	162,886.00	9,526.00
2019 Apr	241,790	SNaive	187,186.00	54,604.00
2019 May	259,714	SNaive	239,851.00	19,863.00
2019 Jun	306,048	SNaive	264,588.00	41,460.00
2019 Jul	360,566	SNaive	339,564.00	21,002.00
2019 Aug	484,403	SNaive	446,375.00	38,028.00
2019 Sep	327,937	SNaive	304,516.00	23,421.00
2019 Oct	238,677	SNaive	230,827.00	7,850.00
2019 Nov	171,296	SNaive	149,080.00	22,216.00
2019 Dec	138,642	SNaive	135,316.00	3,326.00
2020 Jan	126,349	SNaive	114,710.00	11,639.00
2020 Feb	167,411	SNaive	122,635.00	44,776.00
2020 Mar	70,530	SNaive	172,412.00	-101,882.00
2020 Apr	13,892	SNaive	241,790.00	-227,898.00
2020 May	38,343	SNaive	259,714.00	-221,371.00
2020 Jun	159,738	SNaive	306,048.00	-146,310.00
2020 Jul	272,786	SNaive	360,566.00	-87,780.00
2020 Aug	407,020	SNaive	484,403.00	-77,383.00
2020 Sep	258,651	SNaive	327,937.00	-69,286.00
2020 Oct	167,448	SNaive	238,677.00	-71,229.00
2020 Nov	73,734	SNaive	171,296.00	-97,562.00
2020 Dec	73,353	SNaive	138,642.00	-65,289.00
2021 Jan	48,435	SNaive	126,349.00	-77,914.00
2021 Feb	40,443	SNaive	167,411.00	-126,968.00
2021 Mar	60,251	SNaive	70,530.00	-10,279.00
2021 Apr	85,179	SNaive	13,892.00	71,287.00
2021 May	169,690	SNaive	38,343.00	131,347.00
2021 Jun	254,243	SNaive	159,738.00	94,505.00
2021 Jul	329,058	SNaive	272,786.00	56,272.00
2021 Aug	461,844	SNaive	407,020.00	54,824.00
2021 Sep	308,273	SNaive	258,651.00	49,622.00
2021 Oct	250,949	SNaive	167,448.00	83,501.00
2021 Nov	156,624	SNaive	73,734.00	82,890.00
2021 Dec	115,100	SNaive	73,353.00	41,747.00
2022 Jan	96,107	SNaive	48,435.00	47,672.00
2022 Feb	141,508	SNaive	40,443.00	101,065.00
2022 Mar	167,854	SNaive	60,251.00	107,603.00
2022 Apr	248,959	SNaive	85,179.00	163,780.00
2022 May	258,413	SNaive	169,690.00	88,723.00
2022 Jun	300,520	SNaive	254,243.00	46,277.00
2010 Jan	53,653	SNaive_log	50,590.14	3,062.86
2010 Feb	62,257	SNaive_log	64,107.63	-1,850.63
2010 Mar	77,588	SNaive_log	68,401.82	9,186.18
2010 Apr	99,982	SNaive_log	97,261.67	2,720.33
2010 May	101,387	SNaive_log	98,557.70	2,829.30
2010 Jun	108,611	SNaive_log	107,969.06	641.94
2010 Jul	126,498	SNaive_log	114,788.95	11,709.05
2010 Aug	178,380	SNaive_log	177,512.19	867.81
2010 Sep	127,822	SNaive_log	110,247.22	17,574.78
2010 Oct	104,174	SNaive_log	92,931.35	11,242.65
2010 Nov	69,271	SNaive_log	69,035.82	235.18
2010 Dec	62,935	SNaive_log	59,849.09	3,085.91
2011 Jan	60,457	SNaive_log	53,985.00	6,472.00
2011 Feb	67,260	SNaive_log	62,645.54	4,614.46
2011 Mar	83,464	SNaive_log	78,073.53	5,390.47
2011 Apr	102,958	SNaive_log	100,588.35	2,369.65
2011 May	101,223	SNaive_log	101,978.25	-755.25
2011 Jun	120,148	SNaive_log	109,243.75	10,904.25
2011 Jul	136,999	SNaive_log	127,240.93	9,758.07
2011 Aug	212,668	SNaive_log	179,432.22	33,235.78
2011 Sep	129,606	SNaive_log	128,593.97	1,012.03
2011 Oct	101,185	SNaive_log	104,802.48	-3,617.48
2011 Nov	62,121	SNaive_log	69,688.37	-7,567.37
2011 Dec	65,563	SNaive_log	63,315.79	2,247.21
2012 Jan	49,716	SNaive_log	60,823.19	-11,107.19
2012 Feb	58,638	SNaive_log	67,677.07	-9,039.07
2012 Mar	72,210	SNaive_log	83,981.10	-11,771.10
2012 Apr	87,406	SNaive_log	103,581.28	-16,175.28
2012 May	96,946	SNaive_log	101,830.06	-4,884.06
2012 Jun	115,885	SNaive_log	120,852.20	-4,967.20
2012 Jul	139,695	SNaive_log	137,799.79	1,895.21
2012 Aug	194,368	SNaive_log	213,911.18	-19,543.18
2012 Sep	127,610	SNaive_log	130,368.43	-2,758.43
2012 Oct	89,649	SNaive_log	101,779.55	-12,130.55
2012 Nov	58,900	SNaive_log	62,485.18	-3,585.18
2012 Dec	51,122	SNaive_log	65,945.85	-14,823.85
2013 Jan	50,313	SNaive_log	50,012.17	300.83
2013 Feb	58,615	SNaive_log	58,986.49	-371.49
2013 Mar	92,426	SNaive_log	72,612.79	19,813.21
2013 Apr	100,996	SNaive_log	87,918.12	13,077.88
2013 May	123,431	SNaive_log	97,523.38	25,907.62
2013 Jun	143,946	SNaive_log	116,606.12	27,339.88
2013 Jul	171,016	SNaive_log	140,594.64	30,421.36
2013 Aug	252,423	SNaive_log	195,656.35	56,766.65
2013 Sep	158,839	SNaive_log	128,487.92	30,351.08
2013 Oct	109,956	SNaive_log	90,283.68	19,672.32
2013 Nov	82,040	SNaive_log	59,323.34	22,716.66
2013 Dec	72,692	SNaive_log	51,513.47	21,178.53
2014 Jan	56,872	SNaive_log	50,727.14	6,144.86
2014 Feb	64,346	SNaive_log	59,101.53	5,244.47
2014 Mar	102,852	SNaive_log	93,177.50	9,674.50
2014 Apr	151,151	SNaive_log	101,820.95	49,330.05
2014 May	148,593	SNaive_log	124,516.81	24,076.19
2014 Jun	154,231	SNaive_log	145,235.12	8,995.88
2014 Jul	194,227	SNaive_log	172,540.24	21,686.76
2014 Aug	303,902	SNaive_log	254,674.70	49,227.30
2014 Sep	186,247	SNaive_log	160,279.06	25,967.94
2014 Oct	133,884	SNaive_log	110,963.04	22,920.96
2014 Nov	86,161	SNaive_log	82,799.50	3,361.50
2014 Dec	81,830	SNaive_log	73,358.42	8,471.58
2015 Jan	68,436	SNaive_log	57,392.89	11,043.11
2015 Feb	84,417	SNaive_log	64,945.41	19,471.59
2015 Mar	116,291	SNaive_log	103,840.59	12,450.41
2015 Apr	145,183	SNaive_log	152,598.83	-7,415.83
2015 May	172,016	SNaive_log	149,988.00	22,028.00
2015 Jun	182,765	SNaive_log	155,691.37	27,073.63
2015 Jul	238,708	SNaive_log	196,091.82	42,616.18
2015 Aug	358,044	SNaive_log	306,868.88	51,175.12
2015 Sep	216,474	SNaive_log	188,083.53	28,390.47
2015 Oct	148,376	SNaive_log	135,215.87	13,160.13
2015 Nov	99,794	SNaive_log	87,015.13	12,778.87
2015 Dec	93,804	SNaive_log	82,648.26	11,155.74
2016 Jan	74,572	SNaive_log	69,110.51	5,461.49
2016 Feb	97,522	SNaive_log	85,248.31	12,273.69
2016 Mar	144,216	SNaive_log	117,444.81	26,771.19
2016 Apr	153,386	SNaive_log	146,613.37	6,772.63
2016 May	168,235	SNaive_log	173,710.08	-5,475.08
2016 Jun	215,800	SNaive_log	184,560.33	31,239.67
2016 Jul	271,212	SNaive_log	241,040.37	30,171.63
2016 Aug	380,776	SNaive_log	361,539.90	19,236.10
2016 Sep	249,098	SNaive_log	218,556.04	30,541.96
2016 Oct	175,862	SNaive_log	149,809.54	26,052.46
2016 Nov	102,775	SNaive_log	100,769.63	2,005.37
2016 Dec	100,859	SNaive_log	94,714.77	6,144.23
2017 Jan	83,249	SNaive_log	75,297.08	7,951.92
2017 Feb	105,210	SNaive_log	98,475.69	6,734.31
2017 Mar	121,167	SNaive_log	145,628.19	-24,461.19
2017 Apr	217,906	SNaive_log	154,899.26	63,006.74
2017 May	196,622	SNaive_log	169,971.32	26,650.68
2017 Jun	248,582	SNaive_log	218,035.02	30,546.98
2017 Jul	323,496	SNaive_log	274,042.20	49,453.80
2017 Aug	431,571	SNaive_log	384,799.40	46,771.60
2017 Sep	287,242	SNaive_log	251,742.53	35,499.47
2017 Oct	212,357	SNaive_log	177,741.37	34,615.63
2017 Nov	127,745	SNaive_log	103,888.68	23,856.32
2017 Dec	132,238	SNaive_log	101,970.19	30,267.81
2018 Jan	95,453	SNaive_log	84,187.42	11,265.58
2018 Feb	120,303	SNaive_log	106,404.77	13,898.23
2018 Mar	162,886	SNaive_log	122,553.06	40,332.94
2018 Apr	187,186	SNaive_log	220,413.79	-33,227.79
2018 May	239,851	SNaive_log	198,889.67	40,961.33
2018 Jun	264,588	SNaive_log	251,492.85	13,095.15
2018 Jul	339,564	SNaive_log	327,250.21	12,313.79
2018 Aug	446,375	SNaive_log	436,576.62	9,798.38
2018 Sep	304,516	SNaive_log	290,549.93	13,966.07
2018 Oct	230,827	SNaive_log	214,801.12	16,025.88
2018 Nov	149,080	SNaive_log	129,219.15	19,860.85
2018 Dec	135,316	SNaive_log	133,778.09	1,537.91
2019 Jan	114,710	SNaive_log	96,564.79	18,145.21
2019 Feb	122,635	SNaive_log	121,720.65	914.35
2019 Mar	172,412	SNaive_log	164,805.34	7,606.66
2019 Apr	241,790	SNaive_log	189,379.31	52,410.69
2019 May	259,714	SNaive_log	242,732.88	16,981.12
2019 Jun	306,048	SNaive_log	267,773.39	38,274.61
2019 Jul	360,566	SNaive_log	343,685.10	16,880.90
2019 Aug	484,403	SNaive_log	451,777.81	32,625.19
2019 Sep	327,937	SNaive_log	308,211.04	19,725.96
2019 Oct	238,677	SNaive_log	233,608.39	5,068.61
2019 Nov	171,296	SNaive_log	150,867.13	20,428.87
2019 Dec	138,642	SNaive_log	136,950.16	1,691.84
2020 Jan	126,349	SNaive_log	116,093.92	10,255.08
2020 Feb	167,411	SNaive_log	124,111.74	43,299.26
2020 Mar	70,530	SNaive_log	174,560.70	-104,030.70
2020 Apr	13,892	SNaive_log	245,691.72	-231,799.72
2020 May	38,343	SNaive_log	273,716.61	-235,373.61
2020 Jun	159,738	SNaive_log	327,733.98	-167,995.98
2020 Jul	272,786	SNaive_log	386,803.73	-114,017.73
2020 Aug	407,020	SNaive_log	519,812.41	-112,792.41
2020 Sep	258,651	SNaive_log	351,907.96	-93,256.96
2020 Oct	167,448	SNaive_log	256,185.42	-88,737.42
2020 Nov	73,734	SNaive_log	183,960.56	-110,226.56
2020 Dec	73,353	SNaive_log	149,340.77	-75,987.77
2021 Jan	48,435	SNaive_log	136,335.23	-87,900.23
2021 Feb	40,443	SNaive_log	181,325.53	-140,882.53
2021 Mar	60,251	SNaive_log	77,044.95	-16,793.95
2021 Apr	85,179	SNaive_log	15,175.47	70,003.53
2021 May	169,690	SNaive_log	42,464.48	127,225.52
2021 Jun	254,243	SNaive_log	178,542.94	75,700.06
2021 Jul	329,058	SNaive_log	305,170.49	23,887.51
2021 Aug	461,844	SNaive_log	455,405.99	6,438.01
2021 Sep	308,273	SNaive_log	289,408.51	18,864.49
2021 Oct	250,949	SNaive_log	187,383.79	63,565.21
2021 Nov	156,624	SNaive_log	82,563.39	74,060.61
2021 Dec	115,100	SNaive_log	82,328.56	32,771.44
2022 Jan	96,107	SNaive_log	54,393.19	41,713.81
2022 Feb	141,508	SNaive_log	45,505.95	96,002.05
2022 Mar	167,854	SNaive_log	68,231.23	99,622.77
2022 Apr	248,959	SNaive_log	96,850.88	152,108.12
2022 May	258,413	SNaive_log	193,829.52	64,583.48
2022 Jun	300,520	SNaive_log	290,550.28	9,969.72
2010 Jan	53,653	TSLM	57,922.22	-4,269.22
2010 Feb	62,257	TSLM	68,538.17	-6,281.17
2010 Mar	77,588	TSLM	84,701.17	-7,113.17
2010 Apr	99,982	TSLM	100,283.16	-301.16
2010 May	101,387	TSLM	98,458.77	2,928.23
2010 Jun	108,611	TSLM	99,809.99	8,801.01
2010 Jul	126,498	TSLM	115,785.33	10,712.67
2010 Aug	178,380	TSLM	161,027.73	17,352.27
2010 Sep	127,822	TSLM	111,627.11	16,194.89
2010 Oct	104,174	TSLM	91,959.47	12,214.53
2010 Nov	69,271	TSLM	76,372.10	-7,101.10
2010 Dec	62,935	TSLM	69,290.49	-6,355.49
2011 Jan	60,457	TSLM	60,588.64	-131.64
2011 Feb	67,260	TSLM	71,551.36	-4,291.36
2011 Mar	83,464	TSLM	87,050.88	-3,586.88
2011 Apr	102,958	TSLM	103,116.32	-158.32
2011 May	101,223	TSLM	103,648.31	-2,425.31
2011 Jun	120,148	TSLM	105,188.77	14,959.23
2011 Jul	136,999	TSLM	121,177.44	15,821.56
2011 Aug	212,668	TSLM	168,155.43	44,512.57
2011 Sep	129,606	TSLM	118,953.10	10,652.90
2011 Oct	101,185	TSLM	98,949.55	2,235.45
2011 Nov	62,121	TSLM	80,994.54	-18,873.54
2011 Dec	65,563	TSLM	73,142.50	-7,579.50
2012 Jan	49,716	TSLM	64,760.72	-15,044.72
2012 Feb	58,638	TSLM	74,875.89	-16,237.89
2012 Mar	72,210	TSLM	90,311.53	-18,101.53
2012 Apr	87,406	TSLM	106,039.99	-18,633.99
2012 May	96,946	TSLM	107,112.90	-10,166.90
2012 Jun	115,885	TSLM	109,436.35	6,448.65
2012 Jul	139,695	TSLM	124,626.06	15,068.94
2012 Aug	194,368	TSLM	175,850.59	18,517.41
2012 Sep	127,610	TSLM	122,584.25	5,025.75
2012 Oct	89,649	TSLM	101,458.57	-11,809.57
2012 Nov	58,900	TSLM	80,550.92	-21,650.92
2012 Dec	51,122	TSLM	74,035.00	-22,913.00
2013 Jan	50,313	TSLM	63,813.66	-13,500.66
2013 Feb	58,615	TSLM	73,322.75	-14,707.75
2013 Mar	92,426	TSLM	87,038.87	5,387.13
2013 Apr	100,996	TSLM	105,400.65	-4,404.65
2013 May	123,431	TSLM	107,790.46	15,640.54
2013 Jun	143,946	TSLM	112,320.03	31,625.97
2013 Jul	171,016	TSLM	128,731.66	42,284.34
2013 Aug	252,423	TSLM	182,319.31	70,103.69
2013 Sep	158,839	TSLM	128,479.34	30,359.66
2013 Oct	109,956	TSLM	106,824.83	3,131.17
2013 Nov	82,040	TSLM	84,255.68	-2,215.68
2013 Dec	72,692	TSLM	79,043.61	-6,351.61
2014 Jan	56,872	TSLM	69,440.31	-12,568.31
2014 Feb	64,346	TSLM	79,492.29	-15,146.29
2014 Mar	102,852	TSLM	95,281.47	7,570.53
2014 Apr	151,151	TSLM	112,425.27	38,725.73
2014 May	148,593	TSLM	117,983.60	30,609.40
2014 Jun	154,231	TSLM	125,143.56	29,087.44
2014 Jul	194,227	TSLM	142,797.04	51,429.96
2014 Aug	303,902	TSLM	201,260.32	102,641.68
2014 Sep	186,247	TSLM	143,730.28	42,516.72
2014 Oct	133,884	TSLM	119,770.83	14,113.17
2014 Nov	86,161	TSLM	96,283.98	-10,122.98
2014 Dec	81,830	TSLM	90,950.04	-9,120.04
2015 Jan	68,436	TSLM	80,449.65	-12,013.65
2015 Feb	84,417	TSLM	89,697.09	-5,280.09
2015 Mar	116,291	TSLM	109,049.86	7,241.14
2015 Apr	145,183	TSLM	129,117.51	16,065.49
2015 May	172,016	TSLM	133,515.27	38,500.73
2015 Jun	182,765	TSLM	141,350.63	41,414.37
2015 Jul	238,708	TSLM	161,847.01	76,860.99
2015 Aug	358,044	TSLM	226,204.83	131,839.17
2015 Sep	216,474	TSLM	162,744.00	53,730.00
2015 Oct	148,376	TSLM	135,276.54	13,099.46
2015 Nov	99,794	TSLM	109,531.46	-9,737.46
2015 Dec	93,804	TSLM	104,667.93	-10,863.93
2016 Jan	74,572	TSLM	93,709.28	-19,137.28
2016 Feb	97,522	TSLM	104,073.02	-6,551.02
2016 Mar	144,216	TSLM	124,888.22	19,327.78
2016 Apr	153,386	TSLM	147,571.86	5,814.14
2016 May	168,235	TSLM	153,763.64	14,471.36
2016 Jun	215,800	TSLM	162,738.17	53,061.83
2016 Jul	271,212	TSLM	188,001.31	83,210.69
2016 Aug	380,776	TSLM	258,876.68	121,899.32
2016 Sep	249,098	TSLM	185,769.41	63,328.59
2016 Oct	175,862	TSLM	153,791.50	22,070.50
2016 Nov	102,775	TSLM	124,607.45	-21,832.45
2016 Dec	100,859	TSLM	119,794.48	-18,935.48
2017 Jan	83,249	TSLM	108,463.70	-25,214.70
2017 Feb	105,210	TSLM	120,358.99	-15,148.99
2017 Mar	121,167	TSLM	145,421.86	-24,254.86
2017 Apr	217,906	TSLM	165,366.27	52,539.73
2017 May	196,622	TSLM	175,543.11	21,078.89
2017 Jun	248,582	TSLM	190,071.08	58,510.92
2017 Jul	323,496	TSLM	219,472.58	104,023.42
2017 Aug	431,571	TSLM	298,326.37	133,244.63
2017 Sep	287,242	TSLM	216,607.44	70,634.56
2017 Oct	212,357	TSLM	179,276.84	33,080.16
2017 Nov	127,745	TSLM	144,871.59	-17,126.59
2017 Dec	132,238	TSLM	140,145.10	-7,907.10
2018 Jan	95,453	TSLM	129,686.71	-34,233.71
2018 Feb	120,303	TSLM	143,003.34	-22,700.34
2018 Mar	162,886	TSLM	168,059.24	-5,173.24
2018 Apr	187,186	TSLM	196,778.98	-9,592.98
2018 May	239,851	TSLM	203,930.05	35,920.95
2018 Jun	264,588	TSLM	223,810.66	40,777.34
2018 Jul	339,564	TSLM	258,422.02	81,141.98
2018 Aug	446,375	TSLM	341,967.21	104,407.79
2018 Sep	304,516	TSLM	249,913.54	54,602.46
2018 Oct	230,827	TSLM	206,820.58	24,006.42
2018 Nov	149,080	TSLM	165,059.83	-15,979.83
2018 Dec	135,316	TSLM	161,640.20	-26,324.20
2019 Jan	114,710	TSLM	148,730.63	-34,020.63
2019 Feb	122,635	TSLM	163,490.39	-40,855.39
2019 Mar	172,412	TSLM	190,037.87	-17,625.87
2019 Apr	241,790	TSLM	220,814.03	20,975.97
2019 May	259,714	TSLM	232,695.78	27,018.22
2019 Jun	306,048	TSLM	255,707.55	50,340.45
2019 Jul	360,566	TSLM	296,769.61	63,796.39
2019 Aug	484,403	TSLM	385,793.54	98,609.46
2019 Sep	327,937	TSLM	283,198.63	44,738.37
2019 Oct	238,677	TSLM	234,365.68	4,311.32
2019 Nov	171,296	TSLM	186,170.97	-14,874.97
2019 Dec	138,642	TSLM	182,447.79	-43,805.79
2020 Jan	126,349	TSLM	168,136.35	-41,787.35
2020 Feb	167,411	TSLM	182,381.50	-14,970.50
2020 Mar	70,530	TSLM	214,226.62	-143,696.62
2020 Apr	13,892	TSLM	246,239.86	-232,347.86
2020 May	38,343	TSLM	253,383.21	-215,040.21
2020 Jun	159,738	TSLM	273,764.89	-114,026.89
2020 Jul	272,786	TSLM	314,878.02	-42,092.02
2020 Aug	407,020	TSLM	406,867.01	152.99
2020 Sep	258,651	TSLM	291,724.94	-33,073.94
2020 Oct	167,448	TSLM	233,300.31	-65,852.31
2020 Nov	73,734	TSLM	178,510.17	-104,776.17
2020 Dec	73,353	TSLM	169,445.36	-96,092.36
2021 Jan	48,435	TSLM	152,520.35	-104,085.35
2021 Feb	40,443	TSLM	167,867.48	-127,424.48
2021 Mar	60,251	TSLM	184,885.89	-124,634.89
2021 Apr	85,179	TSLM	208,957.71	-123,778.71
2021 May	169,690	TSLM	220,757.04	-51,067.04
2021 Jun	254,243	TSLM	256,184.73	-1,941.73
2021 Jul	329,058	TSLM	309,245.06	19,812.94
2021 Aug	461,844	TSLM	410,384.20	51,459.80
2021 Sep	308,273	TSLM	286,609.10	21,663.90
2021 Oct	250,949	TSLM	221,997.21	28,951.79
2021 Nov	156,624	TSLM	162,970.64	-6,346.64
2021 Dec	115,100	TSLM	156,330.31	-41,230.31
2022 Jan	96,107	TSLM	138,227.40	-42,120.40
2022 Feb	141,508	TSLM	153,025.42	-11,517.42
2022 Mar	167,854	TSLM	172,816.38	-4,962.38
2022 Apr	248,959	TSLM	199,906.77	49,052.23
2022 May	258,413	TSLM	224,048.78	34,364.22
2022 Jun	300,520	TSLM	267,746.28	32,773.72
2010 Jan	53,653	TSLM_log	53,094.80	558.20
2010 Feb	62,257	TSLM_log	65,456.96	-3,199.96
2010 Mar	77,588	TSLM_log	84,464.45	-6,876.45
2010 Apr	99,982	TSLM_log	102,939.74	-2,957.74
2010 May	101,387	TSLM_log	100,416.53	970.47
2010 Jun	108,611	TSLM_log	102,095.98	6,515.02
2010 Jul	126,498	TSLM_log	121,125.64	5,372.36
2010 Aug	178,380	TSLM_log	174,027.33	4,352.67
2010 Sep	127,822	TSLM_log	115,683.54	12,138.46
2010 Oct	104,174	TSLM_log	91,954.77	12,219.23
2010 Nov	69,271	TSLM_log	73,600.33	-4,329.33
2010 Dec	62,935	TSLM_log	64,840.75	-1,905.75
2011 Jan	60,457	TSLM_log	55,324.12	5,132.88
2011 Feb	67,260	TSLM_log	68,235.87	-975.87
2011 Mar	83,464	TSLM_log	86,453.48	-2,989.48
2011 Apr	102,958	TSLM_log	105,594.14	-2,636.14
2011 May	101,223	TSLM_log	106,185.17	-4,962.17
2011 Jun	120,148	TSLM_log	107,919.26	12,228.74
2011 Jul	136,999	TSLM_log	127,151.83	9,847.17
2011 Aug	212,668	TSLM_log	183,311.25	29,356.75
2011 Sep	129,606	TSLM_log	123,366.20	6,239.80
2011 Oct	101,185	TSLM_log	98,764.31	2,420.69
2011 Nov	62,121	TSLM_log	77,499.65	-15,378.65
2011 Dec	65,563	TSLM_log	67,530.78	-1,967.78
2012 Jan	49,716	TSLM_log	58,093.42	-8,377.42
2012 Feb	58,638	TSLM_log	70,155.03	-11,517.03
2012 Mar	72,210	TSLM_log	88,330.83	-16,120.83
2012 Apr	87,406	TSLM_log	107,015.33	-19,609.33
2012 May	96,946	TSLM_log	108,479.81	-11,533.81
2012 Jun	115,885	TSLM_log	110,645.68	5,239.32
2012 Jul	139,695	TSLM_log	128,679.61	11,015.39
2012 Aug	194,368	TSLM_log	188,544.71	5,823.29
2012 Sep	127,610	TSLM_log	125,924.96	1,685.04
2012 Oct	89,649	TSLM_log	100,693.43	-11,044.43
2012 Nov	58,900	TSLM_log	76,700.35	-17,800.35
2012 Dec	51,122	TSLM_log	68,669.31	-17,547.31
2013 Jan	50,313	TSLM_log	57,314.86	-7,001.86
2013 Feb	58,615	TSLM_log	68,166.20	-9,551.20
2013 Mar	92,426	TSLM_log	83,673.60	8,752.40
2013 Apr	100,996	TSLM_log	104,781.36	-3,785.36
2013 May	123,431	TSLM_log	107,678.80	15,752.20
2013 Jun	143,946	TSLM_log	111,976.82	31,969.18
2013 Jul	171,016	TSLM_log	130,821.81	40,194.19
2013 Aug	252,423	TSLM_log	192,848.44	59,574.56
2013 Sep	158,839	TSLM_log	129,702.93	29,136.07
2013 Oct	109,956	TSLM_log	104,098.07	5,857.93
2013 Nov	82,040	TSLM_log	77,588.99	4,451.01
2013 Dec	72,692	TSLM_log	71,159.51	1,532.49
2014 Jan	56,872	TSLM_log	60,008.43	-3,136.43
2014 Feb	64,346	TSLM_log	71,970.68	-7,624.68
2014 Mar	102,852	TSLM_log	90,325.40	12,526.60
2014 Apr	151,151	TSLM_log	111,022.81	40,128.19
2014 May	148,593	TSLM_log	117,212.70	31,380.30
2014 Jun	154,231	TSLM_log	124,347.78	29,883.22
2014 Jul	194,227	TSLM_log	145,499.59	48,727.41
2014 Aug	303,902	TSLM_log	216,740.97	87,161.03
2014 Sep	186,247	TSLM_log	145,489.83	40,757.17
2014 Oct	133,884	TSLM_log	115,767.23	18,116.77
2014 Nov	86,161	TSLM_log	85,849.98	311.02
2014 Dec	81,830	TSLM_log	78,922.09	2,907.91
2015 Jan	68,436	TSLM_log	65,787.11	2,648.89
2015 Feb	84,417	TSLM_log	77,553.70	6,863.30
2015 Mar	116,291	TSLM_log	101,405.71	14,885.29
2015 Apr	145,183	TSLM_log	126,284.88	18,898.12
2015 May	172,016	TSLM_log	131,869.56	40,146.44
2015 Jun	182,765	TSLM_log	140,319.74	42,445.26
2015 Jul	238,708	TSLM_log	165,545.00	73,163.00
2015 Aug	358,044	TSLM_log	246,837.52	111,206.48
2015 Sep	216,474	TSLM_log	164,714.05	51,759.95
2015 Oct	148,376	TSLM_log	128,899.72	19,476.28
2015 Nov	99,794	TSLM_log	94,815.49	4,978.51
2015 Dec	93,804	TSLM_log	87,960.99	5,843.01
2016 Jan	74,572	TSLM_log	73,167.00	1,405.00
2016 Feb	97,522	TSLM_log	87,152.94	10,369.06
2016 Mar	144,216	TSLM_log	114,233.52	29,982.48
2016 Apr	153,386	TSLM_log	144,382.67	9,003.33
2016 May	168,235	TSLM_log	151,628.39	16,606.61
2016 Jun	215,800	TSLM_log	162,798.99	53,001.01
2016 Jul	271,212	TSLM_log	194,684.43	76,527.57
2016 Aug	380,776	TSLM_log	288,114.91	92,661.09
2016 Sep	249,098	TSLM_log	190,283.83	58,814.17
2016 Oct	175,862	TSLM_log	146,991.77	28,870.23
2016 Nov	102,775	TSLM_log	105,652.03	-2,877.03
2016 Dec	100,859	TSLM_log	98,445.41	2,413.59
2017 Jan	83,249	TSLM_log	82,214.01	1,034.99
2017 Feb	105,210	TSLM_log	99,001.17	6,208.83
2017 Mar	121,167	TSLM_log	133,885.36	-12,718.36
2017 Apr	217,906	TSLM_log	163,062.54	54,843.46
2017 May	196,622	TSLM_log	176,331.65	20,290.35
2017 Jun	248,582	TSLM_log	195,409.63	53,172.37
2017 Jul	323,496	TSLM_log	234,714.92	88,781.08
2017 Aug	431,571	TSLM_log	348,970.58	82,600.42
2017 Sep	287,242	TSLM_log	228,891.18	58,350.82
2017 Oct	212,357	TSLM_log	173,910.99	38,446.01
2017 Nov	127,745	TSLM_log	121,169.55	6,575.45
2017 Dec	132,238	TSLM_log	112,728.66	19,509.34
2018 Jan	95,453	TSLM_log	95,926.10	-473.10
2018 Feb	120,303	TSLM_log	116,428.15	3,874.85
2018 Mar	162,886	TSLM_log	155,780.50	7,105.50
2018 Apr	187,186	TSLM_log	198,287.43	-11,101.43
2018 May	239,851	TSLM_log	211,620.36	28,230.64
2018 Jun	264,588	TSLM_log	239,305.87	25,282.13
2018 Jul	339,564	TSLM_log	288,783.06	50,780.94
2018 Aug	446,375	TSLM_log	422,776.55	23,598.45
2018 Sep	304,516	TSLM_log	275,495.32	29,020.68
2018 Oct	230,827	TSLM_log	206,908.17	23,918.83
2018 Nov	149,080	TSLM_log	138,788.85	10,291.15
2018 Dec	135,316	TSLM_log	130,822.82	4,493.18
2019 Jan	114,710	TSLM_log	110,218.29	4,491.71
2019 Feb	122,635	TSLM_log	134,050.82	-11,415.82
2019 Mar	172,412	TSLM_log	178,305.14	-5,893.14
2019 Apr	241,790	TSLM_log	229,117.50	12,672.50
2019 May	259,714	TSLM_log	247,572.06	12,141.94
2019 Jun	306,048	TSLM_log	284,692.71	21,355.29
2019 Jul	360,566	TSLM_log	347,453.42	13,112.58
2019 Aug	484,403	TSLM_log	502,721.49	-18,318.49
2019 Sep	327,937	TSLM_log	324,001.79	3,935.21
2019 Oct	238,677	TSLM_log	240,621.95	-1,944.95
2019 Nov	171,296	TSLM_log	158,268.19	13,027.81
2019 Dec	138,642	TSLM_log	149,849.57	-11,207.57
2020 Jan	126,349	TSLM_log	125,962.59	386.41
2020 Feb	167,411	TSLM_log	150,575.03	16,835.97
2020 Mar	70,530	TSLM_log	206,635.39	-136,105.39
2020 Apr	13,892	TSLM_log	260,303.52	-246,411.52
2020 May	38,343	TSLM_log	272,547.95	-234,204.95
2020 Jun	159,738	TSLM_log	304,514.12	-144,776.12
2020 Jul	272,786	TSLM_log	367,960.81	-95,174.81
2020 Aug	407,020	TSLM_log	519,698.01	-112,678.01
2020 Sep	258,651	TSLM_log	334,613.00	-75,962.00
2020 Oct	167,448	TSLM_log	243,131.37	-75,683.37
2020 Nov	73,734	TSLM_log	157,788.45	-84,054.45
2020 Dec	73,353	TSLM_log	144,929.96	-71,576.96
2021 Jan	48,435	TSLM_log	119,885.03	-71,450.03
2021 Feb	40,443	TSLM_log	142,087.03	-101,644.03
2021 Mar	60,251	TSLM_log	169,370.85	-109,119.85
2021 Apr	85,179	TSLM_log	176,422.40	-91,243.40
2021 May	169,690	TSLM_log	208,461.24	-38,771.24
2021 Jun	254,243	TSLM_log	273,982.03	-19,739.03
2021 Jul	329,058	TSLM_log	347,778.14	-18,720.14
2021 Aug	461,844	TSLM_log	495,125.89	-33,281.89
2021 Sep	308,273	TSLM_log	316,164.91	-7,891.91
2021 Oct	250,949	TSLM_log	224,594.11	26,354.89
2021 Nov	156,624	TSLM_log	140,740.41	15,883.59
2021 Dec	115,100	TSLM_log	132,162.70	-17,062.70
2022 Jan	96,107	TSLM_log	106,363.07	-10,256.07
2022 Feb	141,508	TSLM_log	123,657.13	17,850.87
2022 Mar	167,854	TSLM_log	153,775.79	14,078.21
2022 Apr	248,959	TSLM_log	165,514.00	83,445.00
2022 May	258,413	TSLM_log	214,624.05	43,788.95
2022 Jun	300,520	TSLM_log	290,590.21	9,929.79

# Show Point Forecasts in Plot: 2000-2022
error_fc_alentejo_slide %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_until2022, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2000-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2010-2022
error_fc_alentejo_slide %>%
  filter(year(Month) >= 2010) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_from2010, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2010-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2019-2022
error_fc_alentejo_slide %>%
  filter(year(Month) >= 2019) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_from2019, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2019-2022") +
  ylab("Overnight_Stays")

# Show Point Forecasts in Plot: 2020-2022
error_fc_alentejo_slide %>%
  filter(year(Month) >= 2020) %>%
  autoplot(Point_Forecast) +
  theme(legend.position = "bottom") +
  autolayer(tourism_alentejo_from2020, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts of Models: 2020-2022") +
  ylab("Overnight_Stays")

2.3.2.4 Change of RMSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2019) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2022) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
Drift_STL	13	21,577.49	1	27,520.32
Drift_STL_log	4	15,190.69	2	29,335.51
ARIMA_d1D1	9	17,058.72	3	29,645.78
ARIMA_d0D1	8	16,883.04	4	30,580.20
ETS_auto_log	6	15,918.56	5	30,808.59
ARIMA_auto	10	17,283.48	6	30,821.72
ARIMA_d0D1_log	2	14,725.89	7	31,479.02
ARIMA_auto_log	3	14,784.05	8	31,585.19
HWA_log	5	15,354.53	9	31,631.44
HWA	12	20,985.26	10	32,549.02
ARIMA_d1D1_log	1	13,991.09	11	34,987.62
ETS_auto	7	16,048.79	12	36,535.20
Prophet_log	11	20,196.16	13	47,469.73
TSLM_log	16	30,199.82	14	48,999.68
SNaive	15	23,520.64	15	50,152.41
SNaive_log	14	22,347.37	16	50,651.25
Prophet	17	37,191.81	17	51,864.27
TSLM	18	39,946.57	18	53,414.65
Naive	19	56,208.84	19	61,485.90
Naive_log	20	57,537.80	20	63,181.51

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Save best models according to the RMSE of Forecasts from 2010-2022
best_models_fc_alentejo_slide <- c("ARIMA_d0D1", "Drift_STL", "ARIMA_d1D1", "ARIMA_auto", "HWA_log", "ETS_auto_log", "Naive", "Prophet_log", "TSLM_log", "SNaive")

# Calculate RMSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2019) %>%
  filter(.model %in% best_models_fc_alentejo_slide) %>%
  arrange(RMSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSE_2019 = RMSE) %>%
  select(c(Rank_2019, Model, RMSE_2019))

# Calculate RMSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2022) %>%
  filter(.model %in% best_models_fc_alentejo_slide) %>%
  arrange(RMSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSE_2022 = RMSE) %>%
  select(c(Rank_2022, Model, RMSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSE", "Rank", "RMSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE: 2010-2019 vs. 2010-2022</span>", format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSE	Rank	RMSE
Drift_STL	7	21,577.49	1	27,520.32
ARIMA_d1D1	4	17,058.72	2	29,645.78
ARIMA_d0D1	3	16,883.04	3	30,580.20
ETS_auto_log	2	15,918.56	4	30,808.59
ARIMA_auto	5	17,283.48	5	30,821.72
HWA_log	1	15,354.53	6	31,631.44
Prophet_log	6	20,196.16	7	47,469.73
TSLM_log	9	30,199.82	8	48,999.68
SNaive	8	23,520.64	9	50,152.41
Naive	10	56,208.84	10	61,485.90

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.3.2.5 RMSE Development by including more Years in Time Series

# Compute RMSE and RMSSE for 2010 and create tibble
tourism_until_i <- tourism_alentejo_until2022 %>%
    filter(year(Month) <= 2010)

accuracy_alentejo_slide <- accuracy(fc_alentejo_slide, tourism_until_i) %>%
  select(c(.model, RMSE, RMSSE)) %>%
  mutate(Until_Year = 2010)

# Create tsibble of summarized RMSE and RMSSE, beginning in 2010 and including more years
for (i in 2011:2022){
  tourism_until_i <- tourism_alentejo_until2022 %>%
    filter(year(Month) <= i)

  accuracy_next_year <- accuracy(fc_alentejo_slide, tourism_until_i) %>%
    select(c(.model, RMSE, RMSSE)) %>%
    mutate(Until_Year = i)

  accuracy_alentejo_slide <- rbind(accuracy_alentejo_slide, accuracy_next_year)
}

rm(accuracy_next_year, tourism_until_i) # remove variables from R environment

accuracy_alentejo_slide <- accuracy_alentejo_slide %>%
  rename(Model = .model) %>%
  select(c(Until_Year, Model, RMSE, RMSSE)) %>%
  as_tsibble(key = Model, index = Until_Year)

# Show table
accuracy_alentejo_slide %>%
  mutate(across(RMSE, ~ format(.x, big.mark = ","))) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Development of RMSE and RMSSE by including more Years in Time Series</span>", digits = 2, align = "cccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F) %>%
  scroll_box(height = "400px")

Development of RMSE and RMSSE by including more Years in Time Series

Until_Year	Model	RMSE	RMSSE
2010	ARIMA_auto	7,185.741	0.78
2011	ARIMA_auto	9,938.680	1.05
2012	ARIMA_auto	9,553.392	1.00
2013	ARIMA_auto	10,746.951	0.91
2014	ARIMA_auto	13,956.408	1.05
2015	ARIMA_auto	13,761.975	0.94
2016	ARIMA_auto	13,989.540	0.92
2017	ARIMA_auto	16,296.015	0.95
2018	ARIMA_auto	17,602.382	1.00
2019	ARIMA_auto	17,283.482	0.95
2020	ARIMA_auto	30,526.310	0.95
2021	ARIMA_auto	29,978.311	0.83
2022	ARIMA_auto	30,821.723	0.80
2010	ARIMA_auto_log	5,318.787	0.58
2011	ARIMA_auto_log	7,844.779	0.83
2012	ARIMA_auto_log	8,537.335	0.90
2013	ARIMA_auto_log	9,823.341	0.83
2014	ARIMA_auto_log	12,352.874	0.93
2015	ARIMA_auto_log	11,988.271	0.82
2016	ARIMA_auto_log	12,600.846	0.83
2017	ARIMA_auto_log	13,976.523	0.81
2018	ARIMA_auto_log	14,770.201	0.84
2019	ARIMA_auto_log	14,784.048	0.81
2020	ARIMA_auto_log	29,706.922	0.92
2021	ARIMA_auto_log	29,434.692	0.82
2022	ARIMA_auto_log	31,585.191	0.82
2010	ARIMA_d0D1	7,185.741	0.78
2011	ARIMA_d0D1	9,938.680	1.05
2012	ARIMA_d0D1	9,553.392	1.00
2013	ARIMA_d0D1	10,746.951	0.91
2014	ARIMA_d0D1	13,834.521	1.04
2015	ARIMA_d0D1	13,885.143	0.95
2016	ARIMA_d0D1	14,270.143	0.94
2017	ARIMA_d0D1	16,165.343	0.94
2018	ARIMA_d0D1	17,107.391	0.97
2019	ARIMA_d0D1	16,883.035	0.93
2020	ARIMA_d0D1	30,274.948	0.94
2021	ARIMA_d0D1	29,719.545	0.83
2022	ARIMA_d0D1	30,580.202	0.79
2010	ARIMA_d0D1_log	5,318.787	0.58
2011	ARIMA_d0D1_log	7,844.779	0.83
2012	ARIMA_d0D1_log	8,537.335	0.90
2013	ARIMA_d0D1_log	9,823.341	0.83
2014	ARIMA_d0D1_log	12,352.874	0.93
2015	ARIMA_d0D1_log	11,984.422	0.82
2016	ARIMA_d0D1_log	12,555.567	0.83
2017	ARIMA_d0D1_log	14,066.485	0.82
2018	ARIMA_d0D1_log	14,689.581	0.83
2019	ARIMA_d0D1_log	14,725.894	0.81
2020	ARIMA_d0D1_log	29,662.233	0.92
2021	ARIMA_d0D1_log	29,315.980	0.82
2022	ARIMA_d0D1_log	31,479.022	0.81
2010	ARIMA_d1D1	7,956.651	0.86
2011	ARIMA_d1D1	10,683.231	1.13
2012	ARIMA_d1D1	9,952.627	1.05
2013	ARIMA_d1D1	11,032.197	0.93
2014	ARIMA_d1D1	13,391.917	1.00
2015	ARIMA_d1D1	13,286.348	0.91
2016	ARIMA_d1D1	13,589.708	0.90
2017	ARIMA_d1D1	15,997.232	0.93
2018	ARIMA_d1D1	17,357.051	0.98
2019	ARIMA_d1D1	17,058.717	0.94
2020	ARIMA_d1D1	29,165.248	0.91
2021	ARIMA_d1D1	28,820.788	0.80
2022	ARIMA_d1D1	29,645.784	0.77
2010	ARIMA_d1D1_log	5,812.511	0.63
2011	ARIMA_d1D1_log	8,024.740	0.85
2012	ARIMA_d1D1_log	8,420.015	0.88
2013	ARIMA_d1D1_log	9,139.775	0.77
2014	ARIMA_d1D1_log	10,347.885	0.78
2015	ARIMA_d1D1_log	10,012.765	0.69
2016	ARIMA_d1D1_log	11,023.936	0.73
2017	ARIMA_d1D1_log	12,757.187	0.74
2018	ARIMA_d1D1_log	13,754.396	0.78
2019	ARIMA_d1D1_log	13,991.090	0.77
2020	ARIMA_d1D1_log	31,731.871	0.99
2021	ARIMA_d1D1_log	32,764.932	0.91
2022	ARIMA_d1D1_log	34,987.620	0.90
2010	Drift_STL	6,293.780	0.68
2011	Drift_STL	10,893.233	1.15
2012	Drift_STL	10,199.989	1.07
2013	Drift_STL	12,321.179	1.04
2014	Drift_STL	15,670.527	1.17
2015	Drift_STL	18,174.888	1.24
2016	Drift_STL	19,282.431	1.27
2017	Drift_STL	21,543.380	1.25
2018	Drift_STL	21,709.429	1.23
2019	Drift_STL	21,577.487	1.18
2020	Drift_STL	27,630.231	0.86
2021	Drift_STL	27,592.135	0.77
2022	Drift_STL	27,520.322	0.71
2010	Drift_STL_log	5,669.417	0.62
2011	Drift_STL_log	7,997.188	0.85
2012	Drift_STL_log	7,996.941	0.84
2013	Drift_STL_log	9,074.556	0.77
2014	Drift_STL_log	10,393.530	0.78
2015	Drift_STL_log	10,622.528	0.73
2016	Drift_STL_log	11,247.405	0.74
2017	Drift_STL_log	14,418.915	0.84
2018	Drift_STL_log	15,134.884	0.86
2019	Drift_STL_log	15,190.691	0.83
2020	Drift_STL_log	25,612.350	0.80
2021	Drift_STL_log	25,402.685	0.71
2022	Drift_STL_log	29,335.511	0.76
2010	ETS_auto	7,002.363	0.76
2011	ETS_auto	9,139.322	0.97
2012	ETS_auto	10,032.646	1.05
2013	ETS_auto	11,252.776	0.95
2014	ETS_auto	12,522.629	0.94
2015	ETS_auto	12,684.231	0.87
2016	ETS_auto	13,792.940	0.91
2017	ETS_auto	15,283.284	0.89
2018	ETS_auto	16,393.028	0.93
2019	ETS_auto	16,048.792	0.88
2020	ETS_auto	33,558.760	1.04
2021	ETS_auto	36,891.560	1.03
2022	ETS_auto	36,535.199	0.94
2010	ETS_auto_log	7,639.950	0.83
2011	ETS_auto_log	9,346.931	0.99
2012	ETS_auto_log	10,175.843	1.07
2013	ETS_auto_log	11,489.350	0.97
2014	ETS_auto_log	12,637.481	0.95
2015	ETS_auto_log	12,821.157	0.88
2016	ETS_auto_log	13,496.672	0.89
2017	ETS_auto_log	15,535.321	0.90
2018	ETS_auto_log	15,744.723	0.89
2019	ETS_auto_log	15,918.563	0.87
2020	ETS_auto_log	29,984.665	0.93
2021	ETS_auto_log	29,720.285	0.83
2022	ETS_auto_log	30,808.592	0.80
2010	HWA	9,203.285	1.00
2011	HWA	12,805.358	1.36
2012	HWA	12,233.094	1.28
2013	HWA	13,396.877	1.13
2014	HWA	15,210.676	1.14
2015	HWA	16,524.013	1.13
2016	HWA	18,001.407	1.19
2017	HWA	21,317.904	1.24
2018	HWA	21,573.671	1.22
2019	HWA	20,985.260	1.15
2020	HWA	32,964.582	1.03
2021	HWA	32,808.477	0.91
2022	HWA	32,549.022	0.84
2010	HWA_log	6,474.323	0.70
2011	HWA_log	8,980.098	0.95
2012	HWA_log	10,749.776	1.13
2013	HWA_log	12,896.734	1.09
2014	HWA_log	13,520.010	1.01
2015	HWA_log	13,126.419	0.90
2016	HWA_log	13,677.802	0.90
2017	HWA_log	14,741.462	0.86
2018	HWA_log	15,580.966	0.88
2019	HWA_log	15,354.535	0.84
2020	HWA_log	30,982.961	0.96
2021	HWA_log	30,542.211	0.85
2022	HWA_log	31,631.440	0.82
2010	Naive	26,274.167	2.86
2011	Naive	32,012.238	3.39
2012	Naive	31,732.417	3.33
2013	Naive	34,711.475	2.93
2014	Naive	39,687.032	2.97
2015	Naive	44,420.789	3.04
2016	Naive	47,664.193	3.15
2017	Naive	51,569.749	3.00
2018	Naive	53,793.345	3.05
2019	Naive	56,208.838	3.08
2020	Naive	60,227.475	1.87
2021	Naive	62,111.059	1.73
2022	Naive	61,485.898	1.59
2010	Naive_log	26,794.670	2.91
2011	Naive_log	32,606.980	3.45
2012	Naive_log	32,348.513	3.40
2013	Naive_log	35,366.866	2.99
2014	Naive_log	40,449.959	3.03
2015	Naive_log	45,289.095	3.10
2016	Naive_log	48,640.294	3.21
2017	Naive_log	52,664.399	3.06
2018	Naive_log	55,009.426	3.12
2019	Naive_log	57,537.804	3.16
2020	Naive_log	61,902.275	1.93
2021	Naive_log	64,066.446	1.78
2022	Naive_log	63,181.507	1.63
2010	Prophet	9,576.092	1.04
2011	Prophet	13,541.781	1.43
2012	Prophet	14,966.917	1.57
2013	Prophet	19,212.308	1.62
2014	Prophet	24,036.983	1.80
2015	Prophet	28,412.798	1.95
2016	Prophet	31,676.089	2.09
2017	Prophet	35,107.678	2.04
2018	Prophet	36,240.450	2.05
2019	Prophet	37,191.811	2.04
2020	Prophet	50,106.535	1.56
2021	Prophet	51,820.445	1.44
2022	Prophet	51,864.271	1.34
2010	Prophet_log	8,142.764	0.89
2011	Prophet_log	9,944.287	1.05
2012	Prophet_log	11,433.704	1.20
2013	Prophet_log	17,470.201	1.48
2014	Prophet_log	18,480.222	1.38
2015	Prophet_log	19,193.145	1.31
2016	Prophet_log	19,713.410	1.30
2017	Prophet_log	20,998.322	1.22
2018	Prophet_log	20,522.300	1.16
2019	Prophet_log	20,196.162	1.11
2020	Prophet_log	36,999.776	1.15
2021	Prophet_log	46,185.755	1.28
2022	Prophet_log	47,469.726	1.23
2010	SNaive	8,030.533	0.87
2011	SNaive	9,953.632	1.05
2012	SNaive	10,097.614	1.06
2013	SNaive	16,132.891	1.36
2014	SNaive	18,504.521	1.39
2015	SNaive	20,077.454	1.37
2016	SNaive	20,306.377	1.34
2017	SNaive	23,061.290	1.34
2018	SNaive	23,138.554	1.31
2019	SNaive	23,520.644	1.29
2020	SNaive	42,516.003	1.32
2021	SNaive	46,873.597	1.30
2022	SNaive	50,152.414	1.30
2010	SNaive_log	7,614.197	0.83
2011	SNaive_log	9,550.960	1.01
2012	SNaive_log	10,022.179	1.05
2013	SNaive_log	15,824.006	1.34
2014	SNaive_log	18,003.924	1.35
2015	SNaive_log	19,393.505	1.33
2016	SNaive_log	19,506.525	1.29
2017	SNaive_log	22,093.437	1.28
2018	SNaive_log	22,122.570	1.25
2019	SNaive_log	22,347.367	1.23
2020	SNaive_log	45,252.059	1.41
2021	SNaive_log	48,343.674	1.34
2022	SNaive_log	50,651.251	1.31
2010	TSLM	9,628.729	1.05
2011	TSLM	13,129.746	1.39
2012	TSLM	14,118.230	1.48
2013	TSLM	18,566.756	1.57
2014	TSLM	24,374.513	1.83
2015	TSLM	30,250.744	2.07
2016	TSLM	33,954.719	2.24
2017	TSLM	38,180.186	2.22
2018	TSLM	39,286.691	2.23
2019	TSLM	39,946.575	2.19
2020	TSLM	51,841.132	1.61
2021	TSLM	54,094.581	1.50
2022	TSLM	53,414.651	1.38
2010	TSLM_log	6,303.485	0.69
2011	TSLM_log	8,986.362	0.95
2012	TSLM_log	10,342.269	1.09
2013	TSLM_log	15,425.954	1.30
2014	TSLM_log	21,254.135	1.59
2015	TSLM_log	26,870.966	1.84
2016	TSLM_log	29,863.010	1.97
2017	TSLM_log	32,495.353	1.89
2018	TSLM_log	31,574.739	1.79
2019	TSLM_log	30,199.824	1.66
2020	TSLM_log	48,478.651	1.51
2021	TSLM_log	49,338.969	1.37
2022	TSLM_log	48,999.677	1.27

All Models

# Plot development of RMSE for period 2010-2022
accuracy_alentejo_slide %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_alentejo_slide %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_alentejo_slide %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_alentejo_slide %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_alentejo_slide %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	56,208.84	60,227.48	4,018.64	0.0715
Naive_log	57,537.80	61,902.28	4,364.47	0.0759
Drift_STL	21,577.49	27,630.23	6,052.74	0.2805
TSLM	39,946.57	51,841.13	11,894.56	0.2978
Prophet	37,191.81	50,106.53	12,914.72	0.3472
HWA	20,985.26	32,964.58	11,979.32	0.5708
TSLM_log	30,199.82	48,478.65	18,278.83	0.6053
Drift_STL_log	15,190.69	25,612.35	10,421.66	0.6861
ARIMA_d1D1	17,058.72	29,165.25	12,106.53	0.7097
ARIMA_auto	17,283.48	30,526.31	13,242.83	0.7662
ARIMA_d0D1	16,883.04	30,274.95	13,391.91	0.7932
SNaive	23,520.64	42,516.00	18,995.36	0.8076
Prophet_log	20,196.16	36,999.78	16,803.61	0.8320
ETS_auto_log	15,918.56	29,984.66	14,066.10	0.8836
ARIMA_auto_log	14,784.05	29,706.92	14,922.87	1.0094
ARIMA_d0D1_log	14,725.89	29,662.23	14,936.34	1.0143
HWA_log	15,354.53	30,982.96	15,628.43	1.0178
SNaive_log	22,347.37	45,252.06	22,904.69	1.0249
ETS_auto	16,048.79	33,558.76	17,509.97	1.0910
ARIMA_d1D1_log	13,991.09	31,731.87	17,740.78	1.2680

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

Each Model once

# Plot development of RMSE for period 2010-2022
accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2010-2019
accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSE")

# Zooming in 2020-2022
accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSE")

# Change of RMSE by including 2020 in the time series
RMSE_until2019 <- accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2019) %>%
  rename(RMSE_2019 = RMSE)

RMSE_until2020 <- accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  select(!RMSSE) %>%
  filter(Until_Year == 2020) %>%
  rename(RMSE_2020 = RMSE)

merge(RMSE_until2019, RMSE_until2020, by = "Model") %>%
  select(!c(Until_Year.x, Until_Year.y)) %>%
  mutate(Diff_abs = RMSE_2020 - RMSE_2019) %>%
  mutate(Diff_rel = Diff_abs/(RMSE_2020 - Diff_abs)) %>%
  arrange(Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSE by including 2020 in Time Series</span>", format.args = list(big.mark = ","), digits = c(0,2,2,2,4), align = "lcccc") %>%
  column_spec(2:5, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Change of RMSE by including 2020 in Time Series

Model	RMSE_2019	RMSE_2020	Diff_abs	Diff_rel
Naive	56,208.84	60,227.48	4,018.64	0.0715
Drift_STL	21,577.49	27,630.23	6,052.74	0.2805
TSLM_log	30,199.82	48,478.65	18,278.83	0.6053
ARIMA_d1D1	17,058.72	29,165.25	12,106.53	0.7097
ARIMA_auto	17,283.48	30,526.31	13,242.83	0.7662
ARIMA_d0D1	16,883.04	30,274.95	13,391.91	0.7932
SNaive	23,520.64	42,516.00	18,995.36	0.8076
Prophet_log	20,196.16	36,999.78	16,803.61	0.8320
ETS_auto_log	15,918.56	29,984.66	14,066.10	0.8836
HWA_log	15,354.53	30,982.96	15,628.43	1.0178

rm(RMSE_until2019, RMSE_until2020) # remove variables from R environment

2.3.2.6 RMSE per Year

All Models

# Calculate RMSE per year and save as tsibble
rmse_pyear_alentejo_slide <- error_fc_alentejo_slide %>%
  mutate(Year = year(Month)) %>%
  index_by(Year) %>%
  group_by(Model) %>%
  summarise(RMSE = (mean(Forecast_Error**2))**0.5)

# Create Plot for 2010-2022
rmse_pyear_alentejo_slide %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Create Plot for 2020-2022
rmse_pyear_alentejo_slide %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2))

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_alentejo_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	91,140.01	16,636.19	0.2233
Naive_log	95,104.26	18,477.53	0.2411
TSLM	116,641.52	71,185.04	1.5660
Prophet	117,409.56	72,554.51	1.6175
Drift_STL	61,170.64	40,819.09	2.0057
Drift_STL_log	70,059.59	54,375.58	3.4669
SNaive	119,797.78	93,083.13	3.4843
ETS_auto_log	85,766.40	68,361.23	3.9276
SNaive_log	132,405.40	108,128.34	4.4539
ARIMA_d1D1	80,291.54	66,199.23	4.6975
ARIMA_d0D1_log	86,659.15	71,610.39	4.7586
ARIMA_d0D1	85,040.74	70,330.09	4.7809
ARIMA_auto_log	86,728.50	71,820.40	4.8175
HWA	86,887.80	72,224.86	4.9257
ARIMA_d1D1_log	95,490.95	79,526.76	4.9816
ARIMA_auto	85,224.55	71,132.24	5.0476
Prophet_log	104,785.34	87,803.98	5.1706
HWA_log	90,563.60	77,421.34	5.8910
ETS_auto	99,057.85	86,525.70	6.9043
TSLM_log	129,351.00	117,201.24	9.6464

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_alentejo_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_d0D1	22,731.47	-62,309.28	-0.7327
ARIMA_auto	23,107.98	-62,116.57	-0.7289
HWA_log	25,190.03	-65,373.57	-0.7219
ARIMA_d0D1_log	25,195.07	-61,464.08	-0.7093
ARIMA_auto_log	26,254.52	-60,473.97	-0.6973
ARIMA_d1D1	24,716.89	-55,574.64	-0.6922
ETS_auto_log	26,639.49	-59,126.90	-0.6894
Drift_STL_log	22,970.41	-47,089.18	-0.6721
HWA	31,039.54	-55,848.26	-0.6428
Drift_STL	27,169.55	-34,001.09	-0.5558
ARIMA_d1D1_log	42,502.48	-52,988.47	-0.5549
TSLM_log	57,965.77	-71,385.23	-0.5519
SNaive_log	74,297.32	-58,108.07	-0.4389
Prophet	67,874.80	-49,534.76	-0.4219
ETS_auto	62,799.30	-36,258.55	-0.3660
TSLM	74,512.75	-42,128.77	-0.3612
SNaive	80,510.21	-39,287.58	-0.3279
Naive	79,953.53	-11,186.48	-0.1227
Naive_log	84,281.11	-10,823.15	-0.1138
Prophet_log	102,658.02	-2,127.32	-0.0203

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_alentejo_slide %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ETS_auto	26,586.22	-36,213.08	-0.5766
Naive_log	35,907.41	-48,373.70	-0.5740
TSLM	33,147.51	-41,365.25	-0.5551
Naive	43,887.16	-36,066.38	-0.4511
TSLM_log	40,002.45	-17,963.32	-0.3099
Prophet_log	71,689.59	-30,968.43	-0.3017
Prophet	52,905.21	-14,969.59	-0.2205
HWA	25,543.36	-5,496.18	-0.1771
Drift_STL	25,736.78	-1,432.76	-0.0527
SNaive_log	89,711.05	15,413.72	0.2075
SNaive	100,749.18	20,238.97	0.2514
ARIMA_d1D1_log	69,558.32	27,055.83	0.6366
ARIMA_d1D1	45,127.65	20,410.76	0.8258
ETS_auto_log	50,300.56	23,661.07	0.8882
ARIMA_auto	46,697.81	23,589.83	1.0209
HWA_log	51,243.15	26,053.12	1.0343
ARIMA_d0D1	46,697.81	23,966.34	1.0543
ARIMA_auto_log	64,397.05	38,142.53	1.4528
ARIMA_d0D1_log	64,397.05	39,201.98	1.5559
Drift_STL_log	77,634.99	54,664.58	2.3798

Each Model once

# Create Plot for 2010-2022
rmse_pyear_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2010-2022")

# Create Plot for 2020-2022
rmse_pyear_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  filter(Year > 2019) %>%
  autoplot(RMSE) +
  ggtitle("RMSE per Year: 2020-2022")

# Show RMSE of 2020 with Difference to previous Year
rmse_pyear_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2020) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2020 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2020 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	91,140.01	16,636.19	0.2233
Drift_STL	61,170.64	40,819.09	2.0057
SNaive	119,797.78	93,083.13	3.4843
ETS_auto_log	85,766.40	68,361.23	3.9276
ARIMA_d1D1	80,291.54	66,199.23	4.6975
ARIMA_d0D1	85,040.74	70,330.09	4.7809
ARIMA_auto	85,224.55	71,132.24	5.0476
Prophet_log	104,785.34	87,803.98	5.1706
HWA_log	90,563.60	77,421.34	5.8910
TSLM_log	129,351.00	117,201.24	9.6464

# Show RMSE of 2021 with Difference to previous Year
rmse_pyear_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2021) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2021 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2021 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
ARIMA_d0D1	22,731.47	-62,309.28	-0.7327
ARIMA_auto	23,107.98	-62,116.57	-0.7289
HWA_log	25,190.03	-65,373.57	-0.7219
ARIMA_d1D1	24,716.89	-55,574.64	-0.6922
ETS_auto_log	26,639.49	-59,126.90	-0.6894
Drift_STL	27,169.55	-34,001.09	-0.5558
TSLM_log	57,965.77	-71,385.23	-0.5519
SNaive	80,510.21	-39,287.58	-0.3279
Naive	79,953.53	-11,186.48	-0.1227
Prophet_log	102,658.02	-2,127.32	-0.0203

# Show RMSE of 2022 with Difference to previous Year
rmse_pyear_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  mutate(RMSE_Diff_abs = difference(RMSE,1)) %>%
  filter(Year == 2022) %>%
  as_tibble() %>%
  select(!Year) %>%
  mutate(RMSE_Diff_rel = RMSE_Diff_abs / (RMSE - RMSE_Diff_abs)) %>%
  arrange(RMSE_Diff_rel) %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of 2022 with Difference to previous Year</span>", format.args = list(big.mark = ","), digits = c(0,2,2,4), align = "lccc") %>%
  column_spec(2:4, border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), fixed_thead = T, full_width = F)

RMSE of 2022 with Difference to previous Year

Model	RMSE	RMSE_Diff_abs	RMSE_Diff_rel
Naive	43,887.16	-36,066.38	-0.4511
TSLM_log	40,002.45	-17,963.32	-0.3099
Prophet_log	71,689.59	-30,968.43	-0.3017
Drift_STL	25,736.78	-1,432.76	-0.0527
SNaive	100,749.18	20,238.97	0.2514
ARIMA_d1D1	45,127.65	20,410.76	0.8258
ETS_auto_log	50,300.56	23,661.07	0.8882
ARIMA_auto	46,697.81	23,589.83	1.0209
HWA_log	51,243.15	26,053.12	1.0343
ARIMA_d0D1	46,697.81	23,966.34	1.0543

2.3.2.7 Change of RMSSE: 2010-2019 vs. 2010-2022

All Models

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2019) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2022) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
Drift_STL	13	1.1836	1	0.7115
Drift_STL_log	4	0.8333	2	0.7584
ARIMA_d1D1	9	0.9358	3	0.7664
ARIMA_d0D1	8	0.9261	4	0.7906
ETS_auto_log	6	0.8732	5	0.7965
ARIMA_auto	10	0.9481	6	0.7968
ARIMA_d0D1_log	2	0.8078	7	0.8138
ARIMA_auto_log	3	0.8110	8	0.8166
HWA_log	5	0.8423	9	0.8177
HWA	12	1.1512	10	0.8415
ARIMA_d1D1_log	1	0.7675	11	0.9045
ETS_auto	7	0.8804	12	0.9445
Prophet_log	11	1.1079	13	1.2272
TSLM_log	16	1.6566	14	1.2668
SNaive	15	1.2902	15	1.2966
SNaive_log	14	1.2259	16	1.3095
Prophet	17	2.0402	17	1.3408
TSLM	18	2.1913	18	1.3809
Naive	19	3.0834	19	1.5896
Naive_log	20	3.1563	20	1.6334

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

Each Model once

# Calculate RMSSE for 2010-2019 and according Rank
accuracy_2019 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2019) %>%
  filter(.model %in% best_models_fc_alentejo_slide) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2019 = row_number()) %>%
  rename(Model = .model, RMSSE_2019 = RMSSE) %>%
  select(c(Rank_2019, Model, RMSSE_2019))

# Calculate RMSSE for 2010-2022 and according Rank
accuracy_2022 <- accuracy(fc_alentejo_slide, tourism_alentejo_until2022) %>%
  filter(.model %in% best_models_fc_alentejo_slide) %>%
  arrange(RMSSE) %>%
  mutate(Rank_2022 = row_number()) %>%
  rename(Model = .model, RMSSE_2022 = RMSSE) %>%
  select(c(Rank_2022, Model, RMSSE_2022))

# Merge in one table
summary <- merge(accuracy_2019, accuracy_2022, by = "Model") %>% arrange(Rank_2022)
colnames(summary) <- c("Model", "Rank", "RMSSE", "Rank", "RMSSE")

# Show table
summary %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Change of RMSSE: 2010-2019 vs. 2010-2022</span>", digits = 4, format.args = list(big.mark = ","), align = "lcccc") %>%
  column_spec(c(2, 4), border_left = T) %>%
  column_spec(c(2, 4), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F) %>%
  add_header_above(c(" " = 1, "2010-2019" = 2, "2010-2022" = 2))

Change of RMSSE: 2010-2019 vs. 2010-2022

	2010-2019		2010-2022
Model	Rank	RMSSE	Rank	RMSSE
Drift_STL	7	1.1836	1	0.7115
ARIMA_d1D1	4	0.9358	2	0.7664
ARIMA_d0D1	3	0.9261	3	0.7906
ETS_auto_log	2	0.8732	4	0.7965
ARIMA_auto	5	0.9481	5	0.7968
HWA_log	1	0.8423	6	0.8177
Prophet_log	6	1.1079	7	1.2272
TSLM_log	9	1.6566	8	1.2668
SNaive	8	1.2902	9	1.2966
Naive	10	3.0834	10	1.5896

rm(accuracy_2019, accuracy_2022, summary) # remove variables from R environment

2.3.2.8 RMSSE Development by including more Years in Time Series

All Models

# Plot development of RMSSE for period 2010-2022
accuracy_alentejo_slide %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_alentejo_slide %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_alentejo_slide %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  guides(color = guide_legend(title = "Model", ncol = 2)) +
  xlab("Until Year") +
  ylab("RMSSE")

Each Model once

# Plot development of RMSSE for period 2010-2022
accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "2010 - 2022") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2010-2019
accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  filter(Until_Year <= 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2010-2019") +
  xlab("Until Year") +
  ylab("RMSSE")

# Zooming in 2020-2022
accuracy_alentejo_slide %>%
  filter(Model %in% best_models_fc_alentejo_slide) %>%
  filter(Until_Year > 2019) %>%
  autoplot(RMSSE) +
  ggtitle("RMSSE Development by including more Years in Time Series", subtitle = "Zooming in 2020-2022") +
  xlab("Until Year") +
  ylab("RMSSE")

3 Improving Forecasting Accuracy after Data Anomalies

3.1 Madeira

3.1.1 Outliers: March 2020 to June 2021

3.1.1.1 Outlier Adjustment to Mean per Month of previous 20 years

# Calculate mean per month of 20 years before outliers
madeira_mean_month_20years <- tourism_madeira_until2022 %>%
  filter_index("Mar 2000" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
madeira_mean_month_20years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 20 Years: <br> Mar 2000 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 20 Years:
Mar 2000 - Feb 2020

Month_number	Mean_per_Month
1	389,992.7
2	424,554.5
3	511,037.6
4	557,813.0
5	558,370.0
6	549,829.0
7	611,449.4
8	703,858.2
9	589,975.3
10	527,767.7
11	423,080.6
12	364,309.1

# Save outliers from Mar 2020 to Jun 2021 in tsibble
madeira_outliers_until_jun21 <- tourism_madeira_until2022 %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(madeira_outliers_until_jun21, madeira_mean_month_20years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_until_feb20 <- tourism_madeira_until2022 %>%
  filter_index("Jan 2000" ~ "Feb 2020")

tourism_madeira_from_jul21 <- tourism_madeira_until2022 %>%
  filter_index("Jul 2021" ~ "Jun 2022")

tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jul21)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_20years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.1.2 Outlier Adjustment to Mean per Month of previous 10 years

# Calculate mean per month of 10 years before outliers
madeira_mean_month_10years <- tourism_madeira_until2022 %>%
  filter_index("Mar 2010" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
madeira_mean_month_10years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 10 Years: <br> Mar 2010 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 10 Years:
Mar 2010 - Feb 2020

Month_number	Mean_per_Month
1	413,265.1
2	450,020.2
3	526,686.8
4	578,631.8
5	626,894.2
6	634,106.0
7	711,383.0
8	797,182.4
9	673,678.3
10	586,737.0
11	449,147.8
12	381,301.0

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(madeira_outliers_until_jun21, madeira_mean_month_10years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jul21)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_10years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.1.3 Outlier Adjustment to Mean per Month of previous 5 years

# Calculate mean per month of 5 years before outliers
madeira_mean_month_5years <- tourism_madeira_until2022 %>%
  filter_index("Mar 2015" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
madeira_mean_month_5years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 5 Years: <br> Mar 2015 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 5 Years:
Mar 2015 - Feb 2020

Month_number	Mean_per_Month
1	492,297.2
2	528,344.6
3	612,777.4
4	651,610.6
5	704,457.8
6	740,951.6
7	813,006.6
8	884,893.6
9	761,823.4
10	677,198.0
11	537,370.8
12	457,088.0

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(madeira_outliers_until_jun21, madeira_mean_month_5years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jul21)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_5years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.1.4 Outlier Adjustment by 50% to Mean per Month of previous 20 years

# Save tourism data until 2022 with month number
tourism_madeira_until2022_month_number <- tourism_madeira_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_madeira_until2022_month_number, madeira_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jul21)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_20years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.1.5 Outlier Adjustment by 50% to Mean per Month of previous 10 years

# Save tourism data until 2022 with month number
tourism_madeira_until2022_month_number <- tourism_madeira_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_madeira_until2022_month_number, madeira_mean_month_10years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jul21)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_10years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.1.6 Outlier Adjustment by 50% to Mean per Month of previous 5 years

# Save tourism data until 2022 with month number
tourism_madeira_until2022_month_number <- tourism_madeira_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_madeira_until2022_month_number, madeira_mean_month_5years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jul21)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_5years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.1.7 Summary of Results

# RMSE with original outliers
RMSE_original_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(RMSE_original_Outliers = (mean(Forecast_Error**2))**0.5)

# Merge all calculated RMSE's
RMSE_adjusted_outliers_summary_1 <- cbind(RMSE_original_outliers, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_5years,RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_5years)

rownames(RMSE_adjusted_outliers_summary_1) <- "RMSE"

RMSE_adjusted_outliers_summary_1 <- as.data.frame(t(head(RMSE_adjusted_outliers_summary_1)))

# Show df
RMSE_adjusted_outliers_summary_1 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of various Approaches for Madeira: <br> Forecasts July 2021 - June 2022</span>", digits = 2, format.args = list(big.mark = ","), align = "c") %>%
  column_spec(c(2), border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

RMSE of various Approaches for Madeira:
Forecasts July 2021 - June 2022

	RMSE
RMSE_original_Outliers	81,986.40
Adj_Outliers_20years	73,981.28
Adj_Outliers_10years	83,522.77
Adj_Outliers_5years	100,134.13
Adj_outliers_50perc_20years	74,280.56
Adj_outliers_50perc_10years	75,096.66
Adj_outliers_50perc_5years	79,291.27

3.1.2 Outliers: March 2020 to December 2021

3.1.2.1 Outlier Adjustment to Mean per Month of previous 20 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
madeira_outliers_until_dec21 <- tourism_madeira_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(madeira_outliers_until_dec21, madeira_mean_month_20years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_from_jan22 <- tourism_madeira_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jan22)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_20years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.2.2 Outlier Adjustment to Mean per Month of previous 10 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
madeira_outliers_until_dec21 <- tourism_madeira_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(madeira_outliers_until_dec21, madeira_mean_month_10years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_from_jan22 <- tourism_madeira_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jan22)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_10years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.2.3 Outlier Adjustment to Mean per Month of previous 5 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
madeira_outliers_until_dec21 <- tourism_madeira_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(madeira_outliers_until_dec21, madeira_mean_month_5years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_from_jan22 <- tourism_madeira_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jan22)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_5years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.2.4 Outlier Adjustment by 50% to Mean per Month of previous 20 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_madeira_until2022_month_number, madeira_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jan22)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_20years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.2.5 Outlier Adjustment by 50% to Mean per Month of previous 10 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_madeira_until2022_month_number, madeira_mean_month_10years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jan22)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_10years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.2.6 Outlier Adjustment by 50% to Mean per Month of previous 5 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_madeira_until2022_month_number, madeira_mean_month_5years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_madeira_adjusted_outliers <- bind_rows(tourism_madeira_until_feb20, adjusted_outliers, tourism_madeira_from_jan22)

# Show adjusted time series
tourism_madeira_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_madeira_adjusted_outliers <- tourism_madeira_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_madeira_stretch_adjusted_outliers <- data_stretch_madeira_adjusted_outliers %>%
  model(ARIMA_d0D1 = ARIMA(Overnight_Stays ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_madeira_stretch_adjusted_outliers <- fit_madeira_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_madeira_stretch_adjusted_outliers <- merge(tourism_madeira_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, by = "Month") %>%
  filter(.model == "ARIMA_d0D1") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_5years <- error_fc_madeira_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_madeira_stretch_adjusted_outliers <- error_fc_madeira_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_madeira_stretch_orig_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_madeira_stretch_adjusted_outliers, error_fc_madeira_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_madeira_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.1.2.7 Summary of Results

# RMSE with original outliers
RMSE_original_outliers <- error_fc_madeira_stretch %>%
  filter(Model == "ARIMA_d0D1") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(RMSE_original_Outliers = (mean(Forecast_Error**2))**0.5)

# Merge all calculated RMSE's
RMSE_adjusted_outliers_summary_2 <- cbind(RMSE_original_outliers, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_5years, RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_5years)

rownames(RMSE_adjusted_outliers_summary_2) <- "RMSE"

RMSE_adjusted_outliers_summary_2 <- as.data.frame(t(head(RMSE_adjusted_outliers_summary_2)))

# Show df
RMSE_adjusted_outliers_summary_2 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of various Approaches for Madeira: <br> Forecasts January 2022 - June 2022</span>", digits = 2, format.args = list(big.mark = ","), align = "c") %>%
  column_spec(c(2), border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

RMSE of various Approaches for Madeira:
Forecasts January 2022 - June 2022

	RMSE
RMSE_original_Outliers	94,935.39
Adj_Outliers_20years	76,633.71
Adj_Outliers_10years	78,499.72
Adj_Outliers_5years	86,592.24
Adj_outliers_50perc_20years	87,414.02
Adj_outliers_50perc_10years	87,919.24
Adj_outliers_50perc_5years	92,754.84

3.2 Algarve

3.2.1 Outliers: March 2020 to June 2021

3.2.1.1 Outlier Adjustment to Mean per Month of previous 20 years

# Calculate mean per month of 20 years before outliers
algarve_mean_month_20years <- tourism_algarve_until2022 %>%
  filter_index("Mar 2000" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
algarve_mean_month_20years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 20 Years: <br> Mar 2000 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 20 Years:
Mar 2000 - Feb 2020

Month_number	Mean_per_Month
1	448,554.7
2	641,274.4
3	897,424.3
4	1,194,294.0
5	1,436,188.4
6	1,790,289.6
7	2,281,235.5
8	2,649,770.2
9	1,892,266.9
10	1,343,444.9
11	557,959.3
12	430,118.3

# Save outliers from Mar 2020 to Jun 2021 in tsibble
algarve_outliers_until_jun21 <- tourism_algarve_until2022 %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(algarve_outliers_until_jun21, algarve_mean_month_20years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_until_feb20 <- tourism_algarve_until2022 %>%
  filter_index("Jan 2000" ~ "Feb 2020")

tourism_algarve_from_jul21 <- tourism_algarve_until2022 %>%
  filter_index("Jul 2021" ~ "Jun 2022")

tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jul21)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_20years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.1.2 Outlier Adjustment to Mean per Month of previous 10 years

# Calculate mean per month of 10 years before outliers
algarve_mean_month_10years <- tourism_algarve_until2022 %>%
  filter_index("Mar 2010" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
algarve_mean_month_10years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 10 Years: <br> Mar 2010 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 10 Years:
Mar 2010 - Feb 2020

Month_number	Mean_per_Month
1	439,726.8
2	632,797.0
3	900,664.8
4	1,313,506.6
5	1,583,948.3
6	2,011,993.6
7	2,594,789.4
8	2,991,767.9
9	2,140,784.9
10	1,542,647.2
11	568,957.8
12	436,091.0

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(algarve_outliers_until_jun21, algarve_mean_month_10years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jul21)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_10years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.1.3 Outlier Adjustment to Mean per Month of previous 5 years

# Calculate mean per month of 5 years before outliers
algarve_mean_month_5years <- tourism_algarve_until2022 %>%
  filter_index("Mar 2015" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
algarve_mean_month_5years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 5 Years: <br> Mar 2015 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 5 Years:
Mar 2015 - Feb 2020

Month_number	Mean_per_Month
1	510,348.2
2	736,825.6
3	1,032,451.4
4	1,542,778.8
5	1,889,483.0
6	2,318,381.8
7	2,895,246.4
8	3,283,799.8
9	2,423,698.4
10	1,829,294.0
11	680,936.2
12	515,028.0

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(algarve_outliers_until_jun21, algarve_mean_month_5years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jul21)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_5years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.1.4 Outlier Adjustment by 50% to Mean per Month of previous 20 years

# Save tourism data until 2022 with month number
tourism_algarve_until2022_month_number <- tourism_algarve_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_algarve_until2022_month_number, algarve_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jul21)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_20years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.1.5 Outlier Adjustment by 50% to Mean per Month of previous 10 years

# Save tourism data until 2022 with month number
tourism_algarve_until2022_month_number <- tourism_algarve_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_algarve_until2022_month_number, algarve_mean_month_10years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jul21)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_10years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.1.6 Outlier Adjustment by 50% to Mean per Month of previous 5 years

# Save tourism data until 2022 with month number
tourism_algarve_until2022_month_number <- tourism_algarve_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_algarve_until2022_month_number, algarve_mean_month_5years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jul21)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_5years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.1.7 Summary of Results

# RMSE with original outliers
RMSE_original_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(RMSE_original_Outliers = (mean(Forecast_Error**2))**0.5)

# Merge all calculated RMSE's
RMSE_adjusted_outliers_summary_3 <- cbind(RMSE_original_outliers, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_5years, RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_5years)

rownames(RMSE_adjusted_outliers_summary_3) <- "RMSE"

RMSE_adjusted_outliers_summary_3 <- as.data.frame(t(head(RMSE_adjusted_outliers_summary_3)))

# Show df
RMSE_adjusted_outliers_summary_3 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of various Approaches for Algarve: <br> Forecasts July 2021 - June 2022</span>", digits = 2, format.args = list(big.mark = ","), align = "c") %>%
  column_spec(c(2), border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

RMSE of various Approaches for Algarve:
Forecasts July 2021 - June 2022

	RMSE
RMSE_original_Outliers	287,110.3
Adj_Outliers_20years	331,018.1
Adj_Outliers_10years	360,154.7
Adj_Outliers_5years	407,568.8
Adj_outliers_50perc_20years	295,402.5
Adj_outliers_50perc_10years	306,838.6
Adj_outliers_50perc_5years	322,928.8

3.2.2 Outliers: March 2020 to December 2021

3.2.2.1 Outlier Adjustment to Mean per Month of previous 20 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
algarve_outliers_until_dec21 <- tourism_algarve_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(algarve_outliers_until_dec21, algarve_mean_month_20years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_from_jan22 <- tourism_algarve_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jan22)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_20years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.2.2 Outlier Adjustment to Mean per Month of previous 10 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
algarve_outliers_until_dec21 <- tourism_algarve_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(algarve_outliers_until_dec21, algarve_mean_month_10years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_from_jan22 <- tourism_algarve_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jan22)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_10years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.2.3 Outlier Adjustment to Mean per Month of previous 5 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
algarve_outliers_until_dec21 <- tourism_algarve_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(algarve_outliers_until_dec21, algarve_mean_month_5years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_from_jan22 <- tourism_algarve_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jan22)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_5years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.2.4 Outlier Adjustment by 50% to Mean per Month of previous 20 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_algarve_until2022_month_number, algarve_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jan22)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_20years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.2.5 Outlier Adjustment by 50% to Mean per Month of previous 10 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_algarve_until2022_month_number, algarve_mean_month_10years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jan22)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_10years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.2.6 Outlier Adjustment by 50% to Mean per Month of previous 5 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_algarve_until2022_month_number, algarve_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_algarve_adjusted_outliers <- bind_rows(tourism_algarve_until_feb20, adjusted_outliers, tourism_algarve_from_jan22)

# Show adjusted time series
tourism_algarve_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_algarve_adjusted_outliers <- tourism_algarve_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_algarve_stretch_adjusted_outliers <- data_stretch_algarve_adjusted_outliers %>%
  model(ARIMA_auto = ARIMA(Overnight_Stays))

# Perform a one-step ahead Forecast
fc_algarve_stretch_adjusted_outliers <- fit_algarve_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_algarve_stretch_adjusted_outliers <- merge(tourism_algarve_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_5years <- error_fc_algarve_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_algarve_stretch_adjusted_outliers <- error_fc_algarve_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_algarve_stretch_orig_outliers <- error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_algarve_stretch_adjusted_outliers, error_fc_algarve_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_algarve_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.2.2.7 Summary of Results

# RMSE with original outliers
error_fc_algarve_stretch %>%
  filter(Model == "ARIMA_auto") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(RMSE_original_Outliers = (mean(Forecast_Error**2))**0.5)

# Merge all calculated RMSE's
RMSE_adjusted_outliers_summary_4 <- cbind(RMSE_original_outliers, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_5years, RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_5years)

rownames(RMSE_adjusted_outliers_summary_4) <- "RMSE"

RMSE_adjusted_outliers_summary_4 <- as.data.frame(t(head(RMSE_adjusted_outliers_summary_4)))

# Show df
RMSE_adjusted_outliers_summary_4 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of various Approaches for Algarve: <br> Forecasts January 2022 - June 2022</span>", digits = 2, format.args = list(big.mark = ","), align = "c") %>%
  column_spec(c(2), border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

RMSE of various Approaches for Algarve:
Forecasts January 2022 - June 2022

	RMSE
RMSE_original_Outliers	287,110.3
Adj_Outliers_20years	183,863.7
Adj_Outliers_10years	156,644.1
Adj_Outliers_5years	118,427.7
Adj_outliers_50perc_20years	238,534.1
Adj_outliers_50perc_10years	226,337.9
Adj_outliers_50perc_5years	238,534.1

3.3 Alentejo

3.3.1 Outliers: March 2020 to June 2021

3.3.1.1 Outlier Adjustment to Mean per Month of previous 20 years

# Calculate mean per month of 20 years before outliers
alentejo_mean_month_20years <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2000" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
alentejo_mean_month_20years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 20 Years: <br> Mar 2000 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 20 Years:
Mar 2000 - Feb 2020

Month_number	Mean_per_Month
1	62,461.90
2	76,166.15
3	93,329.85
4	118,244.05
5	123,209.60
6	136,627.20
7	166,659.40
8	236,181.80
9	154,966.75
10	116,416.40
11	81,721.15
12	74,560.40

# Save outliers from Mar 2020 to Jun 2021 in tsibble
alentejo_outliers_until_jun21 <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(alentejo_outliers_until_jun21, alentejo_mean_month_20years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_until_feb20 <- tourism_alentejo_until2022 %>%
  filter_index("Jan 2000" ~ "Feb 2020")

tourism_alentejo_from_jul21 <- tourism_alentejo_until2022 %>%
  filter_index("Jul 2021" ~ "Jun 2022")

tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jul21)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_20years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.1.2 Outlier Adjustment to Mean per Month of previous 10 years

# Calculate mean per month of 10 years before outliers
alentejo_mean_month_10years <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2010" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
alentejo_mean_month_10years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 10 Years: <br> Mar 2010 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 10 Years:
Mar 2010 - Feb 2020

Month_number	Mean_per_Month
1	78,012.7
2	94,635.7
3	114,551.2
4	148,794.4
5	160,801.8
6	186,060.4
7	230,198.1
8	324,291.0
9	211,539.1
10	154,494.7
11	100,918.3
12	93,500.1

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(alentejo_outliers_until_jun21, alentejo_mean_month_10years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jul21)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1))    )

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_10years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.1.3 Outlier Adjustment to Mean per Month of previous 5 years

# Calculate mean per month of 5 years before outliers
alentejo_mean_month_5years <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2015" ~ "Feb 2020") %>%
  mutate(Month_number = month(Month)) %>%
  as_tibble() %>%
  select("Overnight_Stays", "Month_number") %>%
  group_by(Month_number) %>%
  summarize(Mean_per_Month = mean(Overnight_Stays))

# Show table
alentejo_mean_month_5years %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Mean per Month of 5 Years: <br> Mar 2015 - Feb 2020</span>", digits = 2, format.args = list(big.mark = ","), align = "cc") %>%
  column_spec(c(1), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

Mean per Month of 5 Years:
Mar 2015 - Feb 2020

Month_number	Mean_per_Month
1	98,866.6
2	122,616.2
3	143,394.4
4	189,090.2
5	207,287.6
6	243,556.6
7	306,709.2
8	420,233.8
9	277,053.4
10	201,219.8
11	130,138.0
12	120,171.8

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(alentejo_outliers_until_jun21, alentejo_mean_month_5years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jul21)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_5years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.1.4 Outlier Adjustment by 50% to Mean per Month of previous 20 years

# Save tourism data until 2022 with month number
tourism_alentejo_until2022_month_number <- tourism_alentejo_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_alentejo_until2022_month_number, alentejo_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jul21)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_20years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.1.5 Outlier Adjustment by 50% to Mean per Month of previous 10 years

# Save tourism data until 2022 with month number
tourism_alentejo_until2022_month_number <- tourism_alentejo_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_alentejo_until2022_month_number, alentejo_mean_month_10years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jul21)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_10years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.1.6 Outlier Adjustment by 50% to Mean per Month of previous 5 years

# Save tourism data until 2022 with month number
tourism_alentejo_until2022_month_number <- tourism_alentejo_until2022 %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_alentejo_until2022_month_number, alentejo_mean_month_5years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Jun 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jul21)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_5years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jul21, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.1.7 Summary of Results

# RMSE with original outliers
RMSE_original_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jul 2021" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(RMSE_original_Outliers = (mean(Forecast_Error**2))**0.5)

# Merge all calculated RMSE's
RMSE_adjusted_outliers_summary_5 <- cbind(RMSE_original_outliers, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_5years, RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_5years)

rownames(RMSE_adjusted_outliers_summary_5) <- "RMSE"

RMSE_adjusted_outliers_summary_5 <- as.data.frame(t(head(RMSE_adjusted_outliers_summary_5)))

# Show df
RMSE_adjusted_outliers_summary_5 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of various Approaches for Alentejo: <br> Forecasts July 2021 - June 2022</span>", digits = 2, format.args = list(big.mark = ","), align = "c") %>%
  column_spec(c(2), border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

RMSE of various Approaches for Alentejo:
Forecasts July 2021 - June 2022

	RMSE
RMSE_original_Outliers	36,532.77
Adj_Outliers_20years	55,061.13
Adj_Outliers_10years	38,327.68
Adj_Outliers_5years	19,643.98
Adj_outliers_50perc_20years	30,140.17
Adj_outliers_50perc_10years	28,091.84
Adj_outliers_50perc_5years	29,268.17

3.3.2 Outliers: March 2020 to December 2021

3.3.2.1 Outlier Adjustment to Mean per Month of previous 20 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
alentejo_outliers_until_dec21 <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(alentejo_outliers_until_dec21, alentejo_mean_month_20years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_from_jan22 <- tourism_alentejo_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jan22)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_20years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.2.2 Outlier Adjustment to Mean per Month of previous 10 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
alentejo_outliers_until_dec21 <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(alentejo_outliers_until_dec21, alentejo_mean_month_10years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_from_jan22 <- tourism_alentejo_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jan22)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_10years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.2.3 Outlier Adjustment to Mean per Month of previous 5 years

# Save outliers from Mar 2020 to Dec 2021 in tsibble
alentejo_outliers_until_dec21 <- tourism_alentejo_until2022 %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Month_number = month(Month))

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(alentejo_outliers_until_dec21, alentejo_mean_month_5years, by = "Month_number") %>%
  select(Region, Month, Mean_per_Month) %>%
  rename(Overnight_Stays = Mean_per_Month) %>%
  as_tsibble(key = Region, index = Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_from_jan22 <- tourism_alentejo_until2022 %>%
  filter_index("Jan 2022" ~ "Jun 2022")

tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jan22)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays-Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_5years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_Outliers_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.2.4 Outlier Adjustment by 50% to Mean per Month of previous 20 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_alentejo_until2022_month_number, alentejo_mean_month_20years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jan22)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_20years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_20years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.2.5 Outlier Adjustment by 50% to Mean per Month of previous 10 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_alentejo_until2022_month_number, alentejo_mean_month_10years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jan22)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_10years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_10years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.2.6 Outlier Adjustment by 50% to Mean per Month of previous 5 years

# Calculate adjusted outliers and save in tsibble
adjusted_outliers <- merge(tourism_alentejo_until2022_month_number, alentejo_mean_month_5years, by = "Month_number") %>%
  as_tsibble(key = Region, index = Month) %>%
  filter_index("Mar 2020" ~ "Dec 2021") %>%
  mutate(Overnight_Stays = 0.5*Overnight_Stays + 0.5*Mean_per_Month)

# Create tsibble of whole time series with adjusted outliers
tourism_alentejo_adjusted_outliers <- bind_rows(tourism_alentejo_until_feb20, adjusted_outliers, tourism_alentejo_from_jan22)

# Show adjusted time series
tourism_alentejo_adjusted_outliers %>%
  autoplot(Overnight_Stays) +
  ggtitle("Time Series with adjusted Outliers")

# Perform forecasting competition with stretch tsibble based on adjusted outliers

# Cross-Validation with stretching Window to create Training sets
data_stretch_alentejo_adjusted_outliers <- tourism_alentejo_adjusted_outliers %>%
  stretch_tsibble(.init = 120, .step = 1) %>%
  filter (.id != max(.id))

# Fit models
fit_alentejo_stretch_adjusted_outliers <- data_stretch_alentejo_adjusted_outliers %>%
  model(ARIMA_d0D1_log = ARIMA(log(Overnight_Stays) ~ pdq(d=0) + PDQ(D=1)))

# Perform a one-step ahead Forecast
fc_alentejo_stretch_adjusted_outliers <- fit_alentejo_stretch_adjusted_outliers %>% forecast(h=1)

# Calculate forecast error per observation
error_fc_alentejo_stretch_adjusted_outliers <- merge(tourism_alentejo_adjusted_outliers, fc_alentejo_stretch_adjusted_outliers, by = "Month") %>%
  select(Month,Overnight_Stays.x, .model, .mean) %>%
  rename(Point_Forecast = .mean, Overnight_Stays = Overnight_Stays.x, Model = .model) %>%
  mutate(Forecast_Error = Overnight_Stays - Point_Forecast) %>%
  as_tsibble(index = Month, key = Model)

# RMSE with adjusted outliers
RMSE_adjusted_outliers_50perc_5years <- error_fc_alentejo_stretch_adjusted_outliers %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(Adj_outliers_50perc_5years = (mean(Forecast_Error**2))**0.5)

# Show Point Forecasts in Plot
error_fc_alentejo_stretch_adjusted_outliers <- error_fc_alentejo_stretch_adjusted_outliers %>%
  mutate(Database = "Adjusted Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

error_fc_alentejo_stretch_orig_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  mutate(Database = "Original Outliers") %>%
  as_tsibble(index = "Month", key = "Database")

bind_rows(error_fc_alentejo_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers) %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  autoplot(Point_Forecast) +
  autolayer(tourism_alentejo_from_jan22, .vars = Overnight_Stays) +
  ggtitle("Point Forecasts") +
  ylab("Overnight_Stays") +
  guides(color = guide_legend(title = "Database contains"))

3.3.2.7 Summary of Results

RMSE_original_outliers <- error_fc_alentejo_stretch %>%
  filter(Model == "ARIMA_d0D1_log") %>%
  filter_index("Jan 2022" ~ "Jun 2022") %>%
  as_tibble() %>%
  summarise(RMSE_original_Outliers = (mean(Forecast_Error**2))**0.5)

# Merge all calculated RMSE's
RMSE_adjusted_outliers_summary_6 <- cbind(RMSE_original_outliers, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_5years, RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_5years)

rownames(RMSE_adjusted_outliers_summary_6) <- "RMSE"

RMSE_adjusted_outliers_summary_6 <- as.data.frame(t(head(RMSE_adjusted_outliers_summary_6)))

# Show df
RMSE_adjusted_outliers_summary_6 %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>RMSE of various Approaches for Alentejo: <br> Forecasts January 2022 - June 2022</span>", digits = 2, format.args = list(big.mark = ","), align = "c") %>%
  column_spec(c(2), border_left = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = F)

RMSE of various Approaches for Alentejo:
Forecasts January 2022 - June 2022

	RMSE
RMSE_original_Outliers	49,126.65
Adj_Outliers_20years	32,692.21
Adj_Outliers_10years	28,368.60
Adj_Outliers_5years	20,489.61
Adj_outliers_50perc_20years	29,407.60
Adj_outliers_50perc_10years	29,168.61
Adj_outliers_50perc_5years	31,204.13

3.4 Overall Summary

# Merge all summaries
RMSE_adjusted_outliers_summary_total <- cbind(RMSE_adjusted_outliers_summary_1, RMSE_adjusted_outliers_summary_2, RMSE_adjusted_outliers_summary_3, RMSE_adjusted_outliers_summary_4, RMSE_adjusted_outliers_summary_5, RMSE_adjusted_outliers_summary_6)

rownames(RMSE_adjusted_outliers_summary_total) <- c("Original_Outliers", "Adj._Outliers_Mean_20yrs", "Adj._Outliers_Mean_10_yrs", "Adj._Outliers_Mean_5yrs", "Adj._Outliers_50%_Mean_20yrs", "Adj._Outliers_50%_Mean_10yrs", "Adj_Outliers_50%_Mean_5yrs")

colnames(RMSE_adjusted_outliers_summary_total) <- c("Outliers Mar 20 - Jun 21", "Outliers Mar 20 - Dec 21", "Outliers Mar 20 - Jun 21", "Outliers Mar 20 - Dec 21", "Outliers Mar 20 - Jun 21", "Outliers Mar 20 - Dec 21")

# Show df
RMSE_adjusted_outliers_summary_total %>%
  kbl(caption = "<span style='color:black;font-size:medium;font-weight:bold'>Impact of Outlier Adjustments on RMSE - Overall Summary for all three Regions</span>", digits = 2, format.args = list(big.mark = ","), align = "cccccc") %>%
  column_spec(c(2, 4, 6), border_left = T) %>%
  column_spec(c(2, 4, 6), border_right = "2px solid lightgray") %>%
  kable_styling(bootstrap_options = c("striped", "hover","condensed"), full_width = T) %>%
  add_header_above(c(" " = 1, "RMSE Madeira" = 2, "RMSE Algarve" = 2, "RMSE Alentejo" = 2))

Impact of Outlier Adjustments on RMSE - Overall Summary for all three Regions

	RMSE Madeira		RMSE Algarve		RMSE Alentejo
	Outliers Mar 20 - Jun 21	Outliers Mar 20 - Dec 21	Outliers Mar 20 - Jun 21	Outliers Mar 20 - Dec 21	Outliers Mar 20 - Jun 21	Outliers Mar 20 - Dec 21
Original_Outliers	81,986.40	94,935.39	287,110.3	287,110.3	36,532.77	49,126.65
Adj._Outliers_Mean_20yrs	73,981.28	76,633.71	331,018.1	183,863.7	55,061.13	32,692.21
Adj._Outliers_Mean_10_yrs	83,522.77	78,499.72	360,154.7	156,644.1	38,327.68	28,368.60
Adj._Outliers_Mean_5yrs	100,134.13	86,592.24	407,568.8	118,427.7	19,643.98	20,489.61
Adj._Outliers_50%_Mean_20yrs	74,280.56	87,414.02	295,402.5	238,534.1	30,140.17	29,407.60
Adj._Outliers_50%_Mean_10yrs	75,096.66	87,919.24	306,838.6	226,337.9	28,091.84	29,168.61
Adj_Outliers_50%_Mean_5yrs	79,291.27	92,754.84	322,928.8	238,534.1	29,268.17	31,204.13

# Remove all Variables from R Environment which do not add Value
rm(data_stretch_alentejo_adjusted_outliers, data_stretch_algarve_adjusted_outliers, data_stretch_madeira_adjusted_outliers, error_fc_alentejo_stretch_adjusted_outliers, error_fc_algarve_stretch_adjusted_outliers, error_fc_madeira_stretch_adjusted_outliers, error_fc_alentejo_stretch_orig_outliers, error_fc_algarve_stretch_orig_outliers, error_fc_madeira_stretch_orig_outliers, fc_alentejo_stretch_adjusted_outliers, fc_algarve_stretch_adjusted_outliers, fc_madeira_stretch_adjusted_outliers, RMSE_adjusted_outliers_10years, RMSE_adjusted_outliers_20years, RMSE_adjusted_outliers_50perc_10years, RMSE_adjusted_outliers_50perc_20years, RMSE_adjusted_outliers_50perc_5years, RMSE_adjusted_outliers_5years, RMSE_original_outliers)